Analog Circuits and Systems

Prof. K Radhakrishna Rao

Lecture 7 Passive Electronic Devices for Analog

Signal Processing

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Analog signal processing functions

�  Attenuation �  Amplification �  Filtering �  Amplitude modulation and

demodulation �  Frequency modulation and

demodulation �  Mixing (modulation and

demodulation)

�  Digital-to-Analog Converter �  Analog-to-Digital Converter �  Automatic gain control �  Power amplification �  Power supply management �  Signal generation (clock) �  PLL �  FLL

2

Mathematical Operations

All analog signal processing functions can be performed through

�  Multiplication of a variable by a constant

�  Multiplication of two variables

�  Comparison

3

Devices

Devices capable of power amplification - ‘active devices’ Devices that cannot provide power amplification - ‘passive devices’ Devices that perform the core mathematical operations are �  Passive devices: Resistors, Inductors, Capacitors, Crystals and

Diodes �  Active devices: Op Amps, Comparators, Multipliers, FETs and BJTs

4

Resistors LR=Aρ

ρ is the resistivity in ohms - cm, L is the length in cms and A is the area in sq. cm

5

Resistors

are commercially made �  from materials including carbon, wires, metal film and

semiconductors �  available from a fraction of an ohm to several mega ohms �  available with varying tolerances (0.1, 0.5, 1, 5, 10 and 20%) �  for different power capacities �  available in different formats (packages) including axial lead devices

and surface mount devices

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Resistor

can have �  parallel parasitic capacitance �  series inductance �  thermal noise voltage sources Parasitics become important in high frequency and high precision

analog signal processing circuits

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Effects of Parasitics

The equivalent circuit

�  If the shunt capacitance comes into play first the effect is to reduce the

impedance to values < R with the band width of

�  When the inductive effect comes beyond the resonance frequency

of the effect is to increase net impedance

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P

1=RC

ω

P P

1L C

Effects of Parasitics

�  Wire-wound resistors become unusable above 50 kHz

�  Carbon type resistors are usable up to around 1 MHz

�  Foil resistors can cope up with frequencies up to 100 MHz

9

Capacitors

�  Capacitors are generally made with dielectric material sandwiched

between two conductive electrodes.

where e is the permittivity (Farad per cm) of the insulating material

separating the two electrodes with area A in sq. cm., and d is the

distance between the electrodes in cm

ε=A

Cd

10

Capacitors (contd.)

�  The popular dielectric materials used are ceramic, tantalum, polyester (Mylar), polystyrene, polypropylene, polycarbonate, metalized paper, Teflon, air etc.

�  Electrode materials mainly include aluminium and silver

�  Energy is stored in the capacitors as charge in electrostatic form given by 0.5CV2 Joules

�  Polarized Capacitors have pre-specified polarity and offer large capacitance values

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Capacitors (contd.)

are made commercially available �  from a few pico-farads to several hundreds of micro-farads �  with different voltage rating values �  in different formats including axial lead devices and surface mount

devices Capacitors have leakage resistance, equivalent series resistance (ESR)

ranging from a 0.01 to several Ohms, and lead inductance. The effects of these parasitics become important in some of the

analog signal processing circuits

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Effects of Parasitics

Equivalent circuit is a series RLC circuit

�  As frequency increases the net impedance decreases �  When the inductive effect comes beyond the resonance frequency of the effect is to increase net impedance �  Electrolytic capacitors behave as inductors beyond a few MHz,

which is why small ceramic capacitors are put in parallel with them �  Aluminium and tantalum electrolytic capacitors with non solid

electrolyte have high ESR values, up to several ohms

13

P

1L C

Inductors

�  Inductors are coils on a substrate or coils wound around magnetic cores � Unlike resistors and capacitors inductors are not so easily made available

commercially � They are generally made to order and hence are costly � Because of their inconvenient sizes, particularly at low frequencies,

inductors are generally avoided in present day electronics.

m is permeability in Henries per cm, N is the number of turns, A is the cross section area of the coil in cm2 and l is the length of the coil in cm

2 NL =lAµ

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Inductors (contd.,)

Inductor also has an important parameter associated with it:

�  Quality Factor

where w is the operating frequency in radians/sec. �  Inductors store energy given by 0.5LI2 joules in electromagnetic

form

S

ωLQ =R

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Parasitics associated with Inductors

�  An inductance has a series resistance (RS) and a parallel capacitance (CP) as parasitics

�  Inductors have resistance inherent in the metal conductor (of the order of one ohm)

�  An inductor using a core to increase inductance will have hysteresis and eddy current losses in the core.

�  At high frequencies there are also additional losses in the windings due to proximity and skin effect

16

Crystals

�  Crystal is a vibrating mechanical resonant system with an equivalent electrical resonant circuit shown

�  It is mainly a series resonant circuit with very high Q value ranging from 104 to 106.

�  Crystals are available with resonant frequencies ranging from hundreds of kHz to tens of MHz.

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Crystals (contd.,)

It is represented as

�  Mainly used for generation of precision frequency clock signals

�  The impedance function of a crystal is given by ( )

( )

2

2s ss

2 2p

0 2s p pp

s s 1+ +1ω Qω

Z s =ω s s 1s×C + +1ω ω Qω

⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠ ⎣ ⎦

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Crystals (contd.,)

s1 1

1 0 1 1p s s

1 1 0 0 0

0 1

p 1s 1s p

p s

1ω =L C

C +C C Cω = =ω 1+ »ω 1+L C C C 2C C C

ω Lω L Q = ;Q =R1 R1

ω ω

⎛ ⎞⎜ ⎟⎝ ⎠

?

Series resonance frequency

Parallel resonance frequency

where

The quality factors are

As is very close to the quality facto p s Q Qr will be close to

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Ideal Diode

�  is a non linear passive element

20

i 0; v 0v 0; i 0> =< =

Semiconductor diode

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Semiconductor diode (contd.,)

�  The v-i characteristic of the junction diode T

vV

si=I e -1⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

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Diode Equation

�  The current ‘i’ in the forward biased semiconductor diode

�  where Is is the reverse saturation current and is typically in the range of a few micro amperes for (power diodes), nano-amperes for signal diodes and femto amperes for diodes in ICs.

�  Is, the reverse saturation current, is temperature dependent, and doubles for every 10OC rise.

�  VT, thermal voltage is approximately given as T/11600 and becomes about 25 mV at room temperature (300O K).

T

vV

s

s

I e , v>>0.1 Vi=-I v<<-0.1 V

⎧⎪⎨⎪⎩

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Diode Equation (contd.,)

�  v, therefore, is a complex function of temperature �  For a constant forward bias current

�  This property of temperature dependence of a forward biased junction is made use of in sensing temperature.

Ts

iv = V lnI

dv =-1.5mV Cto-2.5mV CdT

° °

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Diode Model

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Diodes

Signal diodes �  signal rectifier diodes �  photo diodes �  light emitting diodes �  opto-couplers/opto-isolators �  sensor diodes �  Varactor diodes �  Schottky Barrier diodes �  ESD (Electrostatic discharge)

diodes �  RF diodes

�  pin diodes �  tunnel diodes Power diodes �  Zener diodes �  Diacs �  Solar cells �  Backward diodes �  Large current rectifier diodes

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Diodes (contd.,)

�  Signal rectifier diodes are less and less used in present day electronic circuits.

�  The power diodes require special arrangement in the form of heat sinks to dissipate the heat generated

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Zener Diodes

�  Zenor Diodes are manufactured for operating specifically in the breakdown region

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Zener Diodes (contd.,)

( )( )( )

zK

D

c

I

P

T % C °

knee current and

maximum power dissipation

temperature coefficient

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Zener diodes

�  are available in the range of a few volts to a few tens of volts �  zener resistance Rz in the working range of currents is in the range

of a few ohms to tens of ohms �  knee current IzK is typically a few hundred micro amperes �  Temperature coefficient is negative for voltages less than 3V, zero

for 3V, and positive for voltages greater than 3V Toshiba CMZB12 is a 12V zener of one watt power dissipation and

has a maximum leakage current of 10 mA (Max), Rz=30 ohms (Max) and a temperature coefficient of 13 mV/OC (Max)

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Sensor Diodes

�  Two matched diodes in one package can be used as a temperature sensor

1 21 2

S S

kT I kT IV ln ; V lnq I q I

q 11,600k

= =

=

where k is Boltzman's constant, q is electronic charge, and

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Sensor Diodes (contd.,)

S

1 2

As the diodes are matched (same I )

the differential voltage

Temperature sensor whose

coefficient is

where I and I are determined

by the designer

11 2

2

1

2

kT IV -V = lnq I

k I ln ;q I

�  The coefficient is less sensitive to the variations in diode currents because of the logarithmic relationship

�  S5813A from Seiko Instrument is one such sensor with a sensitivity of 11.04 mV/OC and output voltage of 1.94 volts at +30OC.

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Example 1

�  Half wave rectifier

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Example 1 (contd.,)

�  Input voltage is a sinusoidal wave of 2 V amplitude and 50 Hz

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Example 2

�  Peak detector

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Example 3

�  Peak detector connected to a load with a zener diode

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Example 3 (contd.,)

�  Waveforms across the capacitor and zenor along with the input

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Example 3 (contd.,)

min

min

max max

max

p z

p z zzK

s L

p z dz

s L z

V -VT

RC

V -V V- >IR R

V -V PV- <R R V

⎛ ⎞⎜ ⎟⎝ ⎠

Ripple peak to peak =

T is time period of the input voltage. The design equations are

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Parameters of Voltage Regulator

�  Load Regulation: % change in output voltage for the load current change from no load to full load for a specified input voltage

�  Line regulation: % change in output voltage for line voltage change from its minimum to maximum for a specified load current

�  Ripple Rejection Factor: % change in output voltage for a % change in input voltage for a given load and input voltage

�  Output Resistance: % change in output voltage for a % change in load current at a given load current

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Full-Wave Rectifier and Zener Regulator

Determine the parameters of the full-wave rectifier zener regulator shown

�  Load Regulation �  Line regulation �  Ripple Rejection Factor �  Output Resistance

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_

Analog Gate (Diode Multiplexer)

�  Analog gate enables an analog signal source to be connected or disconnected to a load

�  Diode bridge is switched ‘on’ by dc current by applying +Vc at A and -Vc at D

�  Diode bridge is switched ‘off ’ by dc voltage by applying -Vn at A and +Vn at D

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Analog Gate (Diode Multiplexer) (contd.,)

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‘ON’ State

�  When all the diodes (D1, D2, D3 and D4 ) are conducting

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‘OFF’ State

�  When all the diodes are reverse biased by applying –VN at A and +VN at D

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‘ON’/’OFF’ State Conditions

( )

max

max

max

max

Sc

C

cS

C

SS

S L C

iV -V- >0

2R 2V -V

i <R

Vi =

R +R R 2

γ

γ

'ON' state conditions

maxn SV > V

'OFF' state conditions

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Example 4

�  A square wave of 6 volts amplitude and 10 kHz is applied as control signal to a diode analog gate shown in the figure which has RC=6KW, RL=600W and RS=600W. Determine maximum signal amplitude (frequency of 1 kHz) that can be applied to the gate. Plot the output signal.

46

Example 4 (contd.,)

s

SS

S

S

V6-0.6 > 0.6×36 0.6+3.6

V0.93> ; V <0.93×1.1 =1.023V0.6+0.5

V <6VV

When the gate is ON

When the gate is OFF

Therefore should be less than 1V47

Example 4 (contd.,)

�  Plot of the output voltage for

T

Time (s)0.00 250.00u 500.00u 750.00u 1.00m

Volta

ge (V

)

-800.00m

-600.00m

-400.00m

-200.00m

0.00

200.00m

400.00m

600.00m

800.00m

SV =0.8sin 2000 tπ

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Conclusion

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