Lecture 7

Frequency Response

Review of CS, CG and CD Amplifier

Voltage Gain of a CS Amplifier

Interpretation: The resistance at the drainDivided 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 ground2. 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

For Same IOUT, L↓→W↓→GDS↑(Ro↓) →CDS ↓

Trade-offs in GDS and parasiticcapacitance.

Specs:AV=10Vo,cm=0.6VI(M1)=10 uA

gm=AV/RDGmoverid_1=16.67

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

For Same IOUT, L↓→W↓→GDS↑(Ro↓) →CDS ↓

Difficult to achieve high gain and high speed at the same time!

Specs:Vo,cm=0.6Vgm=AV/RD

Output Impedance

Only Valid if Rs is large!

Input Impedance

Exclude CGSHigh frequency approximation

(First order model)

Input Impedance (KCL)

Exclude CGSHigh frequency approximation

(In parallel with CGS)

“Nodal Method”(Miller Approximation)

Numerical example:RS=50 OhmsL=2.0 umAV=15

fin=4.65 GHzfout=69.9 MHz

517.8 fF 16(10.40fF)

CDB=27.51 fF, RD=60 KOhm

It is importantto identify the high impedance node!

Transfer Function

“Nodal Method”(Refined Miller Approximation)

(Resistive)(Capacitive)

(If RS is large!)

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 associateeach 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 largeas possible to minimize VDSAT.

Consequence of Limited CMRR

Differential Pair with High Impedance Load

AC Ground

(Dominant Pole)

Differential Pair Example

GM=166.19 uSGDS=1.3552 uSRD=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)