Frequency Response Presentation slides .pdf

Frequency response

1. Lecture 08
Frequency Response (1)
Integrated Circuits Laboratory (ICL)
Electronics and Communications Eng. Dept.
Faculty of Engineering
Ain Shams University
Dr. Hesham A. Omran
Analog IC Design
ًليِلَ ق الَِّإ ِمْلِعْلا
َ
نِم
ْ
م
ُ
تيِتوُأ ا
َ
م
َ
و
26 March 2020 2 نابعش1441

2. Outline
❑Recapping previous key results
❑Bode plot review
❑Where are the capacitors?
❑Approximate analysis techniques
▪Short-circuit time constant (SCTC) and open-circuit time constant (OCTC) techniques
▪Dominant pole approximation
❑IC amplifier frequency response
▪Unity gain frequency (UGF) and gain-bandwidth product (GBW)
❑Calculating zeros and poles by inspection
▪Associating poles with nodes
❑Miller’s theorem
08: Frequency Response (1) 2

3. Outline
❑Recapping previous key results
❑Bode plot review
❑Where are the capacitors?
❑Approximate analysis techniques
▪Short-circuit time constant (SCTC) and open-circuit time constant (OCTC) techniques
▪Dominant pole approximation
❑IC amplifier frequency response
▪Unity gain frequency (UGF) and gain-bandwidth product (GBW)
❑Calculating zeros and poles by inspection
▪Associating poles with nodes
❑Miller’s theorem
08: Frequency Response (1) 3

4. MOSFET in Saturation
❑The channel is pinched off if the difference between the gate and drain voltages is not
sufficientto create an inversion layer
�
��≤�
���??????�
��≥�
��
❑Square-law (long channel MOS)
�
�=
����??????
2
�
??????
⋅�
��
2
1+��
��
�
��↑⇒�
��↑
08: Frequency Response (1) 4n+n+
G
S D
p-sub
p+
B
VGS>VTH VGD<VTH
VDS>Vov
VSB VGS > VTH
VGD < VTH
VDS > Vov VDG < |VTH|
VSG > |VTH|
VSD > |Vov|

5. Regions of Operation Summary
08: Frequency Response (1) 5
OFF
(Subthreshold)
&#3627408457;
&#3627408442;&#3627408454;<&#3627408457;
&#3627408455;&#3627408443;
ON
&#3627408457;
&#3627408442;&#3627408454;>&#3627408457;
&#3627408455;&#3627408443;
Triode
&#3627408457;
&#3627408439;&#3627408454;<&#3627408457;
&#3627408476;&#3627408483;
Or
&#3627408457;
&#3627408442;&#3627408439;>&#3627408457;
&#3627408455;&#3627408443;
&#3627408444;
&#3627408439;=&#3627409159;&#3627408438;
&#3627408476;&#3627408485;
&#3627408458;
??????
&#3627408457;
&#3627408476;&#3627408483;&#3627408457;
&#3627408439;&#3627408454;−
&#3627408457;
&#3627408439;&#3627408454;
2
2
Pinch-Off
(Saturation)
&#3627408457;
&#3627408439;&#3627408454;≥&#3627408457;
&#3627408476;&#3627408483;
Or
&#3627408457;
&#3627408442;&#3627408439;≤&#3627408457;
&#3627408455;&#3627408443;
&#3627408444;
&#3627408439;=
&#3627409159;&#3627408438;
&#3627408476;&#3627408485;
2
&#3627408458;
??????
&#3627408457;
&#3627408476;&#3627408483;
2
1+&#3627409158;&#3627408457;
&#3627408439;&#3627408454;

6. Low-Frequency Small-Signal Model
&#3627408468;
&#3627408474;=
&#3627409173;&#3627408444;
&#3627408439;
&#3627409173;&#3627408457;
&#3627408442;&#3627408454;
=&#3627409159;&#3627408438;
&#3627408476;&#3627408485;
&#3627408458;
??????
&#3627408457;
&#3627408476;&#3627408483;=&#3627409159;&#3627408438;
&#3627408476;&#3627408485;
&#3627408458;
??????
⋅2&#3627408444;
&#3627408439;=
2&#3627408444;
&#3627408439;
&#3627408457;
&#3627408476;&#3627408483;
&#3627408468;
&#3627408474;&#3627408463;=&#3627409154;&#3627408468;
&#3627408474;&#3627409154;≈0.1−0.25
&#3627408479;
&#3627408476;=
1
&#3627409173;&#3627408444;&#3627408439;/&#3627409173;&#3627408457;&#3627408439;&#3627408454;
=
&#3627408457;
??????
&#3627408444;&#3627408439;
=
1
&#3627409158;&#3627408444;&#3627408439;
&#3627408457;
&#3627408436;∝??????↔&#3627409158;∝
1
??????
&#3627408457;
&#3627408439;&#3627408454;↑&#3627408457;
&#3627408436;↑
08: Frequency Response (1) 6gmvgs rogmbvbs
G D
S
B
vgs
vbs

7. Rin/out Shortcuts Summary
08: Frequency Response (1) 7
1
&#3627408468;
&#3627408474;+&#3627408468;
&#3627408474;&#3627408463;
1+
??????
&#3627408439;
&#3627408479;
&#3627408476;
L.I.N.
&#3627408479;
&#3627408476;1+&#3627408468;
&#3627408474;+&#3627408468;
&#3627408474;&#3627408463;??????
&#3627408454;
H.I.N.
∞
At low
frequencies ONLY

8. Active Load (Source OFF)
08: Frequency Response (1) 8ro
ro

9. 1/gm ro
1/gm ro Diode Connected (Source Absorption)
❑Always in saturation (&#3627408457;
&#3627408439;&#3627408454;=&#3627408457;
&#3627408442;&#3627408454;>&#3627408457;
&#3627408476;&#3627408483;)
❑Body effect: &#3627408468;
&#3627408474;→&#3627408468;
&#3627408474;+&#3627408468;
&#3627408474;&#3627408463;(if G is ac gnd)
08: Frequency Response (1) 9

10. Why GmRout?
??????
&#3627408470;&#3627408475;=??????
&#3627408470;&#3627408475;/&#3627408470;
&#3627408470;&#3627408475;
??????
&#3627408476;&#3627408482;&#3627408481;=??????
&#3627408485;/&#3627408470;
&#3627408485;@??????
&#3627408470;&#3627408475;=0
&#3627408442;
&#3627408474;=&#3627408470;
&#3627408476;&#3627408482;&#3627408481;,&#3627408480;&#3627408464;/??????
&#3627408470;&#3627408475;
&#3627408436;
&#3627408483;=&#3627408442;
&#3627408474;??????
&#3627408476;&#3627408482;&#3627408481;
&#3627408436;
&#3627408470;=&#3627408442;
&#3627408474;??????
&#3627408470;&#3627408475;
❑Divide and conquer
▪Rout simplified: vin=0
▪Gm simplified: vout=0
▪We already need Rin/out and Gm
▪We can quickly and easily get Rin/out from the shortcuts
08: Frequency Response (1) 10Avvin
Rout
vin
Rin
vout
iout
iin vin
Rin
vout
iout
iin
Gmvin Rout

11. CS CG CD (SF)
Voltage& currentamplifierVoltage amplifier
Current buffer
Voltage buffer
Current amplifier
Rin ∞ ??????
&#3627408454;||
1
&#3627408468;
&#3627408474;+&#3627408468;
&#3627408474;&#3627408463;
1+
??????
&#3627408439;
&#3627408479;
&#3627408476;
∞
Rout??????
&#3627408439;||&#3627408479;
&#3627408476;1+&#3627408468;
&#3627408474;+&#3627408468;
&#3627408474;&#3627408463;??????
&#3627408454;??????
&#3627408439;||&#3627408479;
&#3627408476;??????
&#3627408454;||
1
&#3627408468;
&#3627408474;+&#3627408468;
&#3627408474;&#3627408463;
1+
??????
&#3627408439;
&#3627408479;
&#3627408476;
Gm
−??????
&#3627408526;
&#3627409359;+??????
&#3627408526;+??????
&#3627408526;&#3627408515;&#3627408505;
&#3627408506;
??????
&#3627408526;+??????
&#3627408526;&#3627408515;
??????
&#3627408526;
&#3627409359;+&#3627408505;
&#3627408491;/&#3627408531;
&#3627408528;
Summary of Basic Topologies
08: Frequency Response (1) 11RD
vout
vin
RS RD
vin
RS
vout RD
vout
vin
RS

12. Outline
❑Recapping previous key results
❑Bode plot review
❑Where are the capacitors?
❑Approximate analysis techniques
▪Short-circuit time constant (SCTC) and open-circuit time constant (OCTC) techniques
▪Dominant pole approximation
❑IC amplifier frequency response
▪Unity gain frequency (UGF) and gain-bandwidth product (GBW)
❑Calculating zeros and poles by inspection
▪Associating poles with nodes
❑Miller’s theorem
08: Frequency Response (1) 12

13. Frequency Response
❑Y-axis: magnitude of frequency response, x-axis: frequency
08: Frequency Response (1) 13
LPF BPF HPF

14. Poles and Zeros
❑Transfer function
&#3627408443;&#3627408480;=
&#3627408449;&#3627408480;
&#3627408439;&#3627408480;
❑Zeros: roots of numerator => &#3627408449;&#3627408480;
❑Poles: roots of denominator => &#3627408439;&#3627408480;
❑Frequency response: &#3627408480;⇒&#3627408471;&#3627409172;
&#3627408443;&#3627408471;&#3627409172;=
&#3627408457;
&#3627408476;&#3627408482;&#3627408481;&#3627408471;&#3627409172;
&#3627408457;
&#3627408470;&#3627408475;&#3627408471;&#3627409172;
=&#3627408443;&#3627408471;&#3627409172;&#3627408466;
&#3627408471;??????
❑Magnitude&#3627408462;+&#3627408471;&#3627408463;=&#3627408479;=&#3627408462;
2
+&#3627408463;
2
❑Phase&#3627408462;+&#3627408471;&#3627408463;=&#3627409155;=tan
−1
&#3627408463;
&#3627408462;
08: Frequency Response (1) 14r
b
a
Re
Im
θ

15. 1
st
Order LPF
&#3627408443;&#3627408480;=
??????
&#3627408476;&#3627408482;&#3627408481;
??????
&#3627408470;&#3627408475;
=
1/&#3627408480;&#3627408438;
??????+1/&#3627408480;&#3627408438;
=
1
1+&#3627408480;??????&#3627408438;
=
1
1+&#3627408480;??????
&#3627408443;&#3627408471;&#3627409172;=
??????
&#3627408476;&#3627408482;&#3627408481;
??????
&#3627408470;&#3627408475;
=
1/&#3627408471;&#3627409172;&#3627408438;
??????+1/&#3627408471;&#3627409172;&#3627408438;
=
1
1+&#3627408471;&#3627409172;??????&#3627408438;
=
1
1+
&#3627408471;&#3627409172;
&#3627409172;
&#3627408464;
❑??????=??????&#3627408438;:time constant
❑&#3627409172;
&#3627408464;=
1
??????
=
1
&#3627408453;&#3627408438;
: cutoff/corner frequency
❑Poles: &#3627408480;
&#3627408477;=−
1
??????
=−&#3627409172;
&#3627408464;, Zeros: ?
❑&#3627408443;&#3627408471;&#3627409172;=
1
1+
??????
????????????
2
❑&#3627408451;&#3627408443;&#3627408471;&#3627409172;=−tan
−1
&#3627409172;
&#3627409172;
??????
08: Frequency Response (1) 15Vout
R
C
Vin
Vout
CIin R

16. Bode Plot Rules
Pole Zero
Magnitude -20dB/decade
Actual Mag @ pole: -3 dB
+20dB/decade
Actual Mag @ zero: +3 dB
Phase -90
o
Actual Phase @ pole: -45
o
LHPzero:
+90
o
Actual Phase @ zero: +45
o
RHPzero:
-90
o
Actual Phase @ zero: -45
o
08: Frequency Response (1) 16
→RHP: Right-half plane (??????&#3627408466;&#3627408480;>0)
→LPH: Left-half plane (??????&#3627408466;&#3627408480;<0)

17. 1
st
Order LPF Bode Plot
08: Frequency Response (1) 17[Sedra/Smith, 2015]
&#3627408490;⇒&#3627408528;.&#3627408516;. &#3627408490;⇒✓
20log&#3627408443;&#3627408471;&#3627409172;&#3627408465;&#3627408437;
&#3627408451;&#3627408443;&#3627408471;&#3627409172;

18. 1
st
Order HPF
&#3627408443;&#3627408480;=
??????
&#3627408476;&#3627408482;&#3627408481;
??????
&#3627408470;&#3627408475;
=
??????
??????+1/&#3627408480;&#3627408438;
=
&#3627408480;??????&#3627408438;
1+&#3627408480;??????&#3627408438;
=
&#3627408480;??????
1+&#3627408480;??????
&#3627408443;&#3627408471;&#3627409172;=
??????
&#3627408476;&#3627408482;&#3627408481;
??????
&#3627408470;&#3627408475;
=
??????
??????+1/&#3627408471;&#3627409172;&#3627408438;
=
&#3627408471;&#3627409172;??????&#3627408438;
1+&#3627408471;&#3627409172;??????&#3627408438;
=
&#3627408471;&#3627409172;
&#3627409172;
&#3627408464;
1+
&#3627408471;&#3627409172;
&#3627409172;
&#3627408464;
❑Poles: &#3627408480;
&#3627408477;=−
1
??????
=−&#3627409172;
&#3627408464;
❑Zeros: &#3627408480;
??????=0
❑&#3627408443;&#3627408471;&#3627409172;=
??????
????????????
1+
??????
????????????
2
❑&#3627408451;&#3627408443;&#3627408471;&#3627409172;=90
o
−tan
−1
&#3627409172;
&#3627409172;??????
08: Frequency Response (1) 18Vout
C
R
Vin

19. Bode Plot Rules
Pole Zero
Magnitude -20dB/decade
Actual Mag @ pole: -3 dB
+20dB/decade
Actual Mag @ zero: +3 dB
Phase -90
o
Actual Phase @ pole: -45
o
LHPzero:
+90
o
Actual Phase @ zero: +45
o
RHPzero:
-90
o
Actual Phase @ zero: -45
o
08: Frequency Response (1) 19
→RHP: Right-half plane (??????&#3627408466;&#3627408480;>0)
→LPH: Left-half plane (??????&#3627408466;&#3627408480;<0)

20. 1
st
Order HPF Bode Plot
08: Frequency Response (1) 20[Sedra/Smith, 2015]
&#3627408490;⇒&#3627408532;.&#3627408516;.&#3627408490;⇒✓
20log&#3627408443;&#3627408471;&#3627409172;&#3627408465;&#3627408437;
&#3627408451;&#3627408443;&#3627408471;&#3627409172;

21. Outline
❑Recapping previous key results
❑Bode plot review
❑Where are the capacitors?
❑Approximate analysis techniques
▪Short-circuit time constant (SCTC) and open-circuit time constant (OCTC) techniques
▪Dominant pole approximation
❑IC amplifier frequency response
▪Unity gain frequency (UGF) and gain-bandwidth product (GBW)
❑Calculating zeros and poles by inspection
▪Associating poles with nodes
❑Miller’s theorem
08: Frequency Response (1) 21

22. Where are the Capacitors?
❑Coupling capacitors: &#3627408438;
&#3627408438;1and &#3627408438;
&#3627408438;2→act as HPF (affect LFR)
❑Bypass capacitor: &#3627408438;
&#3627408454;
❑Usually quite large ~&#3627409159;&#3627408441;
08: Frequency Response (1) 22Rsig
vin
RG1
RG2
RD
vout
M1
vsig
CS
Cc1
Cc2
RL
RS

23. Effect of Bypass Capacitor
❑Does &#3627408438;
&#3627408454;act as a LPF or a HPF?
▪By intuition, at high frequency &#3627408438;
&#3627408454;will increase the gain →HPF
&#3627408442;
&#3627408474;&#3627408480;=
??????&#3627408474;
1+??????
&#3627408474;&#3627408461;
&#3627408454;
&#3627408461;
&#3627408454;=
1
1/&#3627408453;
&#3627408454;+&#3627408480;&#3627408438;
&#3627408454;
=
&#3627408453;&#3627408454;
1+&#3627408480;&#3627408453;
&#3627408454;&#3627408438;
&#3627408454;
&#3627408442;
&#3627408474;&#3627408480;=
??????&#3627408474;1+&#3627408480;&#3627408453;&#3627408454;&#3627408438;&#3627408454;
1+??????
&#3627408474;&#3627408453;
&#3627408454;1+
&#3627408480;&#3627408453;
&#3627408454;
&#3627408438;
&#3627408454;
1+??????&#3627408474;&#3627408453;
&#3627408454;
&#3627408480;
??????=−
1
??????
&#3627408454;&#3627408438;
&#3627408454;
&#3627408462;&#3627408475;&#3627408465;&#3627408480;
&#3627408477;=−
1+&#3627408468;
&#3627408474;??????
&#3627408454;
??????
&#3627408454;&#3627408438;
&#3627408454;
⇒&#3627409172;
&#3627408477;>&#3627409172;
??????⇒&#3627408443;&#3627408451;&#3627408441;
08: Frequency Response (1) 23Rsig
vin
RG1
RG2
RD
vout
M1
vsig
CS
Cc1
Cc2
RL
RS
CL

24. Where are the Capacitors?
❑Gate capacitance (&#3627408438;
????????????=&#3627408438;
??????&#3627408463;+&#3627408438;
??????&#3627408480;+&#3627408438;
??????&#3627408465;)
▪Intrinsic part fundamental to MOSFET operation
▪Parasitic part due to the overlap between gate and S/D (&#3627408438;
&#3627408476;&#3627408483;)
❑S/D capacitance (&#3627408438;
&#3627408480;&#3627408463;&#3627408462;&#3627408475;&#3627408465;&#3627408438;
&#3627408465;&#3627408463;)
▪Parasitic capacitances due to reverse biased pn-junctions
•Bottom-plate (&#3627408438;
&#3627408471;) and side-wall components (&#3627408438;
&#3627408471;&#3627408480;&#3627408484;)
❑Usually quite small ~&#3627408467;&#3627408441;
08: Frequency Response (1) 24n+n+
G
S D
p-sub

25. MOSFET Capacitance
❑&#3627408438;
&#3627408476;&#3627408483;per unit width, &#3627408438;
&#3627408471;per unit area, and &#3627408438;
&#3627408471;&#3627408480;&#3627408484;per unit perimeter
08: Frequency Response (1) 25n+n+
G
S D
p-sub
n+n+
G
S D
p-sub
n+n+
G
S D
p-sub
Cutoff Triode Saturation
&#3627408490;
??????&#3627408515;<&#3627408458;??????&#3627408438;
&#3627408476;&#3627408485;0 &#3627409358;
&#3627408490;
??????&#3627408532;&#3627408458;&#3627408438;
&#3627408476;&#3627408483;
1
2
&#3627408458;??????&#3627408438;
&#3627408476;&#3627408485;+&#3627408458;&#3627408438;
&#3627408476;&#3627408483;
&#3627409360;
&#3627409361;
????????????&#3627408490;
&#3627408528;&#3627408537;+??????&#3627408490;
&#3627408528;&#3627408535;
&#3627408490;
??????&#3627408517;&#3627408458;&#3627408438;
&#3627408476;&#3627408483;
1
2
&#3627408458;??????&#3627408438;
&#3627408476;&#3627408485;+&#3627408458;&#3627408438;
&#3627408476;&#3627408483;
??????&#3627408490;
&#3627408528;&#3627408535;
&#3627408490;
&#3627408532;&#3627408515;&#3627408436;
&#3627408454;&#3627408438;
&#3627408471;+&#3627408451;
&#3627408454;&#3627408438;
&#3627408471;&#3627408480;&#3627408484;
&#3627408436;
&#3627408454;+
&#3627408458;??????
2
&#3627408438;
&#3627408471;+&#3627408451;
&#3627408454;&#3627408438;
&#3627408471;&#3627408480;&#3627408484;
&#3627408488;
&#3627408506;+????????????&#3627408490;
&#3627408523;+??????
&#3627408506;&#3627408490;
&#3627408523;&#3627408532;&#3627408536;
&#3627408490;
&#3627408517;&#3627408515;&#3627408436;
&#3627408439;&#3627408438;
&#3627408471;+&#3627408451;
&#3627408439;&#3627408438;
&#3627408471;&#3627408480;&#3627408484;
&#3627408436;
&#3627408439;+
&#3627408458;??????
2
&#3627408438;
&#3627408471;+&#3627408451;
&#3627408439;&#3627408438;
&#3627408471;&#3627408480;&#3627408484;
&#3627408488;
&#3627408491;&#3627408490;
&#3627408523;+??????
&#3627408491;&#3627408490;
&#3627408523;&#3627408532;&#3627408536;

26. High Frequency Small Signal Model
❑MOSFET capacitances act as LPF (affect HFR)
❑In pinch-off saturation
▪&#3627408438;
??????&#3627408463;≈0(for SI only)
▪&#3627408438;
??????&#3627408480;≫&#3627408438;
??????&#3627408465;(not valid for ??????↓↓, why?)
▪&#3627408438;
&#3627408480;&#3627408463;>&#3627408438;
&#3627408465;&#3627408463;
08: Frequency Response (1) 26Cgs
Cgd
gmvgs rogmbvbs
G D
S
B
Csb
CdbCgb

27. N-Well Capacitance
❑There is an additional junction cap between n-well and p-sub
❑If the n-well is tied to VDD this cap is ac shorted (why?)
❑But if n-well is floating (e.g., PMOS S and B connected) this cap is not ac shorted
▪Usually not modeled in SPICE
▪Must be added manually ~0.05&#3627408467;&#3627408441;/&#3627409159;&#3627408474;
2
08: Frequency Response (1) 27n+n+
G
S D
p-sub
p+
B
VGS>VTH VGD<VTH
VDS>Vov
p+ p+
G
SD
n-well
n+
B
|VGS|>|VTH||VGD|<|VTH|
|VDS|>Vov

28. Outline
❑Recapping previous key results
❑Bode plot review
❑Where are the capacitors?
❑Approximate analysis techniques
▪Short-circuit time constant (SCTC) and open-circuit time constant (OCTC) techniques
▪Dominant pole approximation
❑IC amplifier frequency response
▪Unity gain frequency (UGF) and gain-bandwidth product (GBW)
❑Calculating zeros and poles by inspection
▪Associating poles with nodes
❑Miller’s theorem
08: Frequency Response (1) 28

29. Frequency Response
08: Frequency Response (1) 29
Couplingand
bypass cap
✓ s.c. s.c.
MOSFET and
load cap
o.c. o.c. ✓
[Sedra/Smith, 2015]

30. SCTC and OCTC Techniques
❑Low-frequency range (LFR) => Not common in Analog IC design
▪Only consider one cap at a time →Assume other caps are s.c.→s.c.time constant
(SCTC) technique
▪&#3627409172;
??????,3&#3627408465;&#3627408437;≈&#3627409172;
??????1+&#3627409172;
??????2+⋯
▪Highest pole dominates (L.I.N. dominates)
❑High-frequency range (HFR) => More important in Analog ICs
▪Only consider one cap at a time →Assume other caps are o.c. →o.c. time constant
(OCTC) technique
▪&#3627409172;
&#3627408443;,3&#3627408465;&#3627408437;≈&#3627409172;
&#3627408443;1//&#3627409172;
&#3627408443;2//⋯
▪Lowest pole dominates (H.I.N. dominates)
❑Both SCTC and OCTC provide good approxif one pole is dominant and poles are real
08: Frequency Response (1) 30

31. Dominant Pole Approximation
❑Assume the poles are real and widely separated: &#3627409172;
&#3627408477;1≪&#3627409172;
&#3627408477;2
&#3627408436;
&#3627408483;&#3627408480;≈
&#3627408436;
&#3627408476;
1+
&#3627408480;
&#3627409172;
&#3627408477;1
1+
&#3627408480;
&#3627409172;
&#3627408477;2
=
&#3627408436;
&#3627408476;
1+
1
&#3627409172;
&#3627408477;1
+
1
&#3627409172;
&#3627408477;2
&#3627408480;+
1
&#3627409172;
&#3627408477;1&#3627409172;
&#3627408477;2
&#3627408480;
2
≈
&#3627408436;
&#3627408476;
1+
1
&#3627409172;
&#3627408477;1
&#3627408480;+
1
&#3627409172;
&#3627408477;1&#3627409172;
&#3627408477;2
&#3627408480;
2
=
&#3627408436;
&#3627408476;
1+&#3627408463;
1&#3627408480;+&#3627408463;
2&#3627408480;
2
&#3627409172;
&#3627408477;1≈
1
&#3627408463;1
and&#3627409172;
&#3627408477;2≈
1
&#3627408463;2&#3627409172;&#3627408477;1
=
&#3627408463;
1
&#3627408463;2
❑OCTC provides an approxvalue for dominant pole only
❑Dominant pole approxprovides an approxvalue for both dominant and non-dominant
poles
08: Frequency Response (1) 31

32. Outline
❑Recapping previous key results
❑Bode plot review
❑Where are the capacitors?
❑Approximate analysis techniques
▪Short-circuit time constant (SCTC) and open-circuit time constant (OCTC) techniques
▪Dominant pole approximation
❑IC amplifier frequency response
▪Unity gain frequency (UGF) and gain-bandwidth product (GBW)
❑Calculating zeros and poles by inspection
▪Associating poles with nodes
❑Miller’s theorem
08: Frequency Response (1) 32

33. IC Amplifier Frequency Response
❑&#3627408488;
&#3627408528;is the low-frequency gain (or DC gain) of the amplifier
❑??????
&#3627408529;&#3627409359;is the dominant pole &#3627409172;
&#3627408477;&#3627408465;≈3dB bandwidth =&#3627408437;&#3627408458;=&#3627409172;
3&#3627408465;&#3627408437;
❑??????
&#3627408529;&#3627409360;is the non-dominant pole &#3627409172;
&#3627408477;&#3627408475;&#3627408465;
❑Unity gain frequency (UGF, &#3627409172;
&#3627408482;) is the frequency at which gain is unity (1 = 0dB)
❑Gain-Bandwidth Product (GBW) =&#3627408442;&#3627408462;&#3627408470;&#3627408475;×&#3627408437;&#3627408458;≈&#3627408436;
&#3627408476;&#3627409172;
&#3627408477;1
❑Usually, we design the amplifier such that &#3627409172;
??????2and&#3627409172;
??????>&#3627409172;
&#3627408482;
08: Frequency Response (1) 33
&#3627408436;
&#3627408483;&#3627408480;=
&#3627408436;
&#3627408476;1+
&#3627408480;
&#3627409172;
??????
1+
&#3627408480;
&#3627409172;
&#3627408477;1
1+
&#3627408480;
&#3627409172;
&#3627408477;2ωzωp2
Ao
|Av(jω)|
ωωp1
0dB
??????
&#3627408534;=&#3627408494;&#3627408489;??????

34. UGF and GBW
❑At UGF &#3627409172;=&#3627409172;
&#3627408482;: &#3627409172;≫&#3627409172;
&#3627408477;1&#3627408462;&#3627408475;&#3627408465;&#3627409172;≪&#3627409172;
&#3627408477;2,&#3627409172;
??????
&#3627408436;
&#3627408483;&#3627409172;
&#3627408482;=
&#3627408436;
&#3627408476;1+
&#3627408471;&#3627409172;
&#3627408482;
&#3627409172;
??????
1+
&#3627408471;&#3627409172;
&#3627408482;
&#3627409172;
&#3627408477;1
1+
&#3627408471;&#3627409172;
&#3627408482;
&#3627409172;
&#3627408477;2
≈
&#3627408436;
&#3627408476;
&#3627408471;&#3627409172;
&#3627408482;/&#3627409172;
&#3627408477;1
=1=0&#3627408465;&#3627408437;
&#3627408456;&#3627408442;&#3627408441;=&#3627409172;
&#3627408482;≈&#3627408436;
&#3627408476;&#3627409172;
&#3627408477;1≈&#3627408442;&#3627408462;&#3627408470;&#3627408475;×&#3627408437;&#3627408458;=&#3627408442;&#3627408437;&#3627408458;
08: Frequency Response (1) 34
&#3627408436;
&#3627408483;&#3627408480;=
&#3627408436;
&#3627408476;1+
&#3627408480;
&#3627409172;
??????
1+
&#3627408480;
&#3627409172;
&#3627408477;1
1+
&#3627408480;
&#3627409172;
&#3627408477;2ωzωp2
Ao
|Av(jω)|
ωωp1
0dB
??????
&#3627408534;=&#3627408494;&#3627408489;??????

35. Outline
❑Recapping previous key results
❑Bode plot review
❑Where are the capacitors?
❑Approximate analysis techniques
▪Short-circuit time constant (SCTC) and open-circuit time constant (OCTC) techniques
▪Dominant pole approximation
❑IC amplifier frequency response
▪Unity gain frequency (UGF) and gain-bandwidth product (GBW)
❑Calculating zeros and poles by inspection
▪Associating poles with nodes
❑Miller’s theorem
08: Frequency Response (1) 35

36. Calculating Zeros by Inspection
1.Find the value &#3627408480;=&#3627408480;
??????that makes &#3627408443;&#3627408480;=0⇒??????
&#3627408476;&#3627408482;&#3627408481;=0
❑Ex1: &#3627408438;:??????
&#3627408476;=0&#3627408470;&#3627408467;&#3627408461;
&#3627408438;=∞
▪&#3627408461;
&#3627408438;=
1
&#3627408480;&#3627408438;
▪⇒&#3627408480;
??????=0
❑Ex2: &#3627408438;
&#3627408464;1:??????
&#3627408476;=0&#3627408470;&#3627408467;&#3627408461;
&#3627408438;
1
=∞
▪&#3627408461;
&#3627408438;
1
=
1
&#3627408480;&#3627408438;1
▪⇒&#3627408480;
??????1=0
❑Ex3: &#3627408438;
&#3627408454;:??????
&#3627408476;=0&#3627408470;&#3627408467;&#3627408461;
&#3627408454;=∞
▪&#3627408461;
&#3627408454;=
&#3627408453;
&#3627408454;
1+&#3627408480;&#3627408453;
&#3627408454;&#3627408438;
&#3627408454;
▪⇒&#3627408480;
??????2=−
1
&#3627408453;
&#3627408454;&#3627408438;
&#3627408454;
08: Frequency Response (1) 36Rsig
vin
RG1
RG2
RD
vout
M1
vsig
CS
Cc1
Cc2
RL
RS
CL Vout
C
R
Vin

37. Calculating Poles by Inspection
1.Set ??????
&#3627408480;&#3627408470;??????=0(deactivate independent sources)
2.Calculate Thevenin resistance ??????
&#3627408481;ℎ,&#3627408470;seen by each cap &#3627408438;
&#3627408470;
3.&#3627408480;
&#3627408477;,&#3627408470;=−
1
&#3627408453;
&#3627408481;ℎ,??????&#3627408438;
??????
❑Ex1: &#3627408438;:??????
&#3627408481;ℎ=??????
▪⇒&#3627408480;
&#3627408477;=−
1
&#3627408453;&#3627408438;
❑Ex2: &#3627408438;
&#3627408464;1:??????
&#3627408481;ℎ=??????
&#3627408480;&#3627408470;??????+??????
&#3627408442;
▪⇒&#3627408480;
&#3627408477;1=−
1
&#3627408453;
&#3627408480;????????????+&#3627408453;??????&#3627408438;??????1
❑Ex3: &#3627408438;
&#3627408454;:??????
&#3627408481;ℎ≈??????
&#3627408454;//
1
??????
&#3627408474;
▪⇒&#3627408480;
&#3627408477;2=−
1
&#3627408453;
&#3627408454;//
1
??????&#3627408474;
&#3627408438;
&#3627408454;
08: Frequency Response (1) 37Rsig
vin
RG1
RG2
RD
vout
M1
vsig
CS
Cc1
Cc2
RL
RS
CL Vout
C
R
Vin

38. Associating Poles with Nodes
1.Set ??????
&#3627408480;&#3627408470;??????=0(deactivate independent sources)
2.Calculate Thevenin resistance ??????
&#3627408481;ℎ,&#3627408470;seen by each cap &#3627408438;
&#3627408470;
3.&#3627408480;
&#3627408477;,&#3627408470;=−
1
&#3627408453;
&#3627408481;ℎ,??????&#3627408438;
??????
❑Example: Ignore MOSFET &#3627408479;
&#3627408476;and capacitance
▪Each node is associated with a pole
▪H.I.N. dominates
&#3627408443;&#3627408480;=
&#3627408468;
&#3627408474;1??????
&#3627408439;1&#3627408468;
&#3627408474;2??????
&#3627408439;2
1+&#3627408480;??????
&#3627408480;&#3627408470;??????&#3627408438;
&#3627408470;&#3627408475;1+&#3627408480;??????
&#3627408439;1&#3627408438;
??????11+&#3627408480;??????
&#3627408439;2&#3627408438;
??????2
08: Frequency Response (1) 38Rsig
RD1
vout
M1
vsig
CL1
Cin
RD2
M2 CL2
1
2 3

39. Outline
❑Recapping previous key results
❑Bode plot review
❑Where are the capacitors?
❑Approximate analysis techniques
▪Short-circuit time constant (SCTC) and open-circuit time constant (OCTC) techniques
▪Dominant pole approximation
❑IC amplifier frequency response
▪Unity gain frequency (UGF) and gain-bandwidth product (GBW)
❑Calculating zeros and poles by inspection
▪Associating poles with nodes
❑Miller’s theorem
08: Frequency Response (1) 39

40. Miller’s Theorem
&#3627408436;
&#3627408483;=
&#3627408457;
&#3627408460;
&#3627408457;
&#3627408459;
&#3627408457;
&#3627408459;−&#3627408457;
&#3627408460;
&#3627408461;
&#3627408441;
=
&#3627408457;
&#3627408459;
&#3627408461;
1
&#3627408461;
1=
&#3627408461;
&#3627408441;
1−
&#3627408457;
&#3627408460;
&#3627408457;
&#3627408459;
=
&#3627408461;
&#3627408441;
1−&#3627408436;
&#3627408483;
&#3627408457;
&#3627408460;−&#3627408457;
&#3627408459;
&#3627408461;
&#3627408441;
=
&#3627408457;
&#3627408460;
&#3627408461;
2
&#3627408461;
2=
&#3627408461;
&#3627408441;
1−
&#3627408457;
&#3627408459;
&#3627408457;
&#3627408460;
=
&#3627408461;
&#3627408441;
1−
1
&#3627408436;&#3627408483;
08: Frequency Response (1) 40
❑Note: Miller’s Theorem cannot be used for &#3627408461;
&#3627408476;&#3627408482;&#3627408481;calculation (why?)VX VY
ZF
Av VX VY
Z1 Z2
Av

41. Miller Effect
❑Miller Effect: Capacitance multiplication if &#3627408461;
&#3627408441;=1/&#3627408480;&#3627408438;
&#3627408441;
&#3627408461;
1=
&#3627408461;
&#3627408441;
1+&#3627408436;
&#3627408483;
≈
&#3627408461;
&#3627408441;
&#3627408436;
&#3627408483;
=
1
&#3627408480;&#3627408436;
&#3627408483;&#3627408438;
&#3627408441;
⇒&#3627408490;
&#3627408522;&#3627408527;=&#3627408488;
&#3627408535;&#3627408490;
&#3627408493;
&#3627408461;
2=
&#3627408461;
&#3627408441;
1+
1
&#3627408436;&#3627408483;
≈&#3627408461;
&#3627408441;=
1
&#3627408480;&#3627408438;
&#3627408441;
⇒&#3627408438;
&#3627408476;&#3627408482;&#3627408481;≈&#3627408438;
&#3627408441;
08: Frequency Response (1) 41VX VY
CF
-Av VX VY
Cin Cout
-Av

42. Miller’s Approximation
&#3627408461;
1=
&#3627408461;
&#3627408441;
1−&#3627408436;
&#3627408483;
&&#3627408461;
2=
&#3627408461;
&#3627408441;
1−
1
&#3627408436;&#3627408483;
❑But &#3627408436;
&#3627408483;is a function of frequency!
❑Miller’s Approximation: Substitute with the low frequency gain
▪&#3627408436;
&#3627408483;&#3627408480;≈&#3627408436;
&#3627408476;
▪Gives good approxfor the dominant pole ONLY (why?)
▪It does not tell about the feedforward zero (next slide)
08: Frequency Response (1) 42VX VY
ZF
Av VX VY
Z1 Z2
Av

43. The Feedforward Zero
❑??????
&#3627408476;&#3627408482;&#3627408481;=0→&#3627408470;
&#3627408476;&#3627408482;&#3627408481;=0
❑??????
&#3627408470;&#3627408475;&#3627408480;&#3627408438;
&#3627408441;=−&#3627408442;
&#3627408474;??????
&#3627408470;&#3627408475;
&#3627408532;
??????=−
&#3627408494;
&#3627408526;
&#3627408490;
&#3627408493;
❑LHP zero if &#3627408442;
&#3627408474;is +ve(e.g. CD)
❑RHP zero if &#3627408494;
&#3627408526;is –ve(e.g. CS)
▪Mag incand phase drops
▪Very bad for FB loop stability
▪More on this when we study op-amp design
08: Frequency Response (1) 43Gmvin Rout
vin
Rin
vout
CF
Gmvin vout
CF

44. 08: Frequency Response (1) 44
Thank you!

45. References
❑A. Sedraand K. Smith, “Microelectronic Circuits,” 7
th
ed., Oxford University Press, 2015
❑B. Razavi, “Fundamentals of Microelectronics,” 2
nd
ed., Wiley, 2014
❑B. Razavi, “Design of Analog CMOS Integrated Circuits,” McGraw-Hill, 2
nd
ed., 2017
❑N. Westeand D. Harris, “CMOS VLSI Design,” 4
th
ed., Pearson, 2010
❑T. C. Carusone, D. Johns, and K. W. Martin, “Analog Integrated Circuit Design,” 2
nd
ed.,
Wiley, 2012
❑R. J. Baker, “CMOS circuit design,” 3
rd
ed., Wiley, 2010
❑B. Murmann, EE214 Course Reader, Stanford University
4508: Frequency Response (1)

46. Lecture 09
Frequency Response (2)
Integrated Circuits Laboratory (ICL)
Electronics and Electrical Communication Eng. Dept.
Faculty of Engineering
Ain Shams University
Dr. Hesham A. Omran
Analog IC Design
ًليِلَ ق الَِّإ ِمْلِعْلا
َ
نِم
ْ
م
ُ
تيِتوُأ ا
َ
م
َ
و
11 August 2022 13 مرحم1444

47. Outline
❑Recapping previous key results
❑Frequency response of CS: Midband, LFR, and HFR (Miller’s effect)
❑Frequency response of CG: HFR
❑Frequency response of cascode: HFR
▪Cascode for gain and cascode for BW
❑Frequency response of CD: HFR
▪Frequency domain peaking and time domain ringing
▪&#3627408461;
&#3627408470;&#3627408475;: negative resistance and &#3627408461;
&#3627408476;&#3627408482;&#3627408481;: inductive rise
09: Frequency Response (2) 2

48. Outline
❑Recapping previous key results
❑Frequency response of CS: Midband, LFR, and HFR (Miller’s effect)
❑Frequency response of CG: HFR
❑Frequency response of cascode: HFR
▪Cascode for gain and cascode for BW
❑Frequency response of CD: HFR
▪Frequency domain peaking and time domain ringing
▪&#3627408461;
&#3627408470;&#3627408475;: negative resistance and &#3627408461;
&#3627408476;&#3627408482;&#3627408481;: inductive rise
09: Frequency Response (2) 3

49. MOSFET in Saturation
❑The channel is pinched off if the difference between the gate and drain voltages is not
sufficient to create an inversion layer
&#3627408457;
&#3627408442;&#3627408439;≤&#3627408457;
&#3627408455;&#3627408443;??????&#3627408453;&#3627408457;
&#3627408439;&#3627408454;≥&#3627408457;
&#3627408476;&#3627408483;
❑Square-law (long channel MOS)
??????
&#3627408439;=
&#3627409159;&#3627408475;&#3627408438;&#3627408476;??????
2
&#3627408458;
&#3627408447;
⋅&#3627408457;
&#3627408476;&#3627408483;
2
1+&#3627409158;&#3627408457;
&#3627408439;&#3627408454;
&#3627408457;
&#3627408454;&#3627408437;↑⇒&#3627408457;
&#3627408455;&#3627408443;↑
09: Frequency Response (2) 4n+n+
G
S D
p-sub
p+
B
VGS>VTH VGD<VTH
VDS>Vov
VSB VGS > VTH
VGD < VTH
VDS > Vov VDG < |VTH|
VSG > |VTH|
VSD > |Vov|

50. Regions of Operation Summary
09: Frequency Response (2) 5
OFF
(Subthreshold)
&#3627408457;
&#3627408442;&#3627408454;<&#3627408457;
&#3627408455;&#3627408443;
ON
&#3627408457;
&#3627408442;&#3627408454;>&#3627408457;
&#3627408455;&#3627408443;
Triode
&#3627408457;
&#3627408439;&#3627408454;<&#3627408457;
&#3627408476;&#3627408483;
Or
&#3627408457;
&#3627408442;&#3627408439;>&#3627408457;
&#3627408455;&#3627408443;
??????
&#3627408439;=&#3627409159;&#3627408438;
&#3627408476;??????
&#3627408458;
??????
&#3627408457;
&#3627408476;&#3627408483;&#3627408457;
&#3627408439;&#3627408454;−
&#3627408457;
&#3627408439;&#3627408454;
2
2
Pinch-Off
(Saturation)
&#3627408457;
&#3627408439;&#3627408454;≥&#3627408457;
&#3627408476;&#3627408483;
Or
&#3627408457;
&#3627408442;&#3627408439;≤&#3627408457;
&#3627408455;&#3627408443;
??????
&#3627408439;=
&#3627409159;&#3627408438;
&#3627408476;??????
2
&#3627408458;
??????
&#3627408457;
&#3627408476;&#3627408483;
2
1+&#3627409158;&#3627408457;
&#3627408439;&#3627408454;

51. High Frequency Small Signal Model
&#3627408468;
&#3627408474;=
&#3627409173;&#3627408444;&#3627408439;
&#3627409173;&#3627408457;
&#3627408442;??????
=&#3627409159;&#3627408438;
&#3627408476;??????
&#3627408458;
&#3627408447;
&#3627408457;
&#3627408476;&#3627408483;=&#3627409159;&#3627408438;
&#3627408476;??????
&#3627408458;
&#3627408447;
⋅2??????
&#3627408439;=
2&#3627408444;&#3627408439;
&#3627408457;
&#3627408476;&#3627408483;
&#3627408468;
&#3627408474;??????=&#3627409154;&#3627408468;
&#3627408474;&#3627409154;≈0.1−0.25
&#3627408479;
&#3627408476;=
1
&#3627409173;&#3627408444;
&#3627408439;/&#3627409173;&#3627408457;
&#3627408439;??????
=
&#3627408457;
??????
&#3627408444;
&#3627408439;
=
1
&#3627409158;&#3627408444;
&#3627408439;
&#3627408457;
&#3627408436;∝??????↔&#3627409158;∝
1
&#3627408447;
&#3627408457;
&#3627408439;&#3627408454;↑&#3627408457;
&#3627408436;↑
&#3627408438;
????????????≈0 &#3627408438;
??????&#3627408480;≫&#3627408438;
???????????? &#3627408438;
&#3627408480;??????>&#3627408438;
????????????
09: Frequency Response (2) 6Cgs
Cgd
gmvgs rogmbvbs
G D
S
B
Csb
CdbCgb

52. Rin/out Shortcuts Summary
09: Frequency Response (2) 7
1
&#3627408468;
&#3627408474;+&#3627408468;
&#3627408474;??????
1+
&#3627408453;
&#3627408439;
&#3627408479;
&#3627408476;
L.I.N.
&#3627408479;
&#3627408476;1+&#3627408468;
&#3627408474;+&#3627408468;
&#3627408474;??????&#3627408453;
&#3627408454;
H.I.N.
∞
At low
frequencies ONLY

53. CS CG CD (SF)
Voltage& currentamplifierVoltage amplifier
Current buffer
Voltage buffer
Current amplifier
Rin ∞ &#3627408453;
&#3627408454;||
1
&#3627408468;
&#3627408474;+&#3627408468;
&#3627408474;??????
1+
&#3627408453;
&#3627408439;
&#3627408479;
&#3627408476;
∞
Rout&#3627408453;
&#3627408439;||&#3627408479;
&#3627408476;1+&#3627408468;
&#3627408474;+&#3627408468;
&#3627408474;??????&#3627408453;
&#3627408454;&#3627408453;
&#3627408439;||&#3627408479;
&#3627408476;&#3627408453;
&#3627408454;||
1
&#3627408468;
&#3627408474;+&#3627408468;
&#3627408474;??????
1+
&#3627408453;
&#3627408439;
&#3627408479;
&#3627408476;
Gm
−??????
&#3627408526;
&#3627409359;+??????
&#3627408526;+??????
&#3627408526;??????&#3627408505;
&#3627408506;
??????
&#3627408526;+??????
&#3627408526;??????
??????
&#3627408526;
&#3627409359;+&#3627408505;
&#3627408491;/&#3627408531;
&#3627408528;
Summary of Basic Topologies
09: Frequency Response (2) 8RD
vout
vin
RS RD
vin
RS
vout RD
vout
vin
RS

54. Outline
❑Recapping previous key results
❑Frequency response of CS: Midband, LFR, and HFR (Miller’s effect)
❑Frequency response of CG: HFR
❑Frequency response of cascode: HFR
▪Cascode for gain and cascode for BW
❑Frequency response of CD: HFR
▪Frequency domain peaking and time domain ringing
▪&#3627408461;
&#3627408470;&#3627408475;: negative resistance and &#3627408461;
&#3627408476;&#3627408482;&#3627408481;: inductive rise
09: Frequency Response (2) 9

55. Frequency Response of CS: Midband
&#3627408436;
&#3627408483;=
??????
&#3627408470;&#3627408475;
??????
&#3627408480;&#3627408470;??????
⋅
??????
&#3627408476;&#3627408482;&#3627408481;
??????
&#3627408470;&#3627408475;
??????
&#3627408476;&#3627408482;&#3627408481;
??????
&#3627408470;&#3627408475;
=??????
&#3627408474;&#3627408453;
&#3627408476;&#3627408482;&#3627408481;=−&#3627408468;
&#3627408474;(&#3627408453;
&#3627408439;||&#3627408453;
&#3627408447;||&#3627408479;
&#3627408476;)
??????
&#3627408470;&#3627408475;
??????
&#3627408480;&#3627408470;??????
=
&#3627408453;
&#3627408470;&#3627408475;
&#3627408453;
&#3627408470;&#3627408475;+&#3627408453;
&#3627408480;&#3627408470;??????
,&#3627408453;
&#3627408470;&#3627408475;=&#3627408453;
&#3627408442;=&#3627408453;
&#3627408442;1||&#3627408453;
&#3627408442;2
09: Frequency Response (2) 10Rsig
vin
RG1
RG2
RD
vout
M1
vsig
CS
Cc1
Cc2
RL
RS
CL

56. Frequency Response of CS: LFR
❑&#3627408438;
&#3627408438;1: &#3627408453;
&#3627408481;ℎ=&#3627408453;
&#3627408480;&#3627408470;??????+&#3627408453;
&#3627408442;→??????
&#3627408477;,&#3627408438;&#3627408438;1
=
1
&#3627408453;
&#3627408480;????????????+&#3627408453;&#3627408442;&#3627408438;&#3627408438;1
& ??????
??????,&#3627408438;&#3627408438;1
=0
❑&#3627408438;
&#3627408438;2: &#3627408453;
&#3627408481;ℎ=&#3627408453;
&#3627408447;+&#3627408453;
&#3627408439;||&#3627408479;
&#3627408476;→??????
&#3627408477;,&#3627408438;&#3627408438;2
=
1
&#3627408453;??????+&#3627408453;&#3627408439;||&#3627408479;&#3627408476;&#3627408438;&#3627408438;2
& ??????
??????,&#3627408438;&#3627408438;2
=0
❑&#3627408438;
&#3627408454;: &#3627408453;
&#3627408481;ℎ=&#3627408453;
&#3627408454;||&#3627408453;
&#3627408447;&#3627408441;&#3627408454;→??????
&#3627408477;,&#3627408438;??????
=
1
&#3627408453;
??????||&#3627408453;
??????&#3627408441;??????&#3627408438;
??????
& ??????
??????,&#3627408438;??????
=
1
&#3627408453;
??????&#3627408438;
??????
❑Usually ??????
&#3627408477;,&#3627408438;
??????
is dominant: ??????
&#3627408447;≈??????
&#3627408477;,&#3627408438;
??????
(why?)
❑Note that for IC amplifiers we usually use direct coupling (no LFR)
09: Frequency Response (2) 11Rsig
vin
RG1
RG2
RD
vout
M1
vsig
CS
Cc1
Cc2
RL
RS
CL

57. CS HFR: (1) Miller’s Approx+ OCTC
❑Break the feedback capacitance &#3627408438;
????????????using Miller’s approx
❑Each node is associated with a pole
▪??????
&#3627408470;&#3627408475;node →i/p pole ??????
&#3627408477;,&#3627408470;&#3627408475;
▪??????
&#3627408476;&#3627408482;&#3627408481;node →o/p pole ??????
&#3627408477;,&#3627408476;&#3627408482;&#3627408481;
❑Don’t forget the RHP feedforward zero
??????
??????,&#3627408438;
????????????
=
??????
&#3627408474;
&#3627408438;
????????????
→Usually ??????
??????,&#3627408438;
????????????
is very high (why?)
09: Frequency Response (2) 12Cgs
Cgd
gmvgs ro
Cdb
Rsig
vsig
RG
vout
RLCL
vin
RD

58. CS HFR: (1) Miller’s Approx+ OCTC
❑i/p pole: suffers from Miller effect (capacitance multiplication)
&#3627408453;
&#3627408481;ℎ,&#3627408470;&#3627408475;=&#3627408453;
&#3627408480;&#3627408470;??????||&#3627408453;
&#3627408442;=&#3627408453;
&#3627408480;&#3627408470;??????
′
→??????
&#3627408477;,&#3627408470;&#3627408475;≈
1
&#3627408453;
&#3627408480;????????????
′
&#3627408438;
??????&#3627408480;+&#3627408490;
????????????&#3627409359;+&#3627408488;
&#3627408528;
&#3627408436;
&#3627408476;=
&#3627408483;
&#3627408476;&#3627408482;&#3627408481;
&#3627408483;
??????&#3627408475;
=&#3627408468;
&#3627408474;&#3627408453;
&#3627408476;&#3627408482;&#3627408481;
❑o/p pole: &#3627408453;
&#3627408481;ℎ,&#3627408476;&#3627408482;&#3627408481;=&#3627408453;
&#3627408447;||&#3627408453;
&#3627408439;||&#3627408479;
&#3627408476;
→??????
&#3627408477;,&#3627408476;&#3627408482;&#3627408481;≈
1
&#3627408453;&#3627408476;&#3627408482;&#3627408481;&#3627408438;??????+&#3627408438;
????????????+&#3627408438;
????????????1+
1
??????&#3627408476;
≈
1
&#3627408453;&#3627408476;&#3627408482;&#3627408481;(&#3627408438;&#3627408476;&#3627408482;&#3627408481;+&#3627408438;
????????????)
❑Usually i/p pole is dominant: ??????
&#3627408443;≈??????
&#3627408477;,&#3627408470;&#3627408475;(why?), unless &#3627408453;
&#3627408480;&#3627408470;??????
′
↓↓
09: Frequency Response (2) 13Cgs
Cgd
gmvgs ro
Cdb
Rsig
vsig
RG
vout
RLCL
vin
RD

59. CS HFR: (1) Miller’s Approx+ OCTC
??????
&#3627408443;≈
1
1
??????
&#3627408477;,&#3627408470;&#3627408475;
+
1
??????
&#3627408477;,&#3627408476;&#3627408482;&#3627408481;
=
1
&#3627408453;
&#3627408480;&#3627408470;??????
′
&#3627408438;
??????&#3627408480;+&#3627408438;
????????????1+&#3627408468;
&#3627408474;&#3627408453;
&#3627408476;&#3627408482;&#3627408481;+&#3627408453;
&#3627408476;&#3627408482;&#3627408481;&#3627408438;
&#3627408476;&#3627408482;&#3627408481;+&#3627408438;
????????????
❑If input pole is dominant (e.g., if&#3627408453;
&#3627408480;&#3627408470;??????
′
↑↑or &#3627408438;
&#3627408447;↓↓)
??????
&#3627408443;≈
1
&#3627408453;
&#3627408480;&#3627408470;??????
′
&#3627408438;
??????&#3627408480;+&#3627408438;
????????????1+&#3627408468;
&#3627408474;&#3627408453;
&#3627408476;&#3627408482;&#3627408481;
≈??????
&#3627408477;,&#3627408470;&#3627408475;
❑If output pole is dominant (e.g., if &#3627408453;
&#3627408480;&#3627408470;??????
′
↓↓or &#3627408438;
&#3627408447;↑↑)
??????
&#3627408443;≈
1
&#3627408453;
&#3627408476;&#3627408482;&#3627408481;&#3627408438;
&#3627408476;&#3627408482;&#3627408481;+&#3627408438;
????????????
≈??????
&#3627408477;,&#3627408476;&#3627408482;&#3627408481;
??????&#3627408437;&#3627408458;=&#3627408436;
&#3627408483;??????
&#3627408443;=??????
&#3627408474;&#3627408453;
&#3627408476;&#3627408482;&#3627408481;⋅
1
&#3627408453;&#3627408476;&#3627408482;&#3627408481;&#3627408438;&#3627408476;&#3627408482;&#3627408481;+&#3627408438;
????????????
=
&#3627408442;&#3627408474;
&#3627408438;&#3627408476;&#3627408482;&#3627408481;+&#3627408438;
????????????
→independent of &#3627408453;
&#3627408476;&#3627408482;&#3627408481;!
09: Frequency Response (2) 14

60. CS HFR: (2) Just OCTC Technique
❑&#3627408438;
??????&#3627408480;: &#3627408453;
&#3627408481;ℎ,&#3627408470;&#3627408475;=&#3627408453;
&#3627408480;&#3627408470;??????||&#3627408453;
&#3627408442;=&#3627408453;
&#3627408480;&#3627408470;??????
′
→??????
&#3627408477;,&#3627408438;??????&#3627408480;
=
1
&#3627408453;
&#3627408480;????????????
′
&#3627408438;??????&#3627408480;
❑&#3627408438;
&#3627408476;&#3627408482;&#3627408481;=&#3627408438;
&#3627408447;+&#3627408438;
????????????: &#3627408453;
&#3627408481;ℎ=&#3627408453;
&#3627408447;||&#3627408453;
&#3627408439;||&#3627408479;
&#3627408476;=&#3627408453;
&#3627408476;&#3627408482;&#3627408481;→??????
&#3627408477;,&#3627408438;&#3627408476;&#3627408482;&#3627408481;
=
1
&#3627408453;&#3627408476;&#3627408482;&#3627408481;&#3627408438;&#3627408476;&#3627408482;&#3627408481;
❑&#3627408438;
????????????: &#3627408453;
&#3627408481;ℎ=
&#3627408535;
??????
??????
??????
=&#3627408453;
&#3627408480;&#3627408470;??????
′
1+&#3627408468;
&#3627408474;&#3627408453;
&#3627408476;&#3627408482;&#3627408481;+&#3627408453;
&#3627408476;&#3627408482;&#3627408481;→??????
&#3627408477;,&#3627408438;
????????????
=
1
&#3627408453;
&#3627408480;????????????
′
1+??????
&#3627408474;&#3627408453;
&#3627408476;&#3627408482;&#3627408481;+&#3627408453;
&#3627408476;&#3627408482;&#3627408481;&#3627408438;
????????????
??????
&#3627408443;≈
1
1
??????
&#3627408477;,&#3627408438;
??????&#3627408480;
+
1
??????
&#3627408477;,&#3627408438;
&#3627408476;&#3627408482;&#3627408481;
+
1
??????
&#3627408477;,&#3627408438;
????????????
=
1
&#3627408453;
&#3627408480;&#3627408470;??????
′
&#3627408438;
??????&#3627408480;+&#3627408453;
&#3627408476;&#3627408482;&#3627408481;&#3627408438;
&#3627408476;&#3627408482;&#3627408481;+&#3627408453;
&#3627408480;&#3627408470;??????
′
1+&#3627408468;
&#3627408474;&#3627408453;
&#3627408476;&#3627408482;&#3627408481;+&#3627408453;
&#3627408476;&#3627408482;&#3627408481;&#3627408438;
????????????
09: Frequency Response (2) 15Cgs
Cgd
gmvgs ro
Cdb
Rsig
vsig
RG
vout
RLCL
vin
RD

61. CS HFR: (2) Just OCTC Technique
??????
&#3627408443;≈
1
&#3627408453;
&#3627408480;&#3627408470;??????
′
&#3627408438;
??????&#3627408480;+&#3627408438;
????????????1+&#3627408468;
&#3627408474;&#3627408453;
&#3627408476;&#3627408482;&#3627408481;+&#3627408453;
&#3627408476;&#3627408482;&#3627408481;&#3627408438;
&#3627408476;&#3627408482;&#3627408481;+&#3627408438;
????????????
❑If input pole is dominant (e.g., if &#3627408453;
&#3627408480;&#3627408470;??????
′
↑↑or &#3627408438;
&#3627408447;↓↓)
??????
&#3627408443;≈
1
&#3627408453;
&#3627408480;&#3627408470;??????
′
&#3627408438;
??????&#3627408480;+&#3627408438;
????????????1+&#3627408468;
&#3627408474;&#3627408453;
&#3627408476;&#3627408482;&#3627408481;
≈??????
&#3627408477;,&#3627408470;&#3627408475;
❑If output pole is dominant (e.g., if&#3627408453;
&#3627408480;&#3627408470;??????
′
↓↓or &#3627408438;
&#3627408447;↑↑)
??????
&#3627408443;≈
1
&#3627408453;
&#3627408476;&#3627408482;&#3627408481;&#3627408438;
&#3627408476;&#3627408482;&#3627408481;+&#3627408438;
????????????
≈??????
&#3627408477;,&#3627408476;&#3627408482;&#3627408481;
❑Same as the expressions obtained from Miller approx
09: Frequency Response (2) 16

62. CS HFR: (3) Exact Analysis + Dominant Pole Approx
❑Surprisingly, exact analysis gives a quite complex expression
▪See [Johns & Martin 2012] or [Razavi 2017]
❑If dominant pole approximation is applied
??????
&#3627408477;??????≈
1
&#3627408463;
1
=
1
&#3627408453;
&#3627408480;&#3627408470;??????
′
&#3627408438;
??????&#3627408480;+&#3627408438;
????????????1+&#3627408468;
&#3627408474;&#3627408453;
&#3627408476;&#3627408482;&#3627408481;+&#3627408453;
&#3627408476;&#3627408482;&#3627408481;&#3627408438;
&#3627408476;&#3627408482;&#3627408481;+&#3627408438;
????????????
▪Same result as OCTC (both based on same approximation)
❑Additionally, dominant pole approxgives an expression for ??????
&#3627408477;&#3627408475;??????
??????
&#3627408477;&#3627408475;??????≈
1
&#3627408463;
2??????
&#3627408477;1
=
&#3627408463;
1
&#3627408463;
2
=
&#3627408468;
&#3627408474;&#3627408438;
????????????
&#3627408438;
????????????&#3627408438;
??????&#3627408480;+&#3627408438;
&#3627408476;&#3627408482;&#3627408481;+&#3627408438;
??????&#3627408480;&#3627408438;
&#3627408476;&#3627408482;&#3627408481;
▪If a large cap is connected parallel to &#3627408438;
????????????: ??????
&#3627408477;&#3627408475;??????≈
??????&#3627408474;
&#3627408438;
??????&#3627408480;+&#3627408438;
&#3627408476;&#3627408482;&#3627408481;
•Can be derived intuitively without analysis (how?)
•We will need this case when we study two-stage OTA
09: Frequency Response (2) 17

63. Frequency Response of CS: ??????
??????&#3627408527;
❑With Miller approx.
&#3627408461;
&#3627408470;&#3627408475;=
1
&#3627408480;&#3627408438;
??????&#3627408480;+1+&#3627408468;
&#3627408474;&#3627408453;
&#3627408439;&#3627408438;
????????????
❑Exact Analysis (&#3627408438;
??????&#3627408480;adds in parallel)
&#3627408461;
&#3627408470;&#3627408475;=
&#3627408457;
&#3627408459;
??????
&#3627408459;
=
1+&#3627408480;&#3627408453;
&#3627408439;&#3627408438;
????????????+&#3627408438;
????????????
&#3627408480;&#3627408438;
????????????1+&#3627408468;
&#3627408474;&#3627408453;
&#3627408439;+&#3627408480;&#3627408453;
&#3627408439;&#3627408438;
????????????
▪Extra pole and zero at high frequency (??????
&#3627408477;>??????
??????)
▪At relatively low frequency the exact solution
reduces to Miller approx.
09: Frequency Response (2) 18[Razavi, 2017]

64. Frequency Response of CS: ??????
&#3627408528;&#3627408534;&#3627408533;
❑Can we use Miller?
??????
??????=&#3627408467;??????
??????&#3627408480;=&#3627408468;
&#3627408474;??????
??????&#3627408480;+
??????
??????&#3627408480;1+&#3627408480;&#3627408453;
&#3627408480;&#3627408470;??????&#3627408438;
??????&#3627408480;
&#3627408453;
&#3627408480;&#3627408470;??????
??????
??????=&#3627408467;??????
??????&#3627408480;=??????
??????&#3627408480;+
??????
??????&#3627408480;1+&#3627408480;&#3627408453;
&#3627408480;&#3627408470;??????&#3627408438;
??????&#3627408480;
&#3627408480;&#3627408453;
&#3627408480;&#3627408470;??????&#3627408438;
????????????
&#3627408461;
&#3627408476;&#3627408482;&#3627408481;=
??????
??????
??????
??????
≈
1+&#3627408480;&#3627408453;
&#3627408480;&#3627408470;??????&#3627408438;
??????&#3627408480;+&#3627408438;
????????????
&#3627408480;&#3627408438;
????????????&#3627408468;
&#3627408474;&#3627408453;
&#3627408480;&#3627408470;??????1+&#3627408480;
&#3627408438;
??????&#3627408480;
&#3627408468;
&#3627408474;
❑&#3627408479;
&#3627408476;and &#3627408438;
????????????add in parallel
❑Important special case: If we have a large capacitor parallel
to &#3627408438;
????????????
▪&#3627408461;
&#3627408474;≈1/&#3627408468;
&#3627408474;→We will need this case when we study
Miller OTA
09: Frequency Response (2) 19vx
Cgd
RsigCgs
ix
Zout ωz ωp
|Zout|
ω
|Zm|

65. Outline
❑Recapping previous key results
❑Frequency response of CS: Midband, LFR, and HFR (Miller’s effect)
❑Frequency response of CG: HFR
❑Frequency response of cascode: HFR
▪Cascode for gain and cascode for BW
❑Frequency response of CD: HFR
▪Frequency domain peaking and time domain ringing
▪&#3627408461;
&#3627408470;&#3627408475;: negative resistance and &#3627408461;
&#3627408476;&#3627408482;&#3627408481;: inductive rise
09: Frequency Response (2) 20

66. Frequency Response of CG: HFR
❑i/p pole: ??????
&#3627408477;,&#3627408470;&#3627408475;=
1
&#3627408453;
&#3627408480;????????????||&#3627408453;??????||&#3627408453;??????&#3627408441;??????&#3627408438;??????&#3627408480;+&#3627408438;
&#3627408480;??????
❑o/p pole: ??????
&#3627408477;,&#3627408476;&#3627408482;&#3627408481;=
1
&#3627408453;&#3627408439;||&#3627408453;??????&#3627408441;&#3627408439;&#3627408438;??????+&#3627408438;
????????????+&#3627408438;
????????????
❑Usually o/p pole is dominant: ??????
&#3627408443;≈??????
&#3627408477;,&#3627408476;&#3627408482;&#3627408481;(why?)
❑No FB cap →No Miller effect →&#3627408489;??????
&#3627408490;??????≫&#3627408489;??????
&#3627408490;&#3627408506;
09: Frequency Response (2) 21RD
vout
vsig
RS
Rsig
VB
vin
CL

67. Outline
❑Recapping previous key results
❑Frequency response of CS: Midband, LFR, and HFR (Miller’s effect)
❑Frequency response of CG: HFR
❑Frequency response of cascode: HFR
▪Cascode for gain and cascode for BW
❑Frequency response of CD: HFR
▪Frequency domain peaking and time domain ringing
▪&#3627408461;
&#3627408470;&#3627408475;: negative resistance and &#3627408461;
&#3627408476;&#3627408482;&#3627408481;: inductive rise
09: Frequency Response (2) 22

68. Frequency Response of Cascode: HFR
Case 1: BW limited by o/p pole (&#3627408505;
&#3627408491;↑↑&#3627408505;
&#3627408532;????????????↓↓) (cascode for gain)
❑&#3627408436;
&#3627408483;=
&#3627408483;&#3627408476;&#3627408482;&#3627408481;
&#3627408483;
&#3627408480;????????????
≈&#3627408468;
&#3627408474;1&#3627408479;
&#3627408476;1&#3627408468;
&#3627408474;2&#3627408479;
&#3627408476;2=&#3627408436;
&#3627408483;,&#3627408438;&#3627408454;⋅&#3627408468;
&#3627408474;2&#3627408479;
&#3627408476;2
❑??????
&#3627408477;,&#3627408476;&#3627408482;&#3627408481;≈
1
&#3627408479;&#3627408476;1??????&#3627408474;2&#3627408479;&#3627408476;2&#3627408438;??????+&#3627408438;
????????????2+&#3627408438;
????????????2
=
&#3627409172;
&#3627408477;,&#3627408476;&#3627408482;&#3627408481;,&#3627408438;??????
??????&#3627408474;2&#3627408479;&#3627408476;2
→Dominant
❑??????&#3627408437;&#3627408458;=&#3627408436;
&#3627408483;??????
&#3627408477;,&#3627408476;&#3627408482;&#3627408481;=&#3627408436;
&#3627408483;,&#3627408438;&#3627408454;??????
&#3627408477;,&#3627408476;&#3627408482;&#3627408481;,&#3627408438;&#3627408454;
=
&#3627408442;&#3627408474;
&#3627408438;&#3627408476;&#3627408482;&#3627408481;+&#3627408438;
????????????2
→Same as CS!
❑&#3627408436;
&#3627408476;1=
&#3627408483;??????
&#3627408483;
??????&#3627408475;
=&#3627408468;
&#3627408474;1(&#3627408479;
&#3627408476;1||&#3627408453;
&#3627408447;&#3627408441;&#3627408454;2), &#3627408453;
&#3627408447;&#3627408441;&#3627408454;2=?
▪&#3627408436;
&#3627408476;1≪&#3627408468;
&#3627408474;1&#3627408479;
&#3627408476;1Miller effect reduced
❑??????
&#3627408477;,&#3627408470;&#3627408475;=
1
&#3627408453;
&#3627408480;????????????&#3627408438;
??????&#3627408480;1+&#3627408438;
????????????11+&#3627408436;
&#3627408476;1
=??????
&#3627408477;,&#3627408470;&#3627408475;,&#3627408438;&#3627408454;
❑??????
&#3627408477;,??????=
1
(&#3627408479;
&#3627408476;1||&#3627408453;
??????&#3627408441;??????2)&#3627408438;
??????&#3627408480;2+&#3627408438;
&#3627408480;??????2+&#3627408438;
????????????1+&#3627408438;
????????????11+1/&#3627408436;
&#3627408476;1
09: Frequency Response (2) 23VB
M1
M2
vx
vsig
Rsig
vout
CL
vin

69. Frequency Response of Cascode: HFR
Case 2: BW limited by i/p pole (&#3627408505;
&#3627408491;↓↓&#3627408505;
&#3627408532;????????????↑↑) (cascode for BW)
❑&#3627408436;
&#3627408483;=
&#3627408483;&#3627408476;&#3627408482;&#3627408481;
&#3627408483;
&#3627408480;????????????
≈&#3627408468;
&#3627408474;1&#3627408453;
&#3627408439;≈&#3627408436;
&#3627408483;,&#3627408438;&#3627408454;→Similar to CS!
❑&#3627408436;
&#3627408476;1=
&#3627408483;??????
&#3627408483;
??????&#3627408475;
=&#3627408468;
&#3627408474;1(&#3627408479;
&#3627408476;1||
1
??????
&#3627408474;2
)≈1
❑??????
&#3627408477;,&#3627408470;&#3627408475;≈
1
&#3627408453;
&#3627408480;????????????&#3627408438;??????&#3627408480;1+2&#3627408438;
????????????1
>??????
&#3627408477;,&#3627408470;&#3627408475;,&#3627408438;&#3627408454;
▪Miller effect significantly reduced
▪→BW extension!
❑??????
&#3627408477;,??????≈
1
(&#3627408479;&#3627408476;1||
1
??????&#3627408474;2
)&#3627408438;??????&#3627408480;2+&#3627408438;
&#3627408480;??????2+&#3627408438;
????????????1+2&#3627408438;
????????????1
❑??????
&#3627408477;,&#3627408476;&#3627408482;&#3627408481;≈
1
&#3627408453;
&#3627408439;&#3627408438;
??????+&#3627408438;
????????????2+&#3627408438;
????????????2
❑??????&#3627408437;&#3627408458;=&#3627408436;
&#3627408483;??????
&#3627408477;,&#3627408470;&#3627408475;>??????&#3627408437;&#3627408458;of CS
09: Frequency Response (2) 24VB
M1
M2
vx
vsig
Rsig
vout
CL
vin
RD

70. Cascode HFR: Recapping
❑If BW is limited by o/p pole
▪??????&#3627408437;&#3627408458;=&#3627408436;
&#3627408483;??????
&#3627408477;,&#3627408476;&#3627408482;&#3627408481;=??????
&#3627408474;&#3627408453;
&#3627408476;&#3627408482;&#3627408481;⋅
1
&#3627408453;
&#3627408476;&#3627408482;&#3627408481;&#3627408438;
&#3627408476;&#3627408482;&#3627408481;
=
&#3627408442;&#3627408474;
&#3627408438;
&#3627408476;&#3627408482;&#3627408481;
▪Cascode can be used to trade gain for bandwidthby
modifying &#3627408453;
&#3627408476;&#3627408482;&#3627408481;
▪But ??????&#3627408437;&#3627408458;=&#3627408436;
&#3627408483;??????
&#3627408477;,&#3627408476;&#3627408482;&#3627408481;remain unchanged
❑If BW is limited by i/p pole
▪Cascode can provide higher BW (Miller ↓)
▪The gain may be higher as well
▪??????&#3627408437;&#3627408458;=&#3627408436;
&#3627408483;??????
&#3627408477;,&#3627408470;&#3627408475;increases
▪Also improves reverse isolation (RF LNAs)
❑See Example 10.10 in Sedra/Smith 7
th
ed.
09: Frequency Response (2) 25VB
M1
M2
vx
vsig
Rsig
vout
CL
vin VB
M1
M2
vx
vsig
Rsig
vout
CL
vin
RD

71. Outline
❑Recapping previous key results
❑Frequency response of CS: Midband, LFR, and HFR (Miller’s effect)
❑Frequency response of CG: HFR
❑Frequency response of cascode: HFR
▪Cascode for gain and cascode for BW
❑Frequency response of CD: HFR
▪Frequency domain peaking and time domain ringing
▪&#3627408461;
&#3627408470;&#3627408475;: negative resistance and &#3627408461;
&#3627408476;&#3627408482;&#3627408481;: inductive rise
09: Frequency Response (2) 26

72. Frequency Response of CD: HFR
❑Assume real and widely spaced poles (revisited next slide)
❑Apply Miller: Ideally&#3627408436;
&#3627408476;=??????
&#3627408476;&#3627408482;&#3627408481;/??????
&#3627408470;&#3627408475;≈1➔&#3627408438;
??????&#3627408480;is bootstrapped
❑i/p pole: ??????
&#3627408477;,&#3627408470;&#3627408475;=
1
&#3627408453;
&#3627408480;????????????&#3627408438;
????????????+&#3627408438;
??????&#3627408480;1−&#3627408436;
&#3627408476;
❑o/p pole: ??????
&#3627408477;,&#3627408476;&#3627408482;&#3627408481;=
1
&#3627408453;??????||&#3627408453;??????&#3627408441;??????&#3627408438;??????+&#3627408438;
&#3627408480;??????+&#3627408438;??????&#3627408480;1−1/&#3627408436;&#3627408476;
❑Both poles are at high frequency (why?) →Large BW
❑Don’t forget the LHP feedforward zero: ??????
??????=
??????&#3627408474;
&#3627408438;??????&#3627408480;
↑↑
09: Frequency Response (2) 27vout
RS
vinvsig
Rsig
CL

73. CD HFR: Why Approximations Fail?
❑The two poles are nearby and possibly complex conjugate
❑OCTC technique and Miller approxcannot be used 
09: Frequency Response (2) 28vout
RS
vinvsig
Rsig
CL

74. CD HFR: Exact Analysis
❑Simple circuit, but exact analysis gives a complex expression!
??????
&#3627408476;&#3627408482;&#3627408481;
??????
&#3627408480;&#3627408470;??????
=&#3627408436;
&#3627408448;
1+&#3627408480;/??????
??????
1+
&#3627408480;
??????
&#3627408477;1
1+
&#3627408480;
??????
&#3627408477;2
=&#3627408436;
&#3627408448;
1+&#3627408480;/??????
??????
1+
1
??????
&#3627408477;1
+
1
??????
&#3627408477;2
&#3627408480;+
&#3627408480;
2
??????
&#3627408477;1??????
&#3627408477;2
=&#3627408436;
&#3627408448;
1+&#3627408480;/??????
??????
1+&#3627408463;
1&#3627408480;+&#3627408463;
2&#3627408480;
2
=&#3627408436;
&#3627408448;
1+&#3627408480;/??????
??????
1+
1
&#3627408452;
&#3627408480;
??????
&#3627408476;
+
&#3627408480;
2
??????
&#3627408476;
2
=&#3627408436;
&#3627408448;
1+&#3627408480;/??????
??????
1+2&#3627409153;
&#3627408480;
??????
&#3627408476;
+
&#3627408480;
2
??????
&#3627408476;
2
❑Special case: &#3627408453;
&#3627408454;↑↑(IDC) + CLM and body effect neglected
&#3627408463;
1=&#3627408438;
????????????&#3627408453;
&#3627408480;&#3627408470;??????+
&#3627408438;
??????&#3627408480;+&#3627408438;
&#3627408447;
&#3627408468;
&#3627408474;
&#3627408463;
2=
&#3627408438;
??????&#3627408480;+&#3627408438;
????????????&#3627408438;
&#3627408447;+&#3627408438;
??????&#3627408480;&#3627408438;
????????????
&#3627408468;
&#3627408474;
&#3627408453;
&#3627408480;&#3627408470;??????
??????
??????=
&#3627408468;
&#3627408474;
&#3627408438;
??????&#3627408480;
,??????
&#3627408476;=
1
&#3627408463;
2
,&#3627408504;=
??????
&#3627409360;
??????
&#3627409359;
09: Frequency Response (2) 29[Sedra/Smith, 2015]vout
RS
vinvsig
Rsig
CL

75. Peaking and Ringing
❑??????
??????↑↑is ignored
❑&#3627408452;>0.5(&#3627409153;<1): Underdamped system (complex conj. poles)
▪Ringing (overshoot) in step response (time domain)
%overshoot=100&#3627408466;
−??????
4??????
2
−1
❑&#3627408452;>
1
2
=0.707(&#3627409153;<0.707): Peaking in frequency response
09: Frequency Response (2) 30[Sedra/Smith, 2015] & [Johns and Martin, 2012]

76. Driving Large Capacitive Load
❑Special case: &#3627408453;
&#3627408454;↑↑(IDC) + CLM and body effect neglected + &#3627408490;
??????↑↑
&#3627408463;
1=&#3627408438;
????????????&#3627408453;
&#3627408480;&#3627408470;??????+
&#3627408438;
??????&#3627408480;+&#3627408438;
&#3627408447;
&#3627408468;
&#3627408474;
≈
&#3627408438;
&#3627408447;
&#3627408468;
&#3627408474;
&#3627408463;
2=
&#3627408438;
??????&#3627408480;+&#3627408438;
????????????&#3627408438;
&#3627408447;+&#3627408438;
??????&#3627408480;&#3627408438;
????????????
&#3627408468;
&#3627408474;
&#3627408453;
&#3627408480;&#3627408470;??????≈
&#3627408438;
??????&#3627408480;+&#3627408438;
????????????&#3627408438;
&#3627408447;&#3627408453;
&#3627408480;&#3627408470;??????
&#3627408468;
&#3627408474;
??????
??????=
&#3627408468;
&#3627408474;
&#3627408438;
??????&#3627408480;
??????
&#3627408476;=
1
&#3627408463;
2
≈
&#3627408468;
&#3627408474;
&#3627408438;
??????&#3627408480;+&#3627408438;
????????????&#3627408438;
&#3627408447;&#3627408453;
&#3627408480;&#3627408470;??????
&#3627408452;=
&#3627408463;
2
&#3627408463;
1
≈
&#3627408468;
&#3627408474;&#3627408438;
??????&#3627408480;+&#3627408438;
????????????&#3627408453;
&#3627408480;&#3627408470;??????
&#3627408438;
&#3627408447;
❑Increasing &#3627408438;
&#3627408447;eventually decreases &#3627408452;→??????
&#3627408477;,&#3627408476;&#3627408482;&#3627408481;becomes dominant
09: Frequency Response (2) 31vout
RS
vinvsig
Rsig
CL

77. Suppressing the Overshoot
❑Space the two poles far apart →single dominant pole
▪Increase &#3627408438;
&#3627408447;(till &#3627408452;<0.5)
▪Or increase &#3627408438;
&#3627408470;&#3627408475;(adds to &#3627408438;
????????????) →but buffer becomes less useful!
❑More clever solution
▪A compensation network (&#3627408453;
1&#3627408462;??????&#3627408465;&#3627408438;
1)can be used to compensate for the negative input
impedance and prevent overshoots
▪See [Johns and Martin, 2012] Section 4.4 for more details
09: Frequency Response (2) 32[Johns and Martin, 2012]vout
RS
vinvsig
Rsig
CL

78. ??????
??????&#3627408527;of CD
❑??????
??????&#3627408480;=??????
&#3627408470;&#3627408475;/&#3627408480;&#3627408438;
??????&#3627408480;
❑??????
&#3627408470;&#3627408475;=??????
&#3627408470;&#3627408475;/&#3627408480;&#3627408438;
??????&#3627408480;+??????
&#3627408470;&#3627408475;+&#3627408468;
&#3627408474;??????
&#3627408470;&#3627408475;/&#3627408480;&#3627408438;
??????&#3627408480;&#3627408479;
&#3627408476;||1/&#3627408468;
&#3627408474;??????||1/&#3627408480;&#3627408438;
&#3627408447;
&#3627408461;
&#3627408470;&#3627408475;=
&#3627408483;
??????&#3627408475;
&#3627408470;
??????&#3627408475;
=1/&#3627408480;&#3627408438;
??????&#3627408480;+1+&#3627408468;
&#3627408474;/&#3627408480;&#3627408438;
??????&#3627408480;&#3627408479;
&#3627408476;||1/&#3627408468;
&#3627408474;??????||1/&#3627408480;&#3627408438;
&#3627408447;
❑If 1/&#3627408480;&#3627408438;
&#3627408447;is dominant (e.g., driving large cap load, or @ high freq)
&#3627408461;
&#3627408470;&#3627408475;≈
1
&#3627408480;&#3627408438;??????&#3627408480;
+
1
&#3627408480;&#3627408438;??????
+
??????
&#3627408474;
&#3627408480;
2
&#3627408438;??????&#3627408480;&#3627408438;??????
=
1
&#3627408471;&#3627409172;&#3627408438;??????&#3627408480;
+
1
&#3627408471;&#3627409172;&#3627408438;??????
−
??????
&#3627408474;
&#3627409172;
2
&#3627408438;??????&#3627408480;&#3627408438;??????
→-veres!
❑Can be used in oscillators, andmay make amplifiers unstable!
❑Note that &#3627408438;
????????????shunts &#3627408461;
&#3627408470;&#3627408475;at high frequency
09: Frequency Response (2) 33Zin
CgsCL
−
??????
&#3627408526;
??????
&#3627409360;
&#3627408490;
??????&#3627408532;&#3627408490;
??????vout
vin
CL
Cgs
iin
Zin

79. ??????
&#3627408528;&#3627408534;&#3627408533;of CD
❑??????
??????=
&#3627408483;
??????
1/&#3627408480;&#3627408438;??????&#3627408480;+&#3627408453;
&#3627408480;????????????
+&#3627408468;
&#3627408474;⋅
&#3627408483;
??????
1/&#3627408480;&#3627408438;??????&#3627408480;+&#3627408453;
&#3627408480;????????????
⋅
1
&#3627408480;&#3627408438;??????&#3627408480;
&#3627408461;
&#3627408476;&#3627408482;&#3627408481;=
&#3627408483;
??????
&#3627408470;
??????
=
1
??????
&#3627408474;
1+&#3627408480;&#3627408453;
&#3627408480;????????????&#3627408438;??????&#3627408480;
1+&#3627408480;
&#3627408438;??????&#3627408480;
??????&#3627408474;
❑By intuition: ??????↓↓: &#3627408461;
&#3627408476;&#3627408482;&#3627408481;≈1/&#3627408468;
&#3627408474;and ??????↑↑: &#3627408461;
&#3627408476;&#3627408482;&#3627408481;≈&#3627408453;
&#3627408480;&#3627408470;??????
❑Usually &#3627408453;
&#3627408480;&#3627408470;??????>1/&#3627408468;
&#3627408474;(buffer) →inductive rise
❑Note that &#3627408438;
????????????shunts &#3627408453;
&#3627408480;&#3627408470;??????at high frequency (≈1/&#3627408453;
&#3627408480;&#3627408470;??????&#3627408438;
????????????)
❑Body resistance 1/&#3627408468;
&#3627408474;??????and &#3627408479;
&#3627408476;add to &#3627408461;
&#3627408476;&#3627408482;&#3627408481;in parallel
09: Frequency Response (2) 34vx
Cgs
Rsig
ix
Zout ωz ωp
1/gm
|Zout|
ω
Rsig
Inductive
rise
&#3627408490;
????????????takes
over

80. 09: Frequency Response (2) 35
Thank you!

81. References
❑A. Sedraand K. Smith, “Microelectronic Circuits,” Oxford University Press, 7
th
ed., 2015
❑B. Razavi, “Design of Analog CMOS Integrated Circuits,” McGraw-Hill, 2
nd
ed., 2017
❑T. C. Carusone, D. Johns, and K. W. Martin. “Analog Integrated Circuit Design,” Wiley, 2
nd
ed., 2012
3609: Frequency Response (2)

82. Quiz
❑LD = 100 nH, Cgd= 10 fF, gm = 10 mS, w = 10 Gr/s
❑Ignore VA and other caps
❑Assume Av >> 1
❑Rin = ?
09: Frequency Response (2) 37vout
vin
LD