Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING EE 2301 BASIC ELECTRONIC CIRCUIT

Department of Electronic EngineeringBASIC ELECTRONIC ENGINEERING

EE 2301BASIC ELECTRONIC CIRCUIT


INSTRUCTOR: DR. ANGUS WUOFFICE: G6352PHONE: 9391EMAIL: [email protected]: www.ee.cityu.edu.hk/~ee2301ID: ee2301passwd: ee2301


LECTURE 1


Fundamentals• Charge, Current, Voltage

• Ohm’s Law and Power

• Series Circuits and Kirchhoff’s Voltage Law

• Parallel Circuits and Kirchholf’s Current Law

• Resistive Circuits

• Circuit Analysis Techniques


Charge


The Starting Point: Elements, Atoms and Charge



Charge

• Charge– Force that causes two particles to be attracted

to, or repelled from, each other– Two types – positive and negative– Atom – proton (positive), electron (negative),

neutron (electrically neutral)


• Attraction and Repulsion - Like charges repel each other and opposite charges attract each other

• Ions– Outside force can cause an electron to leave its orbit -

atom is referred to as a positive ion– Outside force can cause an atom to gain an electron -

atom is referred to as a negative ion

• Free Electrons– An electron that is not bound to any particular atom– Can neutralize a positive ion



Current


Current• Current – the directed flow of charge through a

conductor– Thermal energy (heat) is sufficient to free electrons in

copper

– Free electron motion is random unless outside force is applied


Current• Represented by the letter i (for intensity)

• Measured in charge per unit time

where i = the intensity of the currentdq = the amount of chargedt = the time (in seconds) required for the

charge (dq) to pass


Current

• Coulomb (C) – represents the total charge of approximately 6.25 x 1018 electrons

• Unit of Current – Ampere (A) = 1 coulomb/second

• Example: 3 coulombs of charge pass a point in a wire every two seconds. Calculate current.

A 1.5C/s 1.5s 2

C 3

t

QI


Electrical Current

Electrical current is the time rate of flow of electrical charge through a conductor or circuit element. The units are amperes (A), which are equivalent to coulombs per second (C/s).


Electrical Current

t

t

tqdttitq

dt

tdqti

0

)()()(

)()(

0


Electrical Current• Electron Flow Versus Conventional Current

Insert Figure 1.10



Direct Current Alternating Current

When a current is constant with time, we say that we have direct current, abbreviated as dc. On the other hand, a current that varies with time, reversing direction periodically, is called alternating current, abbreviated as ac.


Figure 4.17, 4.18



.




Two different methods of labeling the same current.

(a,b) Incomplete, improper, and incorrect definitions of a current. (c) the correct definition of i1(t).


Current

Insert Figure 1.11


Voltage


Voltage

The voltage associated with a circuit element is the energy transferred per unit of charge that flows through the element. The units of voltage are volts (V), which are equivalent to joules per coulomb (J/C).


Voltage• Voltage – a “difference of potential” that

generates the directed flow of charge (current) through a circuit

Insert Figure 1.12



Voltage

• Often referred to as electromotive force (emf)

• Unit of Voltage – volt (V) = 1 joule/coulomb

• Volt – the difference of potential that uses one joule of energy to move one coulomb of charge.




(a, b) These are inadequate definitions of a voltage. (c) A correct definition includes both a symbol for the variable and a plus-minus symbol pair.

(a, b) Terminal B is 5 V positive with respect to terminal A; (c,d) terminal A is 5 V positive with respect to terminal B.



Ideal voltage sources

Various representations of an electrical system


Symbol for ideal current source


Ohm’s Law and Power


Ohm’s Law• German Physicist – George Simon Ohm

– Found that current is inversely proportional to resistance for a given voltage– Known as Ohm’s law

• The Relationship Between Current and Voltage• The Relationship Between Current and Resistance


Basic Circuit Calculations

• Using Ohm’s Law to Calculate Current

where R = the circuit resistanceV = the applied voltage

R

VI



• Using Ohm’s Law to Calculate Voltage

where I = the circuit currentR = the circuit resistance

IRV



• Using Ohm’s Law to Calculate Resistance

whereV = the circuit voltage I = the circuit current

I

VR


Resistance Element


Power• Power – the amount of energy used per unit time

• Unit of Power – Watt (W) = 1 joule/second

• Calculating Power

whereP = the power used, in watts (W)V = the applied voltage, in volts (V) I = the generated current, in amperes (A)

P = IV


Power• Other Power Equations

– Use IR in place of V

– Use V/R in place of I

RIIIRVIP 2

R

V

R

VVVIP

2


If the current arrow is directed into the “ +” marked terminal of an element, then p = vi yields the absorbed power. A negative value indicates that power is actually being generated by the element.

If the current arrow is directed out of the “ +” terminal of an element, then p = vi yields the supplied power. A negative value in this case indicates that power is actually being absorbed instead of generated.


Passive Sign Conversion


POWER AND ENERGY

2

1

)(

)()()(t

t

dttpw

titvtp

tPW

instantaneous power


Power

• Power and Heat– Resistors and other components convert energy

to heat (transducer)– If power rating is exceeded, the component will

keep getting hotter and be destroyed– Common guideline – select a component with

twice the required power-dissipation capability


Power• Efficiency – the ratio of a circuit or

components output power to its input power

where = the efficiency, as a percentagePo = the output powerPi = the input power

100i

o

P

P


Miscellaneous Topics• Resistor Tolerance

– Resistor value falls within a range– Circuit current also falls within a range

maxmin R

VI

minmax R

VI


Miscellaneous Topics

• Circuit Loads– Source – supplies the power– Load – absorbs (uses) the power– Full Load – one that draws the maximum

current


Practical Voltage Source


Practical Current Source


Circuit Topology Fundamental


Definition of a branch


Definitions of node and supernode


(a) A circuit containing three nodes and five branches.

(b) Node 1 is redrawn to look like two nodes; it is still one node.


Definition of a loop

Definition of a mesh


Series Circuits and

Kirchhoff’s Voltage Law


Voltage Relationships: Kirchhoff’s Voltage Law • Kirchhoff’s Voltage Law

– The sum of the component voltages in a series circuit must equal the source voltage

1840 – German Physicist, Gustav Kirchhoff

– Actual wording – The algebraic sum of the voltages around a closed loop is zero

– The following equation takes polarity into account

nS VVVV ...21

V 0...21 nS VVVV


Kirchhoff’s Voltage Law, • Example:

VS = +10V, V1 = +2V, V2 = +8V

V 0V 8V 2V -1021 VVVS


Series Circuit Characteristics• Series Circuit – a circuit that contains only

one current path

Vin

R5

R4

R6

R3R2R1


(a) Series combination of N resistors. (b) Electrically equivalent circuit.


Series Circuit Characteristics

• Total Series Resistance

whereRT = the total circuit resistanceRn = the highest-numbered resistor

in the circuit

nT RRRR ...21


Series Circuit Characteristics• Current Characteristics – the current at any point

in a series circuit must equal the current at every other point in the circuit

Insert Figure 4.5



• Voltage Characteristics

whereVS = the source (or total) voltageVn = the voltage across the highest numbered

resistor in the circuit

nS VVVV ...21


(a) Series connected voltage sources can be replaced by a single source.

(b) Parallel current sources can be replaced by a single source.


Examples of circuits with multiple sources, some of which are “illegal” as they violate Kirchhoff’s laws.



• Power Characteristics

wherePS = the source (or total) voltagePn = the power that is dissipated across the

highest numbered resistor in the circuit

TS

nS

IV

PPPP

...21



Insert Figure 4.10


Voltage References

• Voltage References - Circuits have a point that serves as the 0 V reference (ground)

Insert Figure 4.12


Voltage Divider

• The Voltage Divider Relationship– Voltage Divider – often used to analyze a series

circuit

Vn

Vs

Rn

RT

Vn VsRn

RT

whereRn = the resistor of interestVn = the voltage drop across Rn

(where n is the component number)

Vs

R1

R2

R T


An illustration of voltage division.

We may find v2 by applying KVL and Ohm’s law:

so

Thus,

or

For a string of N series resistors, we may write:


• Source Resistance: A Practical Consideration– Ideal Voltage Source – maintains a constant output voltage

regardless of the resistance of its load– Real Voltage Source – internal resistance causes a decrease

in load resistance results in a decrease in the source voltage


Insert Figure 4.20

• Source Resistance: A Practical Consideration (Continued)


Maximum Power Transfer Theorem• maximum power transfer from a voltage

source to its load occurs when the load resistance is equal to the source resistance


Series-Connected Voltage Sources• Series-Aiding Voltage Sources – the total

voltage equals the sum of the voltages

• Series-Opposing Voltage Sources – the total voltage equals the difference of the voltages


Earth Ground Versus Chassis Ground

Insert Figure 4.28


Parallel Circuitsand

Kirchholf’s Current Law


Current Relationships: Kirchhoff’s Current Law• Kirchhoff’s Current Law – the algebraic

sum of the currents entering and leaving a point must equal zero– In other words, the total current leaving a point

must equal the total current entering that point

i1i2

i3

01

n

kki



Parallel Circuit Characteristics• Parallel Circuit – a circuit that provides more

than one current path between any two points

Insert Figure 5.1


Parallel Circuit Characteristics

• Current Characteristics

whereIn = the current through the highest-numbered

branch in the circuit

nT IIII ...21



• Voltage and Current Values– Voltage across each component is equal

– Current through each branch is determined by the source voltage and the resistance of the branch.

n

Sn R

VI


Parallel Circuit Characteristics• Resistance Characteristics – the total circuit

resistance is always lower than any of the branch resistance values

Insert Figure 5.5



• Power Characteristics– Total Power – sum of the power dissipation values for

the individual components– The lower value of the branch resistance, the higher

percentage of the total power it dissipates (opposite that of series circuits)



Insert Figure 5.6


Parallel Resistance Relationships• Conductance (G)

– A measure of the ability of a component or circuit to conduct

– Total conductance (GT) in a parallel circuit equals the sum of the branch conductance values

whereGn = the conductance of the highest-numbered

branch in the circuit

nT GGGG ...21


Parallel Resistance Relationships• Calculating Total Resistance: The Reciprocal

Method

n

n

RRRGGG 1

...11

1

...

1

21

21

Proof – Using KVL and KCL


(a) A circuit with N resistors in parallel. (b) Equivalent circuit.

Beginning with a simple KCL equation,

or

Thus,

A special case worth remembering is


Parallel Resistance Relationships

• Calculating Total Resistance: The Product-Over-Sum Method

21

21

RR

RRRT

R2 R1R T


Current Sources• a source that is designed to provide an output

current value that remains relatively constant over a wide range of load resistance values

Insert Figure 5.12


Current Dividers• Current Dividers – the source current is

divided among the branches

Insert Figure 5.15


An illustration of

current division.

The current flowing through R2 is

For a parallel combination of N resistors, the current through Rk is

or


Practical Current Sources:

• The Effects of Source Resistance– Ideal Current Source – constant current and

infinite internal resistance– Real Current Source – current varies for a

change in load resistance and internal resistance is not infinite

– Internal resistance is usually much greater than the load resistance


Maximum Power Transfer– For a fixed value of RS , maximum power transfer

occurs when RL = RS


Series-Parallel Circuits


Series-Parallel Circuits• Connecting Series Circuits in Parallel

Insert Figure 6.3


Series-Parallel Circuits

• Connecting Parallel Circuits in Series

Insert Figure 6.5


Analyzing Series-Parallel Circuits

LEQ RRR ||52 321 || RRREQ


KIRCHHOFF’S VOLTAGE LAW

Formal Expression


KIRCHHOFF’S VOLTAGE LAW

The algebraic sum of the voltages equals zero for any closed path (loop) in an electrical circuit.In a closed path, each element is encountered only once.


Define the voltage for each component



Loop 1-Va + Vb + Vc =0

Loop 2 -Vc – Vd + Ve =0

Loop 3-Ve + Vd – Vb + Va = 0

Va is ‘+’ in loop 3But ‘-’ in loop 1


VOLTAGE SOURCEAND

CURRENT SOURCE



Why ?

As I = V/R, R = 0,implies, I is infinitivePower = VI = infinitive?Theoretical correct but notin real world.





Symbols for dependent sources


KIRCHHOFF’S CURRENT LAW

Formal Expression


KIRCHHOFF’S CURRENT LAW• The net current entering a node is zero.

• Alternatively, the sum of the currents entering a node equals the sum of the currents leaving a node.

01

k

n

k

i

koutput

n

kkinput

n

k

ii

11


(a) i a = 1A + 3A = 4A

(b) i b + 1 A + 3 A = 2 A, i b = - 2A, that is flowing outward

(c) i c + 4 A + 1 A + 3 A = 0, i c = - 8 A, flows outward too

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Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING EE 2301 BASIC ELECTRONIC CIRCUIT