1. Chapter 10 Analog Systems
Microelectronic Circuit Design
Richard C. Jaeger
Travis N. Blalock
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
McGraw-Hill
Chap10 - 1

2. Microelectronic Circuit Design
Chapter Goals
Develop understanding of linear amplification concepts such as:
Voltage gain, current gain, and power gain,
Gain conversion to decibel representation,
Input and output resistances,
Transfer functions and Bode plots,
Cutoff frequencies and bandwidth,
Low-pass, high-pass, band-pass, and band-reject amplifiers,
Biasing for linear amplification,
Distortion in amplifiers,
Two-port representations of amplifiers,
g-, h-, y-, and z-parameters,
Use of transfer function analysis in SPICE.
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
McGraw-Hill
Chap10 - 2

3. Example of Analog Electronic System: FM Stereo Receiver
Linear functions: Radio and audio frequency amplification, frequency selection (tuning), impedance matching(75-W input, tailoring audio frequency response, local oscillator
Nonlinear functions: DC power supply(rectification), frequency conversion (mixing), detection/demodulation
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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Chap10 - 3

4. Amplification: Introduction
A complex periodic signal can be represented as the sum of many individual sine waves. We consider only one component with amplitude VS =1 mV and frequency wS with 0 phase (signal is used as reference):
Amplifier output is sinusoidal with same frequency but different amplitude VO and phase θ:
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
McGraw-Hill
Chap10 - 4

5. Amplification: Introduction (contd.)
Amplifier output power is:
Here, PO = 100 W and RL=8 W
Output power also requires output current which is:
Input current is given by
phase is zero because circuit is purely resistive.
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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Chap10 - 5

6. Microelectronic Circuit Design
Amplification: Gain
Voltage Gain:
Magnitude and phase of voltage gain are given by
and
For our example,
Current Gain:
Magnitude of current gain is given by
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
McGraw-Hill
Chap10 - 6

7. Amplification: Gain (contd.)
Power Gain:
For our example,
On decibel scale, i.e. in dB
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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Chap10 - 7

8. Amplifier Biasing for Linear Operation
VI = dc value of vI,
vi = time-varying component
For linear amplification- vI must be biased in desired region of output characteristic by VI.
If slope of output characteristic is positive, input and output are in phase (amplifier is non-inverting).
If slope of output characteristic is negative, input and output signals are 1800 out of phase (amplifier is inverting).
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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Chap10 - 8

9. Amplifier Biasing for Linear Operation (contd.)
Voltage gain depends on bias point.
Eg: if amplifier is biased at VI = 0.5 V, voltage gain will be +40 for input signals satisfying
If input exceeds this value, output is distorted due to change in amplifier slope.
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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Chap10 - 9

10. Amplifier Biasing for Linear Operation (contd.)
Output signals for 1 kHZ sinusoidal input signal of amplitude 50 mV biased at VI= 0.3 V and 0.5V:
For VI =0.3V:
Gain is 20, output varies about dc level of 4 V.
For VI =0.5V:
Gain is 40, output varies about dc level of 10 V.
Jaeger/Blalock
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Microelectronic Circuit Design
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11. Distortion in Amplifiers
Different gains for positive and negative values of input cause distortion in output.
Total Harmonic Distortion (THD) is a measure of signal distortion that compares undesired harmonic content of a signal to the desired component.
Jaeger/Blalock
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Microelectronic Circuit Design
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12. Total Harmonic Distortiondc
desired output
2nd harmonic distortion
3rd harmonic distortion
Numerator= sum of rms amplitudes of distortion terms,
Denominator= desired component
Jaeger/Blalock
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Microelectronic Circuit Design
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13. Two-port Models for Amplifiers
Simplifies amplifier-behavior modeling in complex systems.
Two-port models are linear network models, valid only under small-signal conditions.
Represented by g-, h-, y- and z-parameters.
(v1, i1) and (v2, i2) represent signal components of voltages and currents at the network ports.
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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14. Microelectronic Circuit Design
g-parameters
Using open-circuit (i=0) and short-circuit (v=0) termination conditions,
Open-circuit input conductance
Reverse short-circuit current gain
Forward open-circuit voltage gain
Short-circuit output resistance
Jaeger/Blalock
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Microelectronic Circuit Design
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15. g-parameters:Example
Problem:Find g-parameters.
Approach: Apply specified boundary conditions for each g-parameter, use circuit analysis.
For g11 and g21: apply voltage v1 to input port and open circuit output port.
For g12 and g22: apply current i2 to output port and short circuit input port.
Jaeger/Blalock
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Microelectronic Circuit Design
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16. Hybrid or h-parameters
Using open-circuit (i=0) and short-circuit (v=0) termination conditions,
Short-circuit input resistance
Reverse open-circuit voltage gain
Forward short-circuit current gain
Open-circuit output conductance
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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Chap

17. h-parameters:Example
Problem:Find h-parameters for the same network (used in g-parameters example).
Approach: Apply specified boundary conditions for each h-parameter, use circuit analysis.
For h11 and h21: apply current i1 to input port and short circuit output port.
For h12 and h22: apply voltage v2 to output port and open circuit input port.
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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18. Admittance or y-parameters
Using open-circuit (i=0) and short-circuit (v=0) termination conditions,
Short-circuit input conductance
Reverse short-circuit transconductance
Forward short-circuit transconductance
Short-circuit output conductance
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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19. y-parameters:Example
Problem:Find y-parameters for the same network (used in g-parameters example).
Approach: Apply specified boundary conditions for each y-parameter, use circuit analysis.
For y11 and y21: apply voltage v1 to input port and short circuit output port.
For y12 and y22: apply voltage v2 to output port and short circuit input port.
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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Chap

20. Impedance or z-parameters
Using open-circuit (i=0) and short-circuit (v=0) termination conditions,
Open-circuit input resistance
Reverse open-circuit transresistance
Forward open-circuit transresistance
Open-circuit output resistance
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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Chap

21. z-parameters:Example
Problem:Find z-parameters for the same network (used in g-parameters example).
Approach: Apply specified boundary conditions for each z-parameter, use circuit analysis.
For z11 and z21: apply current i1 to input port and open circuit output port. For z12 and z22: apply current i2 to output port and open circuit input port.
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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22. Mismatched Source and Load Resistances: Voltage Amplifier
g-parameter representation (g12=0) with Thevenin equivalent of input source:
If Rin >> Rs and Rout<< RL,
In an ideal voltage amplifier, and Rout =0
Jaeger/Blalock
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Microelectronic Circuit Design
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23. Mismatched Source and Load Resistances: Current Amplifier
h-parameter representation (h12=0) with Norton equivalent of input source:
If Rs >> Rin and Rout>> RL,
In an ideal current amplifier, and Rin=0
Jaeger/Blalock
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Microelectronic Circuit Design
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24. Amplifier Transfer Functions
Av(s)=Frequency-dependent voltage gain
Vo(s) and Vs(s) = Laplace Transforms of input and output voltages of amplifier,
(In factorized form)
(-z1, -z2,…-zm)=zeros (frequencies for which transfer function is zero)
(-p1, -p2,…-pm)=poles (frequencies for which transfer function is infinite)
(In polar form)
Bode plots display magnitude of the transfer function in dB and the phase in degrees (or radians) on a logarithmic frequency scale..
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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Chap

25. Low-pass Amplifier: Description
Amplifies signals over a range of frequencies including dc.
Most operational amplifiers are designed as low pass amplifiers.
Simplest (single-pole) low-pass amplifier is described by
Ao = low-frequency gain or mid-band gain
wH = upper cutoff frequency or upper half-power point of amplifier.
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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Chap

26. Low-pass Amplifier: Magnitude Response
For w<<wH :
For w>>wH :
For w=wH :
Gain is unity (0 dB) at w=AowH , called gain-bandwidth product
Bandwidth (frequency range with constant amplification )= wH (rad/s)
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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Chap

27. Low-pass Amplifier: Phase Response
If Ao positive: phase angle = 00
If Ao negative: phase angle = 1800
At wC: phase =450
One decade below wC: phase =5.70
One decade above wC: phase =84.30
Two decades below wC: phase =00
Two decades above wC: phase =900
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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28. Microelectronic Circuit Design
RC Low-pass Filter
Problem: Find voltage transfer
function
Approach: Impedance of the where
capacitor is 1/sC, use voltage
division
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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29. High-pass Amplifier: Description
True high-pass characteristic impossible to obtain as it requires infinite bandwidth.
Combines a single pole with a zero at origin.
Simplest high-pass amplifier is described by
wH = lower cutoff frequency or lower half-power point of amplifier.
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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30. High-pass Amplifier: Magnitude and Phase Response
For w>>wL :
For w<<wL :
For w=wL :
Bandwidth (frequency range with constant amplification ) is infinite
Phase response is given by
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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Chap

31. Microelectronic Circuit Design
RC High-pass Filter
Problem: Find voltage transfer
function
Approach: Impedance of the where
capacitor is 1/sC, use voltage
division
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
McGraw-Hill
Chap

32. Band-pass Amplifier: Description
Band-pass characteristic obtained by combining highpass and low-pass characteristics.
Transfer function of a band-pass amplifier is given by
Ac-coupled amplifier has a band-pass characteristic:
Capacitors added to circuit cause low frequency roll-off
Inherent frequency limitations of solid-state devices cause high-frequency roll-off.
Jaeger/Blalock
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Microelectronic Circuit Design
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33. Band-pass Amplifier: Magnitude and Phase Response
The frequency response shows a wide band of operation.
Mid-band range of frequencies given by , where
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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Chap

34. Band-pass Amplifier: Magnitude and Phase Response (contd.)
At both wH and wL, assuming wL<<wH,
Bandwidth = wH - wL.
The phase response is given by
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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35. Narrow-band or High-Q Band-pass Amplifiers
Gain maximum at center frequency wo and decreases rapidly by 3 dB at wH and wL.
Bandwidth defined as wH - wL, is a small fraction of wo with width determined by:
For high Q, poles will be complex and
Phase response is given by:
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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36. Band-Rejection Amplifier or Notch Filter
Gain maximum at frequencies far from wo and exhibits a sharp null at wo.
To achieve sharp null, transfer function has a pair of zeros on jw axis at notch frequency wo , and poles are complex.
Phase response is given by:
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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37. Microelectronic Circuit Design
All-pass Function
Uniform magnitude response at all frequencies.
Can be used to tailor phase characteristics of a signal
Transfer function is given by:
For positive Ao,
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
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38. Complex Transfer Functions
Amplifier has 2 frequency ranges with constant gain. Midband region is always defined as region of highest gain and cutoff frequencies are defined in terms of midband gain.
Since wH = w4 and wL = w3,
Jaeger/Blalock
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Microelectronic Circuit Design
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39. Microelectronic Circuit Design
Bandwidth Shrinkage
If critical frequencies aren’t widely spaced, the poles and zeros interact and cutoff frequency determination becomes complicated.
Example : for which , Av(0) = Ao
Upper cutoff frequency is defined by or
Solving for wH yields wH =0.644w1.The cutoff frequency of two-pole function is only 64% that of a single-pole function. This is known as bandwidth shrinkage.
Jaeger/Blalock
7/1/03
Microelectronic Circuit Design
McGraw-Hill
Chap