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Sam PalermoAnalog & Mixed-Signal Center
Texas A&M University
ECEN326: Electronic CircuitsFall 2017
Lecture 5: Frequency Response
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Announcements
• HW5 due 11/1• Exam 2 11/6
• 9:10-10:10 (10 extra minutes)• Closed book w/ one standard note sheet• 8.5”x11” front & back• Bring your calculator• Covers through Lecture 6• Sample Exam2 posted on website
• Reading• Razavi Chapter 11
2
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Agenda
• Frequency Response Concepts• High-Frequency Models of Transistors• Frequency Response Analysis Procedure• CE and CS Stages• CB and CG Stages• CC and CD (Follower) Stages• Cascode Stages• Differential Pairs• Additional Examples
3
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44
High Frequency Roll-off of Amplifier
As frequency of operation increases, the amplifier gain decreases
This lecture analyzes this frequency response issue
CH 11 Frequency Response
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5
Example: Human Voice I
Natural human voice spans a frequency range from 20Hz to 20KHz, however conventional telephone system passes frequencies from 400Hz to 3.5KHz. Therefore phone conversation differs from face-to-face conversation.
5
Natural Voice Telephone System
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6
Example: Human Voice II
6
Mouth RecorderAir
Mouth EarAir
Skull
Path traveled by the human voice to the voice recorder
Path traveled by the human voice to the human ear
Since the paths are different, the results will also be different.
CH 11 Frequency Response
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7
Gain Roll-off: Simple Low-pass Filter
In this simple example, as frequency increases the impedance of C1 decreases and the voltage divider consists of C1 and R1 attenuates Vin to a greater extent at the output.
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88
Gain Roll-off: Common Source
The capacitive load, CL, is the culprit for gain roll-off since at high frequency, it will “steal” away some signal current and shunt it to ground.
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99
Frequency Response of the CS Stage
At low frequency, the capacitor is effectively open and the gain is flat. As frequency increases, the capacitor tends to a short and the gain starts to decrease.
A special frequency is ω=1/(RDCL), where the gain drops by 3dB (half-power). In this single-pole circuit, this is also the pole frequency.
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10
Example: Relationship between Frequency Response and Step Response
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The relationship is such that as R1C1 increases, the bandwidth drops and the step response becomes slower.
CH 11 Frequency Response
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1111
Bode Plot
When we hit a zero, ωzj, the Bode magnitude rises with a slope of +20dB/dec.
When we hit a pole, ωpj, the Bode magnitude falls with a slope of -20dB/dec
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1212
Example: Bode Plot
The circuit only has one pole (no zero) at 1/(RDCL), so the slope drops from 0 to -20dB/dec as we pass ωp1.
CH 11 Frequency Response
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1313
Pole Identification Example I
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CH 11 Frequency Response
• Circuit transfer functions can be well approximated by considering that if a node in the signal path has a small-signal resistance Rj and capacitance Cj in parallel to an AC ground, then it contributes a pole of magnitude (RjCj)-1
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1414
Pole Identification Example II
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CH 11 Frequency Response
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1515
Circuit with Floating Capacitor
The pole of a circuit is computed by finding the effective resistance and capacitance from a node to GROUND.
The circuit above creates a problem since neither terminal of CF is grounded.
While we could always derive the transfer function from the small-signal model, there is a useful “Miller’s Theorem” which can be used to approximate the circuit’s poles
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1616
Miller’s Theorem
If Av is the gain from node 1 to 2, then a floating impedance ZF can be converted to two grounded impedances Z1 and Z2.
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1717
Miller Multiplication
With Miller’s theorem, we can separate the floating capacitor. However, the input capacitor is larger than the original floating capacitor. We call this Miller multiplication.
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1818
Example: Miller Theorem
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• Note, this is only a (often good) approximation of the transfer function• Uses only the low-frequency gain• Neglects a zero
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19
High-Pass Filter Response
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19CH 11 Frequency Response
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20
Example: Audio Amplifier
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In order to successfully pass audio band frequencies (20 Hz-20 KHz), large input and output capacitances are needed.
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21
Capacitive Coupling vs. Direct Coupling
Capacitive coupling, also known as AC coupling, passes AC signals from Y to X while blocking DC contents.
This technique allows independent bias conditions between stages. Direct coupling does not.
Capacitive Coupling Direct Coupling 21
Allows for high V(RD) (gain), while also allowing a high output stage gate bias for good output swing
Due to direct coupling, must trade-off AV1 for output stage biasing/swing
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22
Typical Frequency Response
Lower Corner Upper Corner
22CH 11 Frequency Response
Often due to AC coupling
Often due to load/parasitic capacitors
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Agenda
• Frequency Response Concepts• High-Frequency Models of Transistors• Frequency Response Analysis Procedure• CE and CS Stages• CB and CG Stages• CC and CD (Follower) Stages• Cascode Stages• Differential Pairs• Additional Examples
23
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2424
High-Frequency Bipolar Model
At high frequency, capacitive effects come into play C and Cje are the junction capacitances Cb represents the base charge to generate the non-uniform
charge profile required for proper operation (Chapter 4)
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CH 11 Frequency Response
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2525
High-Frequency Model of Integrated Bipolar Transistor
Since an integrated bipolar circuit is fabricated on top of a substrate, another junction capacitance exists between the collector and substrate, namely CCS.
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2626
Example: Capacitance Identification
CH 11 Frequency Response
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2727
MOS Intrinsic Capacitances
For a MOS, there exist oxide capacitance from gate to channel, junction capacitances from source/drain to substrate, and overlap capacitance from gate to source/drain.
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2828
Gate Oxide Capacitance Partition and Full Model
The gate oxide capacitance is often partitioned between source and drain. In saturation, C2 ~ Cgate, and C1 ~ 0. They are in parallel with the overlap capacitance to form CGS and CGD.
CH 11 Frequency Response
Assuming bulk is an AC ground
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2929
Example: Capacitance Identification
CH 11 Frequency Response
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3030
Transit Frequency
Transit frequency, fT, is defined as the frequency where the current gain from input to output drops to 1.
CH 11 Frequency Response
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31
Example: Transit Frequency Calculation
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• Note, this neglects some advanced device physics (carrier velocity saturation) which slows this rate of frequency increase
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Agenda
• Frequency Response Concepts• High-Frequency Models of Transistors• Frequency Response Analysis Procedure• CE and CS Stages• CB and CG Stages• CC and CD (Follower) Stages• Cascode Stages• Differential Pairs• Additional Examples
32
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33
Analysis Summary
The frequency response refers to the magnitude of the transfer function.
Bode’s approximation simplifies the plotting of the frequency response if poles and zeros are known.
In general, it is possible to associate a pole with each node in the signal path.
Miller’s theorem helps to decompose floating capacitors into grounded elements.
Bipolar and MOS devices exhibit various capacitances that limit the speed of circuits.
33CH 11 Frequency Response
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34
High Frequency Circuit Analysis Procedure
Determine which capacitor impact the low-frequency region of the response and calculate the low-frequency pole (neglect transistor capacitance).
Calculate the midband gain by replacing the capacitors with short circuits (neglect transistor capacitance).
Include transistor capacitances. Merge capacitors connected to AC grounds and omit those
that play no role in the circuit. Determine the high-frequency poles and zeros. Plot the frequency response using Bode’s rules or exact
analysis.
34CH 11 Frequency Response
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Agenda
• Frequency Response Concepts• High-Frequency Models of Transistors• Frequency Response Analysis Procedure• CE and CS Stages• CB and CG Stages• CC and CD (Follower) Stages• Cascode Stages• Differential Pairs• Additional Examples
35
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Frequency Response of CS Stagewith Bypassed Degeneration – Input AC Coupling
The input AC coupling forms a high-pass filter which should be designed for a certain minimum cut-off frequency
36CH 11 Frequency Response
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37
Frequency Response of CS Stagewith Bypassed Degeneration – Main Amplifier
In order to increase the midband gain, a capacitor Cb is placed in parallel with Rs.
37CH 11 Frequency Response
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3838
Unified Model for CE and CS Stages
CH 11 Frequency Response
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3939
Unified Model Using Miller’s Theorem
CH 11 Frequency Response
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4040
Unified Model Using Miller’s Theorem
CH 11 Frequency Response
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41
Example: CE Stage
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41CH 11 Frequency Response
RL=2k
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42
Example: Half Width CS Stage
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42CH 11 Frequency Response
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• LF gain, gmRL reduces by 1/2• Assuming gmRL is still high:• The input pole increases by ~4X• The output pole increases by ~2x
• Constant gain-bandwidth product!
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4343
Direct Analysis of CE and CS Stages
Direct analysis yields different pole locations and an extra zero.CH 11 Frequency Response
• For a detailed direct small-signal analysis, see Razavi 11.4.4
ab
b
ssbsas
ssssbsas
CCRCRRCRgbCCCCCCRRa
bsasRgsCs
VV
pp
ppp
p
pppppp
outXYLinThevThevXYLm
outinXYoutXYinLThev
LmXY
Thev
out
21
121
22
2p1
2121
2
21
2
2
and 1
11
ion approximat pole"dominant " a Using
111111
can write wepoles, 2 thefind To1
where1
Exact Expression
![Page 44: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/44.jpg)
4444
Direct Analysis of CE and CS Stages w/ Dominant Pole Approximation
CH 11 Frequency Response
outinXYoutXYinLThev
outXYLinThevThevXYLmp
outXYLinThevThevXYLmp
XY
mz
CCCCCCRRCCRCRRCRgCCRCRRCRg
Cg
1||
11||
||
2
1
• p1 will be lower due to the additional term
• p2 is at a much higher frequency due to “pole splitting”• Discussed more when we talk about stability
![Page 45: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/45.jpg)
4545
Example: CE and CS Direct Analysis (Dominant Pole Approximation)
outinXYoutXYinOOS
outXYOOinSSXYOOmp
outXYOOinSSXYOOmp
CCCCCCrrRCCrrCRRCrrgCCrrCRRCrrg
21
212112
212111
||)(||||1)(||||1
1
CH 11 Frequency Response
221
11
21
, ,
GDDBDBout
GDXYGSin
OOLSThev
CCCCCCCC
rrRRR
![Page 46: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/46.jpg)
46
Example: Comparison Between Different Methods
MHz
MHz
outp
inp
4282
5712
,
,
GHz
MHz
outp
inp
53.42
2642
,
,
GHz
MHz
outp
inp
79.42
2492
,
,
KR
g
fFCfFCfFC
R
L
m
DB
GD
GS
S
20
150
10080250
200
1
Miller’s Exact Dominant Pole
46
Simple Miller theorem analysis vastly overestimates the output pole at a lower frequency
![Page 47: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/47.jpg)
4747
Input Impedance of CE and CS Stages
rsCRgC
ZCm
in ||1
1
sCRgCZ
GDDmGSin
11
CRgCrZ
r
Cmin 1
1at pole a has
:sfrequencie lowAt capacitivepurely aseApproximat
![Page 48: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/48.jpg)
Agenda
• Frequency Response Concepts• High-Frequency Models of Transistors• Frequency Response Analysis Procedure• CE and CS Stages• CB and CG Stages• CC and CD (Follower) Stages• Cascode Stages• Differential Pairs• Additional Examples
48
![Page 49: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/49.jpg)
49
Low Frequency Response of CB and CG Stages
miSm
iCm
in
out
gsCRgsCRgs
VV
1
As with CE and CS stages, the use of capacitive coupling leads to low-frequency roll-off in CB and CG stages (although a CB stage is shown above, a CG stage is similar).
49CH 11 Frequency Response
CR
VA=
mme gg
r 1
![Page 50: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/50.jpg)
5050
Frequency Response of CB Stage
Xm
S
Xp
Cg
R
1||
1,
CCX
YLYp CR
1,
CSY CCC
Or
CH 11 Frequency Response
• No Miller effect• Input pole is ~fT (very
high frequency)
![Page 51: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/51.jpg)
5151
Frequency Response of CG Stage
OrX
mS
Xp
Cg
R
1||
1,
SBGSX CCC
YLYp CR
1,
DBGDY CCC
Similar to a CB stage, the input pole is on the order of fT, so rarely a speed bottleneck.
Or
CH 11 Frequency Response
![Page 52: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/52.jpg)
5252
Example: CG Stage Pole Identification
111
, 1||
1
GDSBm
S
Xp
CCg
R
22112
, 11
DBGSGDDBm
Yp
CCCCg
CH 11 Frequency Response
OrMOSFET Caps
![Page 53: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/53.jpg)
53
Example: Frequency Response of CG Stage
KR
g
fFCCfFCfFC
R
d
m
DBSB
GD
GS
S
20
150
10080
250200
1
MHz
GHz
Yp
Xp
4422
31.52
,
,
53CH 11 Frequency Response
• Input pole is ~fT• Output pole limits bandwidth
![Page 54: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/54.jpg)
Agenda
• Frequency Response Concepts• High-Frequency Models of Transistors• Frequency Response Analysis Procedure• CE and CS Stages• CB and CG Stages• CC and CD (Follower) Stages• Cascode Stages• Differential Pairs• Additional Examples
54
![Page 55: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/55.jpg)
5555
Emitter and Source Followers
The following will discuss the frequency response of emitter and source followers using direct analysis, as this circuit typically has 2 poles that are close together
Emitter follower is treated first and source follower is derived easily by allowing r to go to infinity
![Page 56: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/56.jpg)
5656
Direct Analysis of Emitter Follower
1
1
2
bsas
sgC
VV m
in
out
m
LS
mS
LLm
S
gC
rR
gCCRb
CCCCCCgRa
1
CH 11 Frequency Response
For detailed analysis, see Razavi 11.6
mgr 1 that Assuming
Cgm
z
Generally, this yields 2 close poles, necessitating a direct solution approach
![Page 57: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/57.jpg)
5757
Direct Analysis of Source Follower Stage
1
1
2
bsas
sgC
VV m
GS
in
out
m
SBLGDGDS
SBLGSSBLGDGSGDm
S
gCCCCRb
CCCCCCCCgRa
CH 11 Frequency Response
SBC
GD
GS
CCCC
r
Taking
![Page 58: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/58.jpg)
58
Example: Frequency Response of Source Follower
0
150
10080250
100200
1
m
DB
GD
GS
L
S
g
fFCfFCfFC
fFCR
GHzjGHz
GHzjGHz
p
p
57.279.12
57.279.12
2
1
58CH 11 Frequency Response
2 Complex Conjugate Poles
![Page 59: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/59.jpg)
5959
Example: Source Follower
1
1
2
1
bsas
sg
C
VV m
GS
in
out
1
22111
22111111
))((
m
DBGDSBGDGDS
DBGDSBGSGDGSGDm
S
gCCCCCRb
CCCCCCCgRa
CH 11 Frequency Response
Or
![Page 60: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/60.jpg)
6060
Input Capacitance of Emitter/Source Follower
Or
CH 11 Frequency Response
Lmin Rg
CCC
1
Lm
GSGDin Rg
CCC
1
Lm
Lmv Rg
RgA
1
withTheoremMiller Using
![Page 61: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/61.jpg)
6161
Example: Source Follower Input Capacitance
1211
1 ||11
GSOOm
GDin Crrg
CC
CH 11 Frequency Response
![Page 62: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/62.jpg)
6262
Output Impedance of Emitter Follower
1
sCrRrsCrR
IV SS
X
X
CH 11 Frequency Response
• Need to consider the output resistance of the previous stage, RS
S
Se
S
R
RrRr
:FrequencyHigh 11
:Frequency Low
Neglecting C
Output impedance generally goes up w/ frequency!
![Page 63: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/63.jpg)
6363
Output Impedance of Source Follower
mGS
GSS
X
X
gsCsCR
IV
1
CH 11 Frequency Response
SR :FrequencyHigh g1 :Frequency Lowm
Neglecting CGD
Output impedance generally goes up w/ frequency!
![Page 64: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/64.jpg)
6464
Active Inductor
The plot above shows the output impedance of emitter and source followers. Since a follower’s primary duty is to lower the driving impedance (RS>1/gm), the “active inductor” characteristic on the right is usually observed.
CH 11 Frequency Response
If RS < 1/gm(not usually true)
If RS > 1/gm(general case)
Cr
CrRRr
p
S
Sz
1
FollowerEmitter
GS
mp
GSSz
CgCR
1FollowerSource
![Page 65: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/65.jpg)
6565
Example: Output Impedance
33
321 1||
mGS
GSOO
X
X
gsCsCrr
IV
Or
CH 11 Frequency Response
Note: This neglects the capacitors from M1 and M2
M3 only
![Page 66: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/66.jpg)
Agenda
• Frequency Response Concepts• High-Frequency Models of Transistors• Frequency Response Analysis Procedure• CE and CS Stages• CB and CG Stages• CC and CD (Follower) Stages• Cascode Stages• Differential Pairs• Additional Examples
66
![Page 67: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/67.jpg)
6767
Frequency Response of Cascode Stage
For cascode stages, there are three poles and Miller multiplication is smaller than in the CE/CS stage.
12
1,
m
mXYv g
gAXYx CC 2
CH 11 Frequency Response
Assume (W/L)1 = (W/L)2
![Page 68: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/68.jpg)
6868
Poles of Bipolar Cascode
111, 2||
1
CCrRS
Xp 121
2
,
211
CCC
g CSm
Yp
22,
1
CCR CSL
outp
CH 11 Frequency Response
Comparable to fT
![Page 69: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/69.jpg)
6969
Poles of MOS Cascode
12
11
,
1
1
GDm
mGSS
Xp
CggCR
211
221
2
,
111
SBGDm
mGSDB
m
Yp
CCggCC
g
22,
1GDDBL
outp CCR
CH 11 Frequency Response
![Page 70: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/70.jpg)
70
Example: Frequency Response of Cascode
KR
g
fFCfFCfFC
R
L
m
DB
GD
GS
S
20
150
10080250
200
1
MHz
GHz
GHz
outp
Yp
Xp
4422
73.12
95.12
,
,
,
70CH 11 Frequency Response
GHz
MHz
outp
inp
53.42
2642
,
,
ExactCompare to simple CS
Now output pole sets the bandwidth, and it has increased by 67%
![Page 71: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/71.jpg)
CH 10 Differential Amplifiers 71CH 11 Frequency Response 71
MOS Cascode Example
12
11
,
1
1
GDm
mGSS
Xp
CggCR
3311
221
2
,
111
DBGDGDm
mGSDB
m
Yp
CCCggCC
g
22,
1GDDBL
outp CCR
• Allows for a smaller M2• Improves output pole• Lowers poles at nodes X and Y, but
they should still be relatively high
![Page 72: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/72.jpg)
7272
I/O Impedance of Bipolar Cascode
sCCrZin
111 2
1||
sCC
RZCS
Lout22
1||
AV
(Neglecting RS)
![Page 73: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/73.jpg)
7373
I/O Impedance of MOS Cascode
sCggC
Z
GDm
mGS
in
12
11 1
1
sCCRZ
DBGDLout
22
1||
CH 11 Frequency Response
0
(Neglecting RS)
![Page 74: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/74.jpg)
Cascode Frequency Response Take-Away Points
• Cascode amplifiers offer two good properties• High output impedance to serve as a
good current source and/or amplifier• Reduction of the Miller effect and
better high-frequency performance
• Main cost is higher voltage headroom to keep cascode transistor in saturation• Impacts maximum output swing and
distortion performance74
![Page 75: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/75.jpg)
Agenda
• Frequency Response Concepts• High-Frequency Models of Transistors• Frequency Response Analysis Procedure• CE and CS Stages• CB and CG Stages• CC and CD (Follower) Stages• Cascode Stages• Differential Pairs• Additional Examples
75
![Page 76: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/76.jpg)
7676
Bipolar Differential Pair Frequency Response
Since bipolar differential pair can be analyzed using half-circuit, its transfer function, I/O impedances, locations of poles/zeros are the same as that of the half circuit’s (Slide 43).
Half Circuit
CH 11 Frequency Response
outXYLinThevThevXYLm
outinXYoutXYinLThev
LmXY
Thev
out
CCRCRRCRgbCCCCCCRRa
bsasRgsCs
VV
1
where12
![Page 77: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/77.jpg)
7777
MOS Differential Pair Frequency Response
Since MOS differential pair can be analyzed using half-circuit, its transfer function, I/O impedances, locations of poles/zeros are the same as that of the half circuit’s (Slide 43).
Half Circuit
CH 11 Frequency Response
![Page 78: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/78.jpg)
7878
Example: MOS Differential Pair
33,
311
331
3
,
1311,
1
111
])/1([1
GDDBDoutp
SBGDm
mGSDB
m
Yp
GDmmGSSXp
CCR
CCggCC
g
CggCR
![Page 79: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/79.jpg)
79
Common Mode Frequency Response
Css will lower the total impedance between point P to ground at high frequency, leading to higher CM gain which degrades the CM rejection ratio.
79
12
1121
SSmSSSS
SSSSDm
SSSS
m
D
CM
outRgsCRsCRRg
sCR
g
RVV
![Page 80: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/80.jpg)
80
Tail Node Capacitance Contribution
Source-Body Capacitance of M1, M2
Drain-Body Capacitance of M3 Gate-Drain Capacitance of M3
80CH 11 Frequency Response
• M3 is often a large (wide) transistor in order to have a small compliance (VDS) voltage• Watch out for degraded high-frequency CMRR!
CDB3
![Page 81: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/81.jpg)
Agenda
• Frequency Response Concepts• High-Frequency Models of Transistors• Frequency Response Analysis Procedure• CE and CS Stages• CB and CG Stages• CC and CD (Follower) Stages• Cascode Stages• Differential Pairs• Additional Examples
81
![Page 82: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/82.jpg)
82
Example: Capacitive Coupling (Low-Frequency Cut-Off)
EBin RrRR 1|| 222
HzCRr B
L 5422||
1
1111
82
mAImAI
C
C
13.175.1
2
1
22
22
22
211 inC
in
inC
in
Thev
YRRsC
RsC
RsC
R
RsVV
To find L2:
HzCRR inC
L 9.221
222
The “highest” low-frequency pole (L1 = 542Hz) will set the low-frequency cut-off
![Page 83: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/83.jpg)
83
MHzCRR inD
L 92.621
2212
MHzCR
Rg
CRg
S
Sm
Sm
L 2.37211
111
11
111
1
kkR
kRgA
ARR
in
Dmv
v
Fin
30.167.7
10
67.61501
1
2
222
22
Example: IC Amplifier – Low Frequency Design
83CH 11 Frequency Response
121 150 mm gg
The “highest” low-frequency pole (L1 = 37.2MHz) will set the low-frequency cut-off
![Page 84: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/84.jpg)
84
dBAAAA
RRgvvA
vvv
v
inDmin
Xv
0.281.2567.6
77.3||
21
2
2111
Example: IC Amplifier – Midband Design
84CH 11 Frequency Response
121 150 mm gg
![Page 85: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/85.jpg)
Example: IC Amplifier – High Frequency Design
CH 11 Frequency Response 85
22211
11111121
11211112
11211111
1where
99.221
22221
1
vGDGSDBout
outGSoutGDGDGSinDS
outGDinDGSSSGDvp
outGDinDGSSSGDvp
ACCCC
GHzCCCCCCRRR
CCRRCRRCA
MHzCCRRCRRCA
To get an accurate estimate for p1 and p2, use the dominant pole approximation expressions on Slide 44
![Page 86: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/86.jpg)
Example: IC Amplifier – High Frequency Design
CH 11 Frequency Response 86
MHzC
ACR
GHz
MHz
DBv
GDD
p
p
p
829211
1
99.22
2222
22
22
3
2
1
![Page 87: ECEN326: Electronic Circuits Fall 2017spalermo/ecen326/lecture05_ee326_frequency_response.pdfFrequency Response of the CS Stage At low frequency, the capacitor is effectively open](https://reader034.vdocument.in/reader034/viewer/2022052014/602adea43c7bb02f3b487a68/html5/thumbnails/87.jpg)
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