Lecture 7
Frequency Response
Review of CS, CG and CD
Amplifier
Voltage Gain of a CS Amplifier
Interpretation: The resistance at the drain
Divided by the resistance in the source path
Voltage Gain of a CD Amplifier
Voltage Gain of a CG Amplifier
If RS=0 and channel length modulation is ignored, Av is
Resistance into the Drain
Terminal
Resistance into the Source
Terminal
Miller Effect
Miller’s Theorem
Typical Application of Miller’s
Theorem
Miller’s theorem is useful when Z appears in
parallel with the main signal (i.e. the amplifier)
Limitation of Miller’s Theorem
Limitations:
Interaction of poles through R3 and C3.
Association of Poles with Nodes
Each pole is determined by the product of
1. Total capacitance seen from each node to ground
2. Total resistance seen at the node to ground
“Each node in the circuit contributes one pole to the transfer function”
Common-Gate Example
CS Stage
• Output Impedance
• Input Impedance
• “Nodal Method”
– Miller Approximation
– “Zx” method
• Equivalent Circuit Analysis
– KCL
– Dominant pole
High Frequency Model of CS
Stage
CS Trade-Off
L(um)
W(um)
GDS (uS)
CDB (fF)
CGD(fF)
CGS(fF)
2
5.78
3.613
5.19
1.84
98.16
800n
2.56
3.79
0.915
0.803
17.3
180n
0.86
5.72
0.056
0.273
1.20
120n
0.64
9.55
0.029
0.201
0.55
Specs:
AV=10
Vo,cm=0.6V
I(M1)=10 uA
gm=AV/RD
Gmoverid_1=16.67
For Same IOUT,
L↓→W↓→GDS↑(Ro↓) →CDS ↓
Trade-offs in GDS and parasitic
capacitance.
CS Trade-Off
AV
I (uA)
L(um)
W(um)
GDS (uS)
CDB (fF)
CGD(fF)
CGS(fF)
10
10
2
5.78
3.613
5.19
1.84
98.16
15
10
2
32.5
5.33
27.5
10.4
517.8
20
10
2
668.2
6.66
319.6
239.8
6,041.1
Specs:
Vo,cm=0.6V
gm=AV/RD
For Same IOUT,
L↓→W↓→GDS↑(Ro↓) →CDS ↓
Difficult to achieve high gain and
high speed at the same time!
Output Impedance
Only Valid if Rs is large!
Input Impedance
Exclude CGS
High frequency
approximation
(First order model)
Input Impedance (KCL)
Exclude CGS
High frequency
approximation
(In parallel with CGS)
“Nodal Method”(Miller
Approximation)
It is important
to identify the
high impedance node!
Numerical example:
RS=50 Ohms
L=2.0 um
AV=15
517.8 fF
fin=4.65 GHz
fout=69.9 MHz
16(10.40fF)
CDB=27.51 fF, RD=60 KOhm
Transfer Function
“Nodal Method”(Refined Miller
Approximation)
(If RS is large!)
(Capacitive) (Resistive)
Equivalent Circuit Analysis
Comparison to Miller
Approximation
Dominant Pole Approximation
Transmission Zero
Transmission Zero
Finding a transmission zero in effective Gm.
Source Follower
(Strong interaction between XY, making it difficult to associate
each pole with each node)
Source Follower
Transmission Zero
𝜔𝑧 = −𝑔𝑚/(𝐶𝑔𝑠 + 𝐶𝑔𝑑)
Input Impedance
Analysis of Input Impedance
Miller Approximation:
Av:
(Negative Resistance)
Can be used to oscillators.
Output Impedance
Equivalent Output Impedance
Issues
Common Gate
Cascode
(Gain from A to X)
DC Input Resistance
Will a large Rin increase the miller effect of CS dramatically?
Input Resistance of
Common Gate
Note that ZL is not infinity if RD is replaced by
a current source because ZL is in parallel
with CD.
Differential Pair
(Differential Mode)
(Differential Half Circuit)
Differential Pair
(Common-Mode)
W3 is made as large
as possible to minimize VDSAT.
Consequence of Limited CMRR
Differential Pair with High
Impedance Load
AC Ground
(Dominant Pole)
Differential Pair Example
GM=166.19 uS
GDS=1.3552 uS
RD=90 Kohm
AC analysis
Use the Waveform Calculator
Add voltages to the calculator
Press Eval before you plot
Plot in Magnitude/dB
Transfer Function
3dB Bandwidth: 317.629 MHz
Differential Pair with Current
Mirror
Small Signal Equivalent Model
(Transmission Zero)
Differential Pair with Current
Mirror
(Slow Path)
(Fast Path)