1. Comparison of Amplifier Configurations
Midband Characteristics*
These are approximate expressions neglecting the effects of the biasing resistors R1 and R2
and the source resistance RS.
J. Millman and A. Grabel, Microelectronics, 2nd Ed., McGraw Hill, NY (1987), p. 420.
Ch. 7 Frequency Response Part 5

2. Characteristics of Amplifier Configurations
Current gain is large ( β)
for CE and EF, but < 1 for CB.
Voltage gain is large
for CE and CB, but < 1 for EF.
Input resistance is
Very small (few Ωs) for CB,
Medium (few KΩs) for CE, but
Very large (~ 10’s of KΩs) for EF.
Output resistance is
Very small (few Ωs) for EF,
Very large (~ 100’s of KΩs) for
CE and CB.
Ch. 7 Frequency Response Part 5

3. Ch. 7 Frequency Response Part 5
Numerical Comparison of Amplifier Configurations for the Same Transistor and DC Biasing
These are approximate expressions neglecting the effects of the biasing resistors R1 and R2
and the source resistance RS.
Ch. 7 Frequency Response Part 5

4. Comparison of CB to CE Amplifier (with same Rs = 5 Ω)
CE (with RS = 5 Ω) CB (with RS = 5Ω)
Midband Gain
Low Frequency
Poles and Zeros
High Frequency
Poles and Zeroes
Ch. 7 Frequency Response Part 5

5. Comparison of EF to CE Amplifier (For RS = 5Ω )
CE EF
Midband Gain
Low Frequency
Poles and Zeros
High Frequency
Poles and Zeroes
Ch. 7 Frequency Response Part 5

6. Comparison of Amplifier Configurations
Midband Gain and High and Low Frequency Performance
CE CB EF
Midband Voltage Gain -191 V/V V/V V/V
45.6dB 40.2dB dB
Low 3dB Frequency 1.7x104 rad/s 5.0x104 rad/s 2.6x102 rad/s
High 3dB Frequency 5.0x107 rad/s 7.1x108 rad/s 1.0x1010 rad/s
RS= 5 Ω
Results for all three amplifiers with the smaller (5Ω) source resistance RS.
Ch. 7 Frequency Response Part 5

7. Ch. 7 Frequency Response Part 5
Cascade Amplifier EF CE
Emitter Follower + Common Emitter (EF+CE)
Voltage gain from CE stage, gain of one for EF.
Low output resistance from EF provides a low source resistance for CE amplifier so good matching of output of EF to input of CE amplifier
High frequency response (3dB frequency) for Cascade Amplifier is improved over CE amplifier.
Ch. 7 Frequency Response Part 5

8. Cascade Amplifier - DC analysis
IB1
IB2
IE1
IRE1
Small Signal Parameters
Ch. 7 Frequency Response Part 5

9. Cascade Amplifier - Midband Gain Analysis
Note: rx1 = rx2 = 0 so equivalent circuit is simplified.
Iπ1 + +
Vπ1 _ + Vi
Vπ2 _ _ Ri
Note: Voltage gain is nearly equal to
that of the CE stage, e.g. – 68 !
Ch. 7 Frequency Response Part 5

10. Cascade Amplifier - Low Frequency Poles and Zeroes
Use Gray-Searle (Short Circuit) Technique to find the poles.
Three low frequency poles
Equivalent resistance may depend on rπ for both transistors.
Find three low frequency zeroes.
Ch. 7 Frequency Response Part 5

11. Ch. 7 Frequency Response Part 5
Cascade Amplifier - Analysis of Low Frequency Poles Gray-Searle (Short Circuit) Technique
Input coupling capacitor CC1 = 1 μF
rπ1
Vπ1 +
rπ2
RE1
Vπ2 _ IX
Iπ1 Ri Vi
RE1
rπ2
Ch. 7 Frequency Response Part 5

12. Ch. 7 Frequency Response Part 5
Cascade Amplifier - Analysis of Low Frequency Poles Gray-Searle (Short Circuit) Technique
rX2
CC2 Vo
rπ2
Vπ2
gm2Vπ2 RC RL
RE2 CE
Output coupling capacitor CC2 = 1 μF VX Vo RC RL
Ch. 7 Frequency Response Part 5

13. Ch. 7 Frequency Response Part 5
Cascade Amplifier - Analysis of Low Frequency Poles Gray-Searle (Short Circuit) Technique
Emitter bypass capacitor CE = 47 μF
Iπ1
r π1
gm1Vπ1
Vπ1
VE1
Ie1
Iπ2
re1
rπ2
Vπ2
gm2Vπ2
RE1
VE2 Ix
Ie2
re2
RE2 VX
IE2
Low 3 dB Frequency
The pole for CE is the largest and therefore the
most important in determining the low 3 dB frequency.
Ch. 7 Frequency Response Part 5

14. Cascade Amplifier - Low Frequency Zeros
What are the zeros for the Cascade amplifier?
For CC1 and CC2 , we get zeros at ω = 0 since ZC = 1 / jωC and these capacitors are in the signal line, i.e. ZC  at ω = 0 so Vo  0.
Consider RE in parallel with CE
Impedance given by
When Z’E  , Iπ  0, so gmVπ  0, so Vo  0
Z’E   when s = - 1 / RE2CE so pole for CE is at
Ch. 7 Frequency Response Part 5

15. Cascade Amplifier - High Frequency Poles and Zeroes
Use Gray-Searle (Open Circuit) Technique to find the poles.
Four high frequency poles
Equivalent resistance may depend on rπ for both transistors.
Find four high frequency zeroes.
High Frequency Equivalent Circuit
Ch. 7 Frequency Response Part 5

16. Cascade Amplifier - High Frequency Poles
Pole for Capacitor Cπ1 = 13.9 pF Ix + _ VX
Ix- Iπ1
Iπ1
Ie1
Ch. 7 Frequency Response Part 5

17. Cascade Amplifier - High Frequency Poles
Pole for Capacitor Cμ1 = 2 pF + _ Ix
Iπ1
Ix- Iπ1 VX
Ie1
Ch. 7 Frequency Response Part 5

18. Cascade Amplifier - High Frequency Poles and Zeroes
Simplified Equivalent Circuit
Using Miller’s Theorem,
replace Cμ2 by two capacitors.
Ch. 7 Frequency Response Part 5

19. Cascade Amplifier - High Frequency Poles
Pole for Capacitor CT = 152 pF + _
Iπ1
Vπ1
Ve1
Ie1 Ix
re1 VX
Pole for Output Capacitor Cμ2 = 2 pF
gm2Vπ2 _ + VX
Ch. 7 Frequency Response Part 5

20. Cascade Amplifier - High Frequency Zeroes
When does Vo = 0?
When ω → ∞, ZCμ1→ 0, so signal shorted to ground ωZH1= ∞.
When ω → ∞, ZCπ2→ 0, so rπ2 shorted, so Vπ2 = ωZH2= ∞.
For Cπ1 , we get a zero when Ie1 = 0.
Ie1
Ch. 7 Frequency Response Part 5

21. Cascade Amplifier - High Frequency Zeroes
I Cμ2
IRL’= 0
When does Cμ2 produce a zero, i.e. make Vo = 0?
For Cμ2 , we get a zero when IRL’ = 0, or ICμ2 = gm2Vπ2 , i.e. the output load resistance RL’ is starved of any current.
Zero for Output Capacitor Cμ2 = 2 pF
Ch. 7 Frequency Response Part 5

22. Cascade Amplifier - High Frequency Poles and Zeroes
Ch. 7 Frequency Response Part 5

23. Comparison of Cascade to CE Amplifier
CE* Cascade (EF+CE)
2 X improvement
in voltage gain !
Midband Gain
Low Frequency
Poles and Zeros
High Frequency
Poles and Zeroes
25 X improvement
in bandwidth !
Ch. 7 Frequency Response Part 5
* CE stage with same transistor, biasing resistors, source resistance and load as cascade.

24. Comparison of Cascade to CE Amplifier
Why the better voltage gain for the cascade?
Emitter follower gives no voltage gain!
Cascade has better matching with source than CE.
Cascade amplifier has an input resistance that is higher due to EF first stage.
Versus Ri2 = rπ2 = 2.5 K for CE
So less loss in voltage divider term (Vi / Vs ) with the source resistance.
0.91 for cascade vs 0.37 for CE.
Why better bandwidth?
Low output resistance re1 of EF stage gives smaller effective source resistance for CE stage and higher frequency for dominant pole due to CT (including Cμ2)
Ri1
Ri2
Pole for Capacitor CT = 152 pF
re1
Ch. 7 Frequency Response Part 5

25. Another Useful Amplifier – Cascode (CE+CB) Amplifier
Common Emitter + Common Base (CE + CB) configuration
Voltage gain from both stages
Low input resistance from second CB stage provides first stage CE with low load resistance so Miller Effect multiplication of Cμ1 is much smaller.
High frequency response dramatically improved (3 dB frequency increased).
Bandwidth is much improved (~130 X).
Large Miller Effect
Small Miller Effect
Bandwidth is improved by a factor of 130X
over that for the CE amplifier !
Ch. 7 Frequency Response Part 5

26. Example of Cascode (CE +CB) Amplifier
ECTW Conf. Proceedings 2003.
Ch. 7 Frequency Response Part 5

27. Other Examples of Multistage Amplifiers
CE CE
EF EF
Darlington Pair
Ch. 7 Frequency Response Part 5

28. Other Examples of Multistage Amplifiers
Push – Pull Amplifier
Amplifier with Npn and Pnp Transistors
Amplifier with FETs and Bipolar Transistors
Ch. 7 Frequency Response Part 5

29. Differential Amplifier
Similar to CE amplifier, but two CE’s operated in parallel
Signal applied between two equivalent inputs instead of between one input and ground
Common emitter resistor or current source used
Current shared or switched between two transistors (they compete)
Analyze using equivalent half-circuit
1/2 of signal at input
1/2 of signal at output
1/2 of source resistance
Gain and frequency response similar to CE amplifier for high frequencies
Advantage:
Rejects common noise pickup on input
No coupling capacitors so can operate down to zero frequency. _ + Vo
Ch. 7 Frequency Response Part 5

30. Differential Amplifier Analysis
Midband Gain Vo
Vo /2
Low Frequency Poles and Zeros
* Direct coupled so no coupling capacitors
and no emitter bypass capacitor
* No low frequency poles and zeros
* Flat (frequency independent) gain
down to zero frequency
High Frequency Poles and Zeros
Vo /2
Dominant pole using Miller’s Thoerem
High frequency performance is very similar to CE amplifier.
Ch. 7 Frequency Response Part 5

31. Ch. 7 Frequency Response Part 5
Summary
In this chapter we have shown how to analyze the high and low frequency dependence of the gain for an amplifier.
Analyzed the effects of the coupling capacitors on the low frequency response
Found the expressions for the corresponding poles and zeros.
Demonstrated Bode plots of magnitude and phase.
Analyzed the effects of the capacitances within the transistor on the high frequency response.
Demonstrated Bode plots of the magnitude and phase.
Analyzed the high and low frequency performance of the three bipolar transistor amplifiers: common emitter, common base and emitter follower.
Demonstrated how to find the expressions for the gain and the high and low frequency poles and zeros for multistage amplifiers.
Ch. 7 Frequency Response Part 5