Lecture 20: Frequency Response: Miller Effectee105/fa03/handouts/...Department of EECS University of...
Transcript of Lecture 20: Frequency Response: Miller Effectee105/fa03/handouts/...Department of EECS University of...
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Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20
Lecture 20:Frequency Response: Miller Effect
Prof. Niknejad
![Page 2: Lecture 20: Frequency Response: Miller Effectee105/fa03/handouts/...Department of EECS University of California, Berkeley EECS 105Fall 2003, Lecture 20 Prof. A. Niknejad CS Short-Circuit](https://reader033.fdocuments.in/reader033/viewer/2022042103/5e80df917b08ef4aa94afd94/html5/thumbnails/2.jpg)
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
Lecture Outline
� Frequency response of the CE as voltage amp
� The Miller approximation
� Frequency Response of Voltage Buffer
![Page 3: Lecture 20: Frequency Response: Miller Effectee105/fa03/handouts/...Department of EECS University of California, Berkeley EECS 105Fall 2003, Lecture 20 Prof. A. Niknejad CS Short-Circuit](https://reader033.fdocuments.in/reader033/viewer/2022042103/5e80df917b08ef4aa94afd94/html5/thumbnails/3.jpg)
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
Last Time: CE Amp with Current Input
Calculate the short circuit current gain of device (BJT or MOS)
Can be MOS
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Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
CS Short-Circuit Current Gain
( )1 /( )
( ) ( )m gd m m
igs gd gs gd
g j C g gA j
j C C j C C
ωω
ω ω−
= ≈+ +
MOS Case
0 dB
MOS
BJT
Tω zω
Note: Zero occurs when all of “gm” current flows into Cgd:
m gs gs gdg v v j Cω=
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Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
Common-Emitter Voltage Amplifier
Small-signal model:omit Ccs to avoid complicated analysis
Can solve problem directlyby phasor analysis or using2-port models of transistor
OK if circuit is “small”(1-2 nodes)
![Page 6: Lecture 20: Frequency Response: Miller Effectee105/fa03/handouts/...Department of EECS University of California, Berkeley EECS 105Fall 2003, Lecture 20 Prof. A. Niknejad CS Short-Circuit](https://reader033.fdocuments.in/reader033/viewer/2022042103/5e80df917b08ef4aa94afd94/html5/thumbnails/6.jpg)
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
CE Voltage Amp Small-Signal Model
Two Nodes! Easy
Same circuit works for CS with rπ → ∞
![Page 7: Lecture 20: Frequency Response: Miller Effectee105/fa03/handouts/...Department of EECS University of California, Berkeley EECS 105Fall 2003, Lecture 20 Prof. A. Niknejad CS Short-Circuit](https://reader033.fdocuments.in/reader033/viewer/2022042103/5e80df917b08ef4aa94afd94/html5/thumbnails/7.jpg)
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
Frequency Response
KCL at input and output nodes; analysis is made complicated due to Zµ branch � see H&S pp. 639-640.
[ ]( )
( )( )21 /1/1
/1||||
pp
zLocoS
m
in
out
jj
jRrrRr
rg
V
V
ωωωω
ωωπ
π
++
−
+−
=
Low-frequency gain:
Zero:µπ
ωωCC
gmTz +
=>
[ ]( )
( )( ) [ ]|| || 1 0
|| ||1 0 1 0
m o oc LSout
m o oc Lin S
rg r r R j
r RV rg r r R
V j j r R
π
π π
π
− − + = → − + + +
�
Two Poles
Zero
Note: Zero occurs due to feed-forwardcurrent cancellation as before
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Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
Exact Poles
( ) ( ){ } µµππ
ωCRCRgCrR outoutmS
p ′+′++≈
1||
11
( )( ) ( ){ } µµππ
πωCRCRgCrR
rRR
outoutmS
Soutp ′+′++
′≈
1||
||/2
These poles are calculated after doing some algebraic manipulations on the circuit. It’s hard to get any intuition from the above expressions.
Usually >> 1
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Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
Miller Approximation
Results of complete analysis: not exact and little insight
Look at how Zµ affects the transfer function: find Zin
![Page 10: Lecture 20: Frequency Response: Miller Effectee105/fa03/handouts/...Department of EECS University of California, Berkeley EECS 105Fall 2003, Lecture 20 Prof. A. Niknejad CS Short-Circuit](https://reader033.fdocuments.in/reader033/viewer/2022042103/5e80df917b08ef4aa94afd94/html5/thumbnails/10.jpg)
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
Input Impedance Zin(jωωωω)
At output node:
µZVVI outtt /)( −=
outtmoutttmout RVgRIVgV ′−≈′−−= )( Why?
µµZVAVI tvCtt /)( −=
µ
µ
vCttin A
ZIVZ
−==
1/
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Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
Miller Capacitance CM
Effective input capacitance:
( )[ ]µµµ ωωωµ
CAjCjACjZ
vCvCMin −
=
−==
1
11
1
11
AV,Cx
+
─
+
─
Vin
Vout
Cx
AV,Cx
+
─
+
─
Vout(1-Av,Cx)Cx
(1-1/Av,Cx)Cx
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Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
Some Examples
Common emitter/source amplifier:
=µvCA Negative, large number (-100)
Common collector/drain amplifier:
=πvCA Slightly less than 1
,(1 ) 100M V CC A C Cµ µ µ= − �
,(1 ) 0M V CC A Cπ π= − �
Miller Multiplied Cap has Detrimental Impact on bandwidth
“Bootstrapped” cap has negligible impact on bandwidth!
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Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
CE Amplifier using Miller Approx.
Use Miller to transform Cµ
Analysis is straightforward now … single pole!
||SR rπ
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Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
Comparison with “Exact Analysis”
Miller result (calculate RC time constant of input pole):
Exact result:
( ) ( ){ } µµππω CRCRgCrR outoutmSp ′+′++=− 1||11
( ) ( ){ }11 || 1p S m outR r C g R Cπ π µω − ′= + +
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Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
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
,1 2
1p domω
τ τ=
+ +�
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Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
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…
![Page 17: Lecture 20: Frequency Response: Miller Effectee105/fa03/handouts/...Department of EECS University of California, Berkeley EECS 105Fall 2003, Lecture 20 Prof. A. Niknejad CS Short-Circuit](https://reader033.fdocuments.in/reader033/viewer/2022042103/5e80df917b08ef4aa94afd94/html5/thumbnails/17.jpg)
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
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
1 MC C Cπ= +
||M SR r Rπ=
( ) ( ){ }1 || 1S m outR r C g R Cπ π µτ ′= + +
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Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
Common-Collector Amplifier
Procedure:
1. Small-signal two-port model
2. Add device (andother) capacitors
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Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
Two-Port CC Model with Capacitors
Find Miller capacitor for Cπ -- note that the base-emitter capacitor is between the input and output
Gain ~ 1
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Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
Voltage Gain AvCππππ Across Cππππ
/( ) 1vC out out LA R R Rπ
≈ + ∼
Note: this voltage gain is neither the two-port gain nor the “loaded” voltage gain
πµµ πCACCCC vCMin )1( −+=+=
1
1inm L
C C Cg Rµ π= +
+
inC Cµ≈
1out
m
Rg
=1m Lg R >>
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Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 20 Prof. A. Niknejad
Bandwidth of CC Amplifier
Input low-pass filter’s –3 dB frequency:
( )
++=−
LminSp Rg
CCRR
1||1 π
µω
Substitute favorable values of RS, RL:
mS gR /1≈ mL gR /1>>
( ) mmp gCBIG
CCg /
1/11
µπ
µω ≈
++≈−
/p m Tg Cµω ω≈ >
Model not valid at these high frequencies