1. Lecture 20: Frequency Response: Miller Effect
Prof. Niknejad

2. Lecture Outline Frequency response of the CE as voltage amp
The Miller approximation
Frequency Response of Voltage Buffer
Department of EECS
University of California, Berkeley

3. Last Time: CE Amp with Current Input
Can be MOS
Calculate the short circuit current gain of device
(BJT or MOS)
Department of EECS
University of California, Berkeley

4. CS Short-Circuit Current Gain
MOS Case
MOS
BJT
0 dB
Note: Zero occurs when all of “gm” current flows into Cgd:
Department of EECS
University of California, Berkeley

5. Common-Emitter Voltage Amplifier
Small-signal model:
omit Ccs to avoid
complicated analysis
Can solve problem directly
by phasor analysis or using
2-port models of transistor
OK if circuit is “small”
(1-2 nodes)
Department of EECS
University of California, Berkeley

6. CE Voltage Amp Small-Signal Model
Two Nodes! Easy
Same circuit works for CS with
Department of EECS
University of California, Berkeley

7. Frequency Response
KCL at input and output nodes; analysis is made complicated due to Z branch  see H&S pp
Zero
Low-frequency gain:
Two Poles 
Note: Zero occurs due to feed-forward
current cancellation as before
Zero:
Department of EECS
University of California, Berkeley

8. Exact Poles
Usually >> 1
These poles are calculated after doing some algebraic manipulations on the circuit. It’s hard to get any intuition from the above expressions.
Department of EECS
University of California, Berkeley

9. Miller Approximation
Results of complete analysis: not exact and little insight
Look at how Z affects the transfer function: find Zin
Department of EECS
University of California, Berkeley

10. Input Impedance Zin(j)
At output node:
Why?
Department of EECS
University of California, Berkeley

11. Miller Capacitance CM Effective input capacitance: Cx + + AV,Cx AV,Cx─
Vin
Vout Cx
AV,Cx + ─
Vout
(1-Av,Cx)Cx
(1-1/Av,Cx)Cx
Department of EECS
University of California, Berkeley

12. Some Examples Common emitter/source amplifier:
Negative, large number (-100)
Miller Multiplied Cap has Detrimental Impact on bandwidth
Common collector/drain amplifier:
Slightly less than 1
“Bootstrapped” cap has negligible impact on bandwidth!
Department of EECS
University of California, Berkeley

13. CE Amplifier using Miller Approx.
Use Miller to transform C
Analysis is straightforward now … single pole!
Department of EECS
University of California, Berkeley

14. Comparison with “Exact Analysis”
Miller result (calculate RC time constant of input pole):
Exact result:
Department of EECS
University of California, Berkeley

15. Method of Open Circuit Time Constants
This is a technique to find the dominant pole of a circuit (only valid if there really is a dominant pole!)
For each capacitor in the circuit you calculate an equivalent resistor “seen” by capacitor and form the time constant τi=RiCi
The dominant pole then is the sum of these time constants in the circuit
Department of EECS
University of California, Berkeley

16. Equivalent Resistance “Seen” by Capacitor
For each “small” capacitor in the circuit:
Open-circuit all other “small” capacitors
Short circuit all “big” capacitors
Turn off all independent sources
Replace cap under question with current or voltage source
Find equivalent input impedance seen by cap
Form RC time constant
This procedure is best illustrated with an example…
Department of EECS
University of California, Berkeley

17. Example Calculation Consider the input capacitance
Open all other “small” caps (get rid of output cap)
Turn off all independent sources
Insert a current source in place of cap and find impedance seen by source
Department of EECS
University of California, Berkeley

18. Common-Collector Amplifier
Procedure:
Small-signal two- port model
Add device (and other) capacitors
Department of EECS
University of California, Berkeley

19. Two-Port CC Model with Capacitors
Gain ~ 1
Find Miller capacitor for C -- note that the base-emitter capacitor is between the input and output
Department of EECS
University of California, Berkeley

20. Voltage Gain AvC Across C
Note: this voltage gain is neither the two-port gain nor the
“loaded” voltage gain
Department of EECS
University of California, Berkeley

21. Bandwidth of CC Amplifier
Input low-pass filter’s –3 dB frequency:
Substitute favorable values of RS, RL:
Model not valid at these high frequencies
Department of EECS
University of California, Berkeley