lecture 7 frequency response

7/28/2019 Lecture 7 Frequency Response

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Lecture 7

Frequency Response


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Review of CS, CG and CD

Amplifier


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Voltage Gain of a CS Amplifier

Interpretation: The resistance at the drain

Divided by the resistance in the source path


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Voltage Gain of a CD Amplifier


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Voltage Gain of a CG Amplifier

If RS=0 and channel length modulation is ignored, Av is


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Resistance into the Drain

Terminal


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Resistance into the Source

Terminal


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Miller Effect


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Millers Theorem


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Typical Application of MillersTheorem

Millers theorem is useful when Z appears in

parallel with the main signal (i.e. the amplifier)


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Limitation of Millers Theorem

Limitations:

Interaction of poles through R3 and C3.


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Association of Poles with Nodes

Each pole is determined by the product of1. 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


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Common-Gate Example


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CS Stage

Output Impedance

Input Impedance

Nodal Method Miller Approximation

Zx method

Equivalent Circuit Analysis KCL

Dominant pole


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High Frequency Model of CS

Stage


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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 1.20120n 0.64 9.55 0.029 0.201 0.55

For Same IOUT,

LWGDS(Ro) CDS

Trade-offs in GDS and parasiticcapacitance.

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

gm=AV/RD

Gmoverid_1=16.67


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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,

LWGDS(Ro) CDS

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

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


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Output Impedance

Only Valid if Rs is large!


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Input Impedance

Exclude CGSHigh frequencyapproximation

(First order model)


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Input Impedance (KCL)

Exclude CGSHigh frequencyapproximation

(In parallel with CGS)


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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 thehigh impedance node!


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Transfer Function

( fi i


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Nodal Method(Refined Miller

Approximation)

Resistive(Capacitive)

(If RS is large!)


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Equivalent Circuit Analysis


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Comparison to Miller

Approximation


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Dominant Pole Approximation


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Transmission Zero

Transmission Zero

Finding a transmission zero in effective Gm.


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Source Follower

(Strong interaction between XY, making it difficult to associateeach pole with each node)


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Source Follower


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Transmission Zero

= /( + )


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Input Impedance


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Analysis of Input Impedance

Miller Approximation:Av:

(Negative Resistance)Can be used to oscillators.


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Output Impedance


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Equivalent Output Impedance


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Issues


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Common Gate


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Cascode

(Gain from A to X)


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DC Input Resistance

Will a large Rin increase the miller effect of CS dramatically?


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Input Resistance of

Common Gate

Note that ZL is not infinity if RD is replaced bya current source because ZL is in parallelwith CD.


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Differential Pair

(Differential Mode)

(Differential Half Circuit)


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Differential Pair

(Common-Mode)

W3 is made as largeas possible to minimize VDSAT.


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Consequence of Limited CMRR


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Differential Pair with High

Impedance Load

AC Ground

(Dominant Pole)


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Differential Pair Example

GM=166.19 uSGDS=1.3552 uSRD=90 Kohm


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AC analysis


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Use the Waveform Calculator

Add voltages to the calculator

Press Eval before you plot


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Plot in Magnitude/dB


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Transfer Function

3dB Bandwidth: 317.629 MHz

Diff ti l P i ith C t


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Differential Pair with Current

Mirror


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Small Signal Equivalent Model

(Transmission Zero)

Diff ti l P i ith C t


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Differential Pair with Current

Mirror

(Slow Path)

(Fast Path)

lecture 7 frequency response

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