Fundamentals ofElectronics

Dr Artur Jędrusyna

1

2

CONTENTS

1 Basic Literature

2 Fundamental definitions

bull Electric voltage

bull Electric current

bull Resistance and Ohmrsquos Law

bull Current flow convention

bull Kirchhoffs circuit laws

bull Theacutevenins theorem

bull Electric power

bull Signals

bull Decibel gain

Contents ndash cont

3 Passive electronic components

bullResistors

bullCapacitors

bullInductors

bullTransformers

4Active electronic components

bullDiodes

bullBipolar transistors

bullBJT as a switch

bullCommon collector amplifier

bullCommon emitter amplifier

Contents ndash cont

5Operational amplifier

bullThe assumptions of an ideal operational amplifier

bullThe basic circuits

bullA hardware implementation of mathematical operations

bullA Wien sine wave oscillator

bullFunction generator

5

Basic Literature

[1] Horowitz P Hill Wndash The Art of Electronics

[2] Tietze U Schenk Ch Electronic Circuits --- Handbook for Design and Applications 2nd edition 2008 with CD-ROM ISBN 978-3-540-00429-5

[3] Op Amp Applications Handbook (Analog Devices Series) [Paperback] Walt Jung (Author)

[4] Various catalogues and application notes by the compomentsmanufacturers

Fundamental definitions

VoltageVEB ndash the difference of potentials between the points E and

B where VE potential is positive related to VB potential

An example UEB = 07 VUBE = - 07 V

where VE gt VBAn ideal voltage source symbol

Fundamental definitions (cont)

Electric Current ndasha flow of electric charge This flowing

electric charge is typically carried by moving electrons in a conductor such as wire

I

IdQ

dt=

where Q is the electric charge transferred through the surface over some time t If Q and t are measured in coulombs and seconds respectively I is in amperes

Fundamental definitions (cont)

E I

U1=IR1

U2=IR2

U3=IR3

R1

R2

R3

An electric current can flowonly through a closed path called an electric circuit

In order to produce a current flow at least one current source (eg a battery) must be present in the circuit

An ideal currentsource symbol

Fundamental definitions (cont)

Resistance and Ohmrsquos Law

Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them

The mathematical equation that describes this relationship is

R=UI

The unit is Ohm [ Ω ] = [ V ] [ A ]

10

Current flow convention

The electrons in a electrical circuit flow in the opposite direction of the conventional electric current

copyWikipedia

Fundamental definitions (cont)

Kirchhoffs circuit laws

Kirchhoffs current law (KCL)

At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node

or

The algebraic sum of currents in a network of conductors meeting at a point is zero

I iisum = 0

Fundamental definitions (cont)

Kirchhoffs voltage law (KVL)

The directed sum of the electrical potential differences (voltage) around any closed circuit is zero

or

More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei

isum =

Fundamental definitions (cont)

In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R

Theacutevenins theorem

Where UT= open circuit voltage between points A and B

And RT = UTIT where IT is the short circuit current flowing between points A and B

Fundamental definitions (cont)

Electric power

An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law

P = UI

The unit

[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]

Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor

P = I2 R and respectively P = U2R

Fundamental definitions (cont)

SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information

Sinuisoidal signal

U = Umsin ω t

whereUm - amplitude ω =2πf ndash pulsation[rads]

t ndash time [s] f ndash frequency [Hz]

Other parameters

Vp-p = Peak-to-Peak value

Root-Mean_Square value (RMS)

For sinusoidal signal

Vp-p = 2Um

VRMS=0707Um

dttUT

UT

RMS int=0

2 )(1

Fundamental definitions (cont)

Square wave signal

For this signal URMS=UM

Other parameters

Risetime

Fall time

Highlow amplitude

Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero

For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

2

CONTENTS

1 Basic Literature

2 Fundamental definitions

bull Electric voltage

bull Electric current

bull Resistance and Ohmrsquos Law

bull Current flow convention

bull Kirchhoffs circuit laws

bull Theacutevenins theorem

bull Electric power

bull Signals

bull Decibel gain

Contents ndash cont

3 Passive electronic components

bullResistors

bullCapacitors

bullInductors

bullTransformers

4Active electronic components

bullDiodes

bullBipolar transistors

bullBJT as a switch

bullCommon collector amplifier

bullCommon emitter amplifier

Contents ndash cont

5Operational amplifier

bullThe assumptions of an ideal operational amplifier

bullThe basic circuits

bullA hardware implementation of mathematical operations

bullA Wien sine wave oscillator

bullFunction generator

5

Basic Literature

[1] Horowitz P Hill Wndash The Art of Electronics

[2] Tietze U Schenk Ch Electronic Circuits --- Handbook for Design and Applications 2nd edition 2008 with CD-ROM ISBN 978-3-540-00429-5

[3] Op Amp Applications Handbook (Analog Devices Series) [Paperback] Walt Jung (Author)

[4] Various catalogues and application notes by the compomentsmanufacturers

Fundamental definitions

VoltageVEB ndash the difference of potentials between the points E and

B where VE potential is positive related to VB potential

An example UEB = 07 VUBE = - 07 V

where VE gt VBAn ideal voltage source symbol

Fundamental definitions (cont)

Electric Current ndasha flow of electric charge This flowing

electric charge is typically carried by moving electrons in a conductor such as wire

I

IdQ

dt=

where Q is the electric charge transferred through the surface over some time t If Q and t are measured in coulombs and seconds respectively I is in amperes

Fundamental definitions (cont)

E I

U1=IR1

U2=IR2

U3=IR3

R1

R2

R3

An electric current can flowonly through a closed path called an electric circuit

In order to produce a current flow at least one current source (eg a battery) must be present in the circuit

An ideal currentsource symbol

Fundamental definitions (cont)

Resistance and Ohmrsquos Law

Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them

The mathematical equation that describes this relationship is

R=UI

The unit is Ohm [ Ω ] = [ V ] [ A ]

10

Current flow convention

The electrons in a electrical circuit flow in the opposite direction of the conventional electric current

copyWikipedia

Fundamental definitions (cont)

Kirchhoffs circuit laws

Kirchhoffs current law (KCL)

At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node

or

The algebraic sum of currents in a network of conductors meeting at a point is zero

I iisum = 0

Fundamental definitions (cont)

Kirchhoffs voltage law (KVL)

The directed sum of the electrical potential differences (voltage) around any closed circuit is zero

or

More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei

isum =

Fundamental definitions (cont)

In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R

Theacutevenins theorem

Where UT= open circuit voltage between points A and B

And RT = UTIT where IT is the short circuit current flowing between points A and B

Fundamental definitions (cont)

Electric power

An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law

P = UI

The unit

[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]

Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor

P = I2 R and respectively P = U2R

Fundamental definitions (cont)

SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information

Sinuisoidal signal

U = Umsin ω t

whereUm - amplitude ω =2πf ndash pulsation[rads]

t ndash time [s] f ndash frequency [Hz]

Other parameters

Vp-p = Peak-to-Peak value

Root-Mean_Square value (RMS)

For sinusoidal signal

Vp-p = 2Um

VRMS=0707Um

dttUT

UT

RMS int=0

2 )(1

Fundamental definitions (cont)

Square wave signal

For this signal URMS=UM

Other parameters

Risetime

Fall time

Highlow amplitude

Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero

For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Contents ndash cont

3 Passive electronic components

bullResistors

bullCapacitors

bullInductors

bullTransformers

4Active electronic components

bullDiodes

bullBipolar transistors

bullBJT as a switch

bullCommon collector amplifier

bullCommon emitter amplifier

Contents ndash cont

5Operational amplifier

bullThe assumptions of an ideal operational amplifier

bullThe basic circuits

bullA hardware implementation of mathematical operations

bullA Wien sine wave oscillator

bullFunction generator

5

Basic Literature

[1] Horowitz P Hill Wndash The Art of Electronics

[2] Tietze U Schenk Ch Electronic Circuits --- Handbook for Design and Applications 2nd edition 2008 with CD-ROM ISBN 978-3-540-00429-5

[3] Op Amp Applications Handbook (Analog Devices Series) [Paperback] Walt Jung (Author)

[4] Various catalogues and application notes by the compomentsmanufacturers

Fundamental definitions

VoltageVEB ndash the difference of potentials between the points E and

B where VE potential is positive related to VB potential

An example UEB = 07 VUBE = - 07 V

where VE gt VBAn ideal voltage source symbol

Fundamental definitions (cont)

Electric Current ndasha flow of electric charge This flowing

electric charge is typically carried by moving electrons in a conductor such as wire

I

IdQ

dt=

where Q is the electric charge transferred through the surface over some time t If Q and t are measured in coulombs and seconds respectively I is in amperes

Fundamental definitions (cont)

E I

U1=IR1

U2=IR2

U3=IR3

R1

R2

R3

An electric current can flowonly through a closed path called an electric circuit

In order to produce a current flow at least one current source (eg a battery) must be present in the circuit

An ideal currentsource symbol

Fundamental definitions (cont)

Resistance and Ohmrsquos Law

Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them

The mathematical equation that describes this relationship is

R=UI

The unit is Ohm [ Ω ] = [ V ] [ A ]

10

Current flow convention

The electrons in a electrical circuit flow in the opposite direction of the conventional electric current

copyWikipedia

Fundamental definitions (cont)

Kirchhoffs circuit laws

Kirchhoffs current law (KCL)

At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node

or

The algebraic sum of currents in a network of conductors meeting at a point is zero

I iisum = 0

Fundamental definitions (cont)

Kirchhoffs voltage law (KVL)

The directed sum of the electrical potential differences (voltage) around any closed circuit is zero

or

More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei

isum =

Fundamental definitions (cont)

In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R

Theacutevenins theorem

Where UT= open circuit voltage between points A and B

And RT = UTIT where IT is the short circuit current flowing between points A and B

Fundamental definitions (cont)

Electric power

An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law

P = UI

The unit

[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]

Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor

P = I2 R and respectively P = U2R

Fundamental definitions (cont)

SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information

Sinuisoidal signal

U = Umsin ω t

whereUm - amplitude ω =2πf ndash pulsation[rads]

t ndash time [s] f ndash frequency [Hz]

Other parameters

Vp-p = Peak-to-Peak value

Root-Mean_Square value (RMS)

For sinusoidal signal

Vp-p = 2Um

VRMS=0707Um

dttUT

UT

RMS int=0

2 )(1

Fundamental definitions (cont)

Square wave signal

For this signal URMS=UM

Other parameters

Risetime

Fall time

Highlow amplitude

Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero

For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Contents ndash cont

5Operational amplifier

bullThe assumptions of an ideal operational amplifier

bullThe basic circuits

bullA hardware implementation of mathematical operations

bullA Wien sine wave oscillator

bullFunction generator

5

Basic Literature

[1] Horowitz P Hill Wndash The Art of Electronics

[2] Tietze U Schenk Ch Electronic Circuits --- Handbook for Design and Applications 2nd edition 2008 with CD-ROM ISBN 978-3-540-00429-5

[3] Op Amp Applications Handbook (Analog Devices Series) [Paperback] Walt Jung (Author)

[4] Various catalogues and application notes by the compomentsmanufacturers

Fundamental definitions

VoltageVEB ndash the difference of potentials between the points E and

B where VE potential is positive related to VB potential

An example UEB = 07 VUBE = - 07 V

where VE gt VBAn ideal voltage source symbol

Fundamental definitions (cont)

Electric Current ndasha flow of electric charge This flowing

electric charge is typically carried by moving electrons in a conductor such as wire

I

IdQ

dt=

where Q is the electric charge transferred through the surface over some time t If Q and t are measured in coulombs and seconds respectively I is in amperes

Fundamental definitions (cont)

E I

U1=IR1

U2=IR2

U3=IR3

R1

R2

R3

An electric current can flowonly through a closed path called an electric circuit

In order to produce a current flow at least one current source (eg a battery) must be present in the circuit

An ideal currentsource symbol

Fundamental definitions (cont)

Resistance and Ohmrsquos Law

Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them

The mathematical equation that describes this relationship is

R=UI

The unit is Ohm [ Ω ] = [ V ] [ A ]

10

Current flow convention

The electrons in a electrical circuit flow in the opposite direction of the conventional electric current

copyWikipedia

Fundamental definitions (cont)

Kirchhoffs circuit laws

Kirchhoffs current law (KCL)

At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node

or

The algebraic sum of currents in a network of conductors meeting at a point is zero

I iisum = 0

Fundamental definitions (cont)

Kirchhoffs voltage law (KVL)

The directed sum of the electrical potential differences (voltage) around any closed circuit is zero

or

More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei

isum =

Fundamental definitions (cont)

In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R

Theacutevenins theorem

Where UT= open circuit voltage between points A and B

And RT = UTIT where IT is the short circuit current flowing between points A and B

Fundamental definitions (cont)

Electric power

An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law

P = UI

The unit

[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]

Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor

P = I2 R and respectively P = U2R

Fundamental definitions (cont)

SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information

Sinuisoidal signal

U = Umsin ω t

whereUm - amplitude ω =2πf ndash pulsation[rads]

t ndash time [s] f ndash frequency [Hz]

Other parameters

Vp-p = Peak-to-Peak value

Root-Mean_Square value (RMS)

For sinusoidal signal

Vp-p = 2Um

VRMS=0707Um

dttUT

UT

RMS int=0

2 )(1

Fundamental definitions (cont)

Square wave signal

For this signal URMS=UM

Other parameters

Risetime

Fall time

Highlow amplitude

Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero

For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

5

Basic Literature

[1] Horowitz P Hill Wndash The Art of Electronics

[2] Tietze U Schenk Ch Electronic Circuits --- Handbook for Design and Applications 2nd edition 2008 with CD-ROM ISBN 978-3-540-00429-5

[3] Op Amp Applications Handbook (Analog Devices Series) [Paperback] Walt Jung (Author)

[4] Various catalogues and application notes by the compomentsmanufacturers

Fundamental definitions

VoltageVEB ndash the difference of potentials between the points E and

B where VE potential is positive related to VB potential

An example UEB = 07 VUBE = - 07 V

where VE gt VBAn ideal voltage source symbol

Fundamental definitions (cont)

Electric Current ndasha flow of electric charge This flowing

electric charge is typically carried by moving electrons in a conductor such as wire

I

IdQ

dt=

where Q is the electric charge transferred through the surface over some time t If Q and t are measured in coulombs and seconds respectively I is in amperes

Fundamental definitions (cont)

E I

U1=IR1

U2=IR2

U3=IR3

R1

R2

R3

An electric current can flowonly through a closed path called an electric circuit

In order to produce a current flow at least one current source (eg a battery) must be present in the circuit

An ideal currentsource symbol

Fundamental definitions (cont)

Resistance and Ohmrsquos Law

Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them

The mathematical equation that describes this relationship is

R=UI

The unit is Ohm [ Ω ] = [ V ] [ A ]

10

Current flow convention

The electrons in a electrical circuit flow in the opposite direction of the conventional electric current

copyWikipedia

Fundamental definitions (cont)

Kirchhoffs circuit laws

Kirchhoffs current law (KCL)

At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node

or

The algebraic sum of currents in a network of conductors meeting at a point is zero

I iisum = 0

Fundamental definitions (cont)

Kirchhoffs voltage law (KVL)

The directed sum of the electrical potential differences (voltage) around any closed circuit is zero

or

More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei

isum =

Fundamental definitions (cont)

In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R

Theacutevenins theorem

Where UT= open circuit voltage between points A and B

And RT = UTIT where IT is the short circuit current flowing between points A and B

Fundamental definitions (cont)

Electric power

An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law

P = UI

The unit

[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]

Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor

P = I2 R and respectively P = U2R

Fundamental definitions (cont)

SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information

Sinuisoidal signal

U = Umsin ω t

whereUm - amplitude ω =2πf ndash pulsation[rads]

t ndash time [s] f ndash frequency [Hz]

Other parameters

Vp-p = Peak-to-Peak value

Root-Mean_Square value (RMS)

For sinusoidal signal

Vp-p = 2Um

VRMS=0707Um

dttUT

UT

RMS int=0

2 )(1

Fundamental definitions (cont)

Square wave signal

For this signal URMS=UM

Other parameters

Risetime

Fall time

Highlow amplitude

Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero

For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Fundamental definitions

VoltageVEB ndash the difference of potentials between the points E and

B where VE potential is positive related to VB potential

An example UEB = 07 VUBE = - 07 V

where VE gt VBAn ideal voltage source symbol

Fundamental definitions (cont)

Electric Current ndasha flow of electric charge This flowing

electric charge is typically carried by moving electrons in a conductor such as wire

I

IdQ

dt=

where Q is the electric charge transferred through the surface over some time t If Q and t are measured in coulombs and seconds respectively I is in amperes

Fundamental definitions (cont)

E I

U1=IR1

U2=IR2

U3=IR3

R1

R2

R3

An electric current can flowonly through a closed path called an electric circuit

In order to produce a current flow at least one current source (eg a battery) must be present in the circuit

An ideal currentsource symbol

Fundamental definitions (cont)

Resistance and Ohmrsquos Law

Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them

The mathematical equation that describes this relationship is

R=UI

The unit is Ohm [ Ω ] = [ V ] [ A ]

10

Current flow convention

The electrons in a electrical circuit flow in the opposite direction of the conventional electric current

copyWikipedia

Fundamental definitions (cont)

Kirchhoffs circuit laws

Kirchhoffs current law (KCL)

At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node

or

The algebraic sum of currents in a network of conductors meeting at a point is zero

I iisum = 0

Fundamental definitions (cont)

Kirchhoffs voltage law (KVL)

The directed sum of the electrical potential differences (voltage) around any closed circuit is zero

or

More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei

isum =

Fundamental definitions (cont)

In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R

Theacutevenins theorem

Where UT= open circuit voltage between points A and B

And RT = UTIT where IT is the short circuit current flowing between points A and B

Fundamental definitions (cont)

Electric power

An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law

P = UI

The unit

[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]

Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor

P = I2 R and respectively P = U2R

Fundamental definitions (cont)

SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information

Sinuisoidal signal

U = Umsin ω t

whereUm - amplitude ω =2πf ndash pulsation[rads]

t ndash time [s] f ndash frequency [Hz]

Other parameters

Vp-p = Peak-to-Peak value

Root-Mean_Square value (RMS)

For sinusoidal signal

Vp-p = 2Um

VRMS=0707Um

dttUT

UT

RMS int=0

2 )(1

Fundamental definitions (cont)

Square wave signal

For this signal URMS=UM

Other parameters

Risetime

Fall time

Highlow amplitude

Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero

For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Fundamental definitions (cont)

Electric Current ndasha flow of electric charge This flowing

electric charge is typically carried by moving electrons in a conductor such as wire

I

IdQ

dt=

where Q is the electric charge transferred through the surface over some time t If Q and t are measured in coulombs and seconds respectively I is in amperes

Fundamental definitions (cont)

E I

U1=IR1

U2=IR2

U3=IR3

R1

R2

R3

An electric current can flowonly through a closed path called an electric circuit

In order to produce a current flow at least one current source (eg a battery) must be present in the circuit

An ideal currentsource symbol

Fundamental definitions (cont)

Resistance and Ohmrsquos Law

Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them

The mathematical equation that describes this relationship is

R=UI

The unit is Ohm [ Ω ] = [ V ] [ A ]

10

Current flow convention

The electrons in a electrical circuit flow in the opposite direction of the conventional electric current

copyWikipedia

Fundamental definitions (cont)

Kirchhoffs circuit laws

Kirchhoffs current law (KCL)

At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node

or

The algebraic sum of currents in a network of conductors meeting at a point is zero

I iisum = 0

Fundamental definitions (cont)

Kirchhoffs voltage law (KVL)

The directed sum of the electrical potential differences (voltage) around any closed circuit is zero

or

More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei

isum =

Fundamental definitions (cont)

In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R

Theacutevenins theorem

Where UT= open circuit voltage between points A and B

And RT = UTIT where IT is the short circuit current flowing between points A and B

Fundamental definitions (cont)

Electric power

An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law

P = UI

The unit

[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]

Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor

P = I2 R and respectively P = U2R

Fundamental definitions (cont)

SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information

Sinuisoidal signal

U = Umsin ω t

whereUm - amplitude ω =2πf ndash pulsation[rads]

t ndash time [s] f ndash frequency [Hz]

Other parameters

Vp-p = Peak-to-Peak value

Root-Mean_Square value (RMS)

For sinusoidal signal

Vp-p = 2Um

VRMS=0707Um

dttUT

UT

RMS int=0

2 )(1

Fundamental definitions (cont)

Square wave signal

For this signal URMS=UM

Other parameters

Risetime

Fall time

Highlow amplitude

Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero

For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Fundamental definitions (cont)

E I

U1=IR1

U2=IR2

U3=IR3

R1

R2

R3

An electric current can flowonly through a closed path called an electric circuit

In order to produce a current flow at least one current source (eg a battery) must be present in the circuit

An ideal currentsource symbol

Fundamental definitions (cont)

Resistance and Ohmrsquos Law

Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them

The mathematical equation that describes this relationship is

R=UI

The unit is Ohm [ Ω ] = [ V ] [ A ]

10

Current flow convention

The electrons in a electrical circuit flow in the opposite direction of the conventional electric current

copyWikipedia

Fundamental definitions (cont)

Kirchhoffs circuit laws

Kirchhoffs current law (KCL)

At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node

or

The algebraic sum of currents in a network of conductors meeting at a point is zero

I iisum = 0

Fundamental definitions (cont)

Kirchhoffs voltage law (KVL)

The directed sum of the electrical potential differences (voltage) around any closed circuit is zero

or

More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei

isum =

Fundamental definitions (cont)

In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R

Theacutevenins theorem

Where UT= open circuit voltage between points A and B

And RT = UTIT where IT is the short circuit current flowing between points A and B

Fundamental definitions (cont)

Electric power

An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law

P = UI

The unit

[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]

Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor

P = I2 R and respectively P = U2R

Fundamental definitions (cont)

SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information

Sinuisoidal signal

U = Umsin ω t

whereUm - amplitude ω =2πf ndash pulsation[rads]

t ndash time [s] f ndash frequency [Hz]

Other parameters

Vp-p = Peak-to-Peak value

Root-Mean_Square value (RMS)

For sinusoidal signal

Vp-p = 2Um

VRMS=0707Um

dttUT

UT

RMS int=0

2 )(1

Fundamental definitions (cont)

Square wave signal

For this signal URMS=UM

Other parameters

Risetime

Fall time

Highlow amplitude

Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero

For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Fundamental definitions (cont)

Resistance and Ohmrsquos Law

Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them

The mathematical equation that describes this relationship is

R=UI

The unit is Ohm [ Ω ] = [ V ] [ A ]

10

Current flow convention

The electrons in a electrical circuit flow in the opposite direction of the conventional electric current

copyWikipedia

Fundamental definitions (cont)

Kirchhoffs circuit laws

Kirchhoffs current law (KCL)

At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node

or

The algebraic sum of currents in a network of conductors meeting at a point is zero

I iisum = 0

Fundamental definitions (cont)

Kirchhoffs voltage law (KVL)

The directed sum of the electrical potential differences (voltage) around any closed circuit is zero

or

More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei

isum =

Fundamental definitions (cont)

In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R

Theacutevenins theorem

Where UT= open circuit voltage between points A and B

And RT = UTIT where IT is the short circuit current flowing between points A and B

Fundamental definitions (cont)

Electric power

An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law

P = UI

The unit

[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]

Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor

P = I2 R and respectively P = U2R

Fundamental definitions (cont)

SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information

Sinuisoidal signal

U = Umsin ω t

whereUm - amplitude ω =2πf ndash pulsation[rads]

t ndash time [s] f ndash frequency [Hz]

Other parameters

Vp-p = Peak-to-Peak value

Root-Mean_Square value (RMS)

For sinusoidal signal

Vp-p = 2Um

VRMS=0707Um

dttUT

UT

RMS int=0

2 )(1

Fundamental definitions (cont)

Square wave signal

For this signal URMS=UM

Other parameters

Risetime

Fall time

Highlow amplitude

Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero

For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

10

Current flow convention

The electrons in a electrical circuit flow in the opposite direction of the conventional electric current

copyWikipedia

Fundamental definitions (cont)

Kirchhoffs circuit laws

Kirchhoffs current law (KCL)

At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node

or

The algebraic sum of currents in a network of conductors meeting at a point is zero

I iisum = 0

Fundamental definitions (cont)

Kirchhoffs voltage law (KVL)

The directed sum of the electrical potential differences (voltage) around any closed circuit is zero

or

More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei

isum =

Fundamental definitions (cont)

In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R

Theacutevenins theorem

Where UT= open circuit voltage between points A and B

And RT = UTIT where IT is the short circuit current flowing between points A and B

Fundamental definitions (cont)

Electric power

An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law

P = UI

The unit

[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]

Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor

P = I2 R and respectively P = U2R

Fundamental definitions (cont)

SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information

Sinuisoidal signal

U = Umsin ω t

whereUm - amplitude ω =2πf ndash pulsation[rads]

t ndash time [s] f ndash frequency [Hz]

Other parameters

Vp-p = Peak-to-Peak value

Root-Mean_Square value (RMS)

For sinusoidal signal

Vp-p = 2Um

VRMS=0707Um

dttUT

UT

RMS int=0

2 )(1

Fundamental definitions (cont)

Square wave signal

For this signal URMS=UM

Other parameters

Risetime

Fall time

Highlow amplitude

Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero

For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Fundamental definitions (cont)

Kirchhoffs circuit laws

Kirchhoffs current law (KCL)

At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node

or

The algebraic sum of currents in a network of conductors meeting at a point is zero

I iisum = 0

Fundamental definitions (cont)

Kirchhoffs voltage law (KVL)

The directed sum of the electrical potential differences (voltage) around any closed circuit is zero

or

More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei

isum =

Fundamental definitions (cont)

In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R

Theacutevenins theorem

Where UT= open circuit voltage between points A and B

And RT = UTIT where IT is the short circuit current flowing between points A and B

Fundamental definitions (cont)

Electric power

An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law

P = UI

The unit

[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]

Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor

P = I2 R and respectively P = U2R

Fundamental definitions (cont)

SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information

Sinuisoidal signal

U = Umsin ω t

whereUm - amplitude ω =2πf ndash pulsation[rads]

t ndash time [s] f ndash frequency [Hz]

Other parameters

Vp-p = Peak-to-Peak value

Root-Mean_Square value (RMS)

For sinusoidal signal

Vp-p = 2Um

VRMS=0707Um

dttUT

UT

RMS int=0

2 )(1

Fundamental definitions (cont)

Square wave signal

For this signal URMS=UM

Other parameters

Risetime

Fall time

Highlow amplitude

Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero

For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Fundamental definitions (cont)

Kirchhoffs voltage law (KVL)

The directed sum of the electrical potential differences (voltage) around any closed circuit is zero

or

More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei

isum =

Fundamental definitions (cont)

In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R

Theacutevenins theorem

Where UT= open circuit voltage between points A and B

And RT = UTIT where IT is the short circuit current flowing between points A and B

Fundamental definitions (cont)

Electric power

An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law

P = UI

The unit

[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]

Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor

P = I2 R and respectively P = U2R

Fundamental definitions (cont)

SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information

Sinuisoidal signal

U = Umsin ω t

whereUm - amplitude ω =2πf ndash pulsation[rads]

t ndash time [s] f ndash frequency [Hz]

Other parameters

Vp-p = Peak-to-Peak value

Root-Mean_Square value (RMS)

For sinusoidal signal

Vp-p = 2Um

VRMS=0707Um

dttUT

UT

RMS int=0

2 )(1

Fundamental definitions (cont)

Square wave signal

For this signal URMS=UM

Other parameters

Risetime

Fall time

Highlow amplitude

Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero

For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Fundamental definitions (cont)

In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R

Theacutevenins theorem

Where UT= open circuit voltage between points A and B

And RT = UTIT where IT is the short circuit current flowing between points A and B

Fundamental definitions (cont)

Electric power

An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law

P = UI

The unit

[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]

Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor

P = I2 R and respectively P = U2R

Fundamental definitions (cont)

SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information

Sinuisoidal signal

U = Umsin ω t

whereUm - amplitude ω =2πf ndash pulsation[rads]

t ndash time [s] f ndash frequency [Hz]

Other parameters

Vp-p = Peak-to-Peak value

Root-Mean_Square value (RMS)

For sinusoidal signal

Vp-p = 2Um

VRMS=0707Um

dttUT

UT

RMS int=0

2 )(1

Fundamental definitions (cont)

Square wave signal

For this signal URMS=UM

Other parameters

Risetime

Fall time

Highlow amplitude

Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero

For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Fundamental definitions (cont)

Electric power

An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law

P = UI

The unit

[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]

Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor

P = I2 R and respectively P = U2R

Fundamental definitions (cont)

SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information

Sinuisoidal signal

U = Umsin ω t

whereUm - amplitude ω =2πf ndash pulsation[rads]

t ndash time [s] f ndash frequency [Hz]

Other parameters

Vp-p = Peak-to-Peak value

Root-Mean_Square value (RMS)

For sinusoidal signal

Vp-p = 2Um

VRMS=0707Um

dttUT

UT

RMS int=0

2 )(1

Fundamental definitions (cont)

Square wave signal

For this signal URMS=UM

Other parameters

Risetime

Fall time

Highlow amplitude

Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero

For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Fundamental definitions (cont)

SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information

Sinuisoidal signal

U = Umsin ω t

whereUm - amplitude ω =2πf ndash pulsation[rads]

t ndash time [s] f ndash frequency [Hz]

Other parameters

Vp-p = Peak-to-Peak value

Root-Mean_Square value (RMS)

For sinusoidal signal

Vp-p = 2Um

VRMS=0707Um

dttUT

UT

RMS int=0

2 )(1

Fundamental definitions (cont)

Square wave signal

For this signal URMS=UM

Other parameters

Risetime

Fall time

Highlow amplitude

Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero

For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Fundamental definitions (cont)

Square wave signal

For this signal URMS=UM

Other parameters

Risetime

Fall time

Highlow amplitude

Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero

For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Fundamental definitions (cont)

Sawtooth signal (sawtooth wave)

sawtooth wave ramps upward and then sharply drops

Pulses

A rapid transient changes in the amplitude of a signal

Step signals amp glitches

Useful mostly for theoretical analysis

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Fundamental definitions (cont)

Decibel gain

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula

ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals

Examples

ku ku [dB]

01 -20dB

0707 -3dB

1 0dB

141 3dB

10 20dB

100 40dB

1000 60dB

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Passive components

Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law

Generic graphic symbol

aMetalized resistor

bWirewound resistor

cCarbon resistor

dResistor ladder

eThick-film resistor

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

The primary characteristics of a resistor

Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Series and parallel resistors

The equivalent resistance of tworesistors in series connection

R=R1+R2

The equivalent resistance of tworesistors in parallel connection

1R=1R1+1R2

For n resistors

R=R1+R2+R3+Rn

For n resistors

1R=1R1+1R2+1R3+1Rn

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Resistive divider

copy Wikipedia

If R1=R2 then Vout = Vin2

The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Loaded voltage divider

The voltage between points A and B

U = UT = UINmiddot [R2 (R1 + R2)]

According to Theveninrsquostheorem

RT = (R1 middot R2) (R1+ R2)

In practical projects we often

assume that RL should be 10 times higher than RT

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Potentiometers

A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Capacitors

copy Wikipedia

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)

An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them

The properties of capacitor are expressed by an equation

C=QU

Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Capacitors ndashinternal structure

a) Film capacitor

b) Metalised plastic film capacitor

c) Ceramic disc capacitor

d) Tubular ceramic capacitor

e) Multilayer ceramic capacitor

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Supercapacitors

Maxwell Technologies supercapacitors

Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor

They are characterized by a very shortcharging time (seconds to minutes)

Possible applications ndash electriccars power tools emergencypower supplies

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Supercapacitors ndash cont

Pros very short charging time

Cons relatively high price

Supercapacitors vs standard capacitors

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

New generation of supercapacitotors

Second generation of supercapacitors by ioxuscom (2010)

From left 220F800F1000F Operating voltage 23V max

copy wwwioxuscom

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Capacitors ndash cont

Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)

If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Capacitors ndash cont

Most imporant capacitor parameters

bullCapacitance [microF] [nF] or [pF]

bullTolerance []

bullRated voltage [V]

bullDischarge rate (leakage current)

bullTemperature coefficient of capacitance

bullEquivalent series resitance (ESR)

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Capacitors ndash cont

a)Aluminium electrolytic capacitor

b)Tantalum electrolytic capacitor

c)Polyesther capacitor

d)Ceramic disc capacitor

e)Mylar capacitor

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Capacitors ndash cont

Capacitors in series connection

For two capacitors in series the equivalent capacitance is

For parallel configuration

For two capacitors in parallel the equivalent capacitance is

C=C1+C2

For n capacitors (general case)

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Capacitors ndash cont

Capacitor discharge through a resistor

If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge

The discharge rate is expressed by an equation

Where RC is called time constant

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Capacitors ndash cont

Capacitor charging through a resistor

If a capacitor C will be charged from source of voltage UWE

through a resistor R the voltage change across its terminals will be described by the following equations

The final solution is

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Inductors

An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it

An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material

Graphic symbola) Toroidal core inductor b)cylindrical core inductor

The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L

where L is expressed in H (Henryrsquos) but most often in mH or microH

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Inductors ndash cont

Different variations of inductors

Surface mount(SMT) inductors

Cylindricalcoreinductors

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Inductor parameters

bullInductance [H]

bullRated voltage [V]

bullTolerance []

bullSaturation DC current [A]

bullMaximal RMS current [A]

bullSelf-resonance frequency [Hz]

bullDC resistance [Ω]

Typical set of parameters

Coilcraft DO3340P-104M inductor

L-100microH tol-20 Isat-25A Irms-12A

SRF-5MHz(typ) RDC-022Ω

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Transformers

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation

Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Transformer ndash cont

The current I2 flowing in the secondary winding is inversely proportional

to the current I1 flowing in the primary winding

Moreover the impedance connected to the transformer is transformed by the square of the turns ratio

Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Transformers ndash cont

The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit

Examples of low power transformers

Toroidal coretransformer

Toroidal core variabletransformer

(autotransformer)

Laminatedcore EI transformers

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Diodes

A diode is a two-terminal electronic component that conducts electric current in only one direction

When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Diodes ndash cont

The currentndashvoltage characteristic of a diodeWhere

ID is diode current

If is forward diode current

IFmax is maximum diode

current

UF is forward diode voltage

UR is reverse diode voltage

URmax is the maximum

reverse voltage diodevoltage

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Diodes ndash cont

For common types of diodes the value of UF voltage is

bullFor Germanium junction diode 02 04V

bullFor Silicone junction diode 05 08V

bullFor Schottky diode 0204V

An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation

Where I is the diode current

IS is the reverse bias saturation current (or scale current)

VD is the voltage across the diode

VT is the thermal voltage and

n is the ideality factor also known as the quality factor

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Diodes ndashcont

The thermal voltage VT is approximately 2585 mV at 300 K

At any other temperature it is given by an equation

where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Diodes ndash cont

The typical I-V characteristics of for germaniumand silicone junction diode

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Diodes ndash cont

Diode as a switching element

Following the end of forward conduction in a PN type diode a

reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called

reverse recovery time and usually is between tens and hundreds of

ns (ie between 1e-8 and 1e-7 s)

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Diodes ndash cont

Diode as a rectifier

A half wave rectifier

A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Diodes ndash cont

A full-wave rectifier

This kind of a circuit is also known as the bridge rectifier

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Diodes ndash cont

A rectifier in a DC voltage supply

Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge

In general case the simple design rule should be followed

RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Diodes ndash cont

Another application ndash diode-based voltage limiter

The cathode of a diode has a potential equal to 4V

U out max = 4V + 06 V = 46 V

If UINlt46V then UOUT = UIN

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Bipolar Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals

Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors

B=base C=collector E= emitter

Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Transistors ndash cont

The history of the transistor

The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work

The first silicon transistors were produced by Western Electric and TexasInstruments in 1954

Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)

copy wwwporticusorg

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Transistors ndash cont

An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased

NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

The first transistor

copy Bell Labs

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Transistor ndash cont

Transistor as an amplifier

A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated

The relations between currents in BJT copy radartutorialeu

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Transistor ndash cont

The most often used amplifier circuits

highmediumlowBandwidth4

00001800Phase Shift between input and output signals

3

lt 1highhighCurrent gain2

highlt 1highVoltage gain1

COMMON BASE

COMMON COLLECTOR

COMMON EMITTER

AMPLIFIER

Nr

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Transistors ndash cont

If transistor is in an active mode then the following formula is true

IC = hFEmiddot IB = β middot IB

Where β coefficient is called the common-emitter current gain

The value of β is usually between 50 and 300

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Transistors ndash cont

Current-voltage characteristics of a BJT

The DC emitter and collector currents in active mode can be

described by a following equation

For ICgtgt IC0

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Transistors ndash cont

The input I-V characteristic The relation between ICand IB

The relation between βand IC

Please note that β is not constant and it remains a function of Ic

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Transistors ndash cont

Safe Operating Area (SOA) of a BJT

copy MOSPEC

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Transistors ndash cont

BJT ndash typical values of parameters copy ONsemi

a)Low power ndash BC548 b)high power ndash TIP122

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

BJT as a switch

a) An incandescent light bulb driver b) An electromagnetic relay driver

(the diode protects BJT againstvoltage spikes)

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Common collector amplifier

+Ucc

R

The output voltage

UE = UB ndash 06V

Input impedance = high outputimpedance = low voltageamplification lt1

A simple application ndashZener-diode based DC voltage regulator

Uout=Uz ndash 06V

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Small signal amplifiers

+Ucc

RER2

R1C1

C2

C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz

A small-signal common collector amplifier

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Small signal amplifiers

A common ndash emitter AC signal amplifier

+Ucc

RER2

R1C1

RC

C2

Parameters

UCC = 20V

R1 = 110kΩ R2 = 10kΩ

C1 = 01microF C2 = 1microF

RC = 10kΩ RE = 1kΩ

Voltage gain

kU = UOUTUIN = -RCRE

Here kU=-100001000 [VV] = -10 [VV]

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Operational amplifier

An ideal operational amplifier assumptions

copy Texas

Instruments

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Operational amplifier ndash cont

The basic circuits

copy National Semiconductor

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Operational amplifier ndash cont

copy National Semiconductor

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Operational amplifier ndash cont

A hardware implementation of mathematical operations copy National Semicond

Operational amplifier ndash cont

Operational amplifer ndash cont

Operational amplifier ndash cont

Operational amplifer ndash cont

Operational amplifer ndash cont