Chapter 16 CMOS Amplifiers 16.1 General Considerations 16.2 Operating Point Analysis and Design ...

Chapter 16 CMOS Amplifiers

16.1 General Considerations 16.2 Operating Point Analysis and Design 16.3 CMOS Amplifier Topologies 16.4 Common-Source Topology 16.5 Summary and Additional Examples 16.6 Chapter Summary

1

Chapter Outline

2CH 16 CMOS Amplifiers

Example: Desired I/O Impedances


inR 0ampR

Method to Measure the I/O Impedances


To measure Rin(Rout), deactivate all the other independent sources in the circuit and find the ratio of vX/iX.

X

Xin i

vR

X

Xout i

vR

Example: Input Impedance of a Simple Amplifier


inX Ri 0

The Concept of Impedance at a Node


When the other node of a port is grounded, it is more convenient to use the concept of impedance at a node.

Example: Impedance Seen at Drain


Oout rR

Example: Impedance Seen at Source


mout g

R1

Impedance Summary


Looking into the gate, we see infinity. Looking into the drain, we see rO if the source is (ac) grounded.

Looking into the source, we see 1/gm if the gate is (ac) grounded and rO is neglected.

Bias and Signal Levels for a MOS Transistor


Bias point analysis establishes the region of operation and the small-signal parameters.

On top of the bias point, small signals are applied to the circuit.

General Steps in Circuit Analysis


First, the effects of constant voltage/current sources are analyzed when signal sources are deactivated.

Second, small-signal analysis is done when constant sources are set to zero.

Simplification of Supply Voltage Notation


Example: Amplifier Driven by a Microphone


20mV

0V

Microphone Output

Since the DC (average) value is at zero, and 20mV is not sufficient to turn on M1, M1 is off and Vout is at VDD.

Example: Amplifier with Gate Tied to VDD


Since the gate voltage level is fixed at VDD, no signal current will be produced my M1, leading to no amplification.

Example: Amplifier with Gate Bias


With proper value of VB, M1 can operate in the desired saturation region and amplify the incoming voice signal.

Simple Biasing


In (a), VGS=VDD, whereas in (b) VGS equals to a fraction of VDD.

DDGS VRR

RV

21

2

Example: Bias Current and Maximum RD


KR

KR

LW

VAC

VV

oxn

TH

15

20

0

18.05

/100

5.0

2

1

2

KRVVVVV

AVVRR

R

L

WCI

DRDTHGSD

THDDoxnD

15529.1271.0

1022

1

maxmin

2

21

2

Capacitive Coupling


Capacitive coupling is used to block the zero DC output value of the microphone and pass the voice signal to the amplifier.

Biasing with Source Degeneration


Soxn

THDD

THGS

RLW

CV

VRR

VRVVVVV

1

2

1

21

21

211

Example: ID and Maximum RD for Source Degeneration Biasing


0

18.0/5/

/100

5.02

LW

VAC

VV

oxn

TH

KI

VVVR

VVRR

VRVVVVV

VR

LW

CV

D

THXDDD

THDD

THGS

Soxn

25.3)(

974.02

36.01

21

21

211

1

Example: Maximum W/L and Minimum RS


0

5.2

/100

5.02

KR

VAC

VV

D

oxn

TH

2.56

38.050406

max

2

2max

L

W

VL

W

V

AA

R

VVI

D

YDDD

604

041.12

minD

GSXS

oxn

DTHGS

I

VVR

V

LW

C

IVV

Self-Biased MOS Stage


2

2

1THDDSDDoxnD VIRRV

L

WCI

The gate voltage is provided by the drain with no voltage drop across RG and M1 is always in saturation.

Example: Self-Biased MOS Stage


0

5.0

/100 2

VV

VAC

TH

oxn

KRAI

AI

DD

D

867.2278

556

Example: PMOS Stage with Biasing

VV

KR

KR

LW

VAC

TH

oxp

5.0

15

20

0

18.05

/50

2

1

2

KRSaturation

AVVL

WCI

VVRR

RV

D

THGSoxpD

DDGS

3.27

562

1

771.0

max

2

21

2


Example: PMOS Stage with Self-Biasing

VV

LW

VAC

TH

oxp

5.0

0

18.05

/50 2

AI

VRIVL

WCI

D

THDDDDoxpD

4182

1 2


Good Example of Current Source

As long as a MOS transistor is in saturation region and λ=0, the current is independent of the drain voltage and it behaves as an ideal current source seen from the drain terminal.


Bad Example of Current Source

Since the variation of the source voltage directly affects the current of a MOS transistor, it does not operate as a good current source if seen from the source terminal


Possible I/O Connections to a MOS Transistor

Of all the possible I/O connections to a MOS transistor, only (a,d), (a,e) and (b,d) are functional.


Common Source (CS) Stage

If the input is applied to the gate and the output is sensed at the drain, the circuit is called a “common-source” (CS) stage.


Small-Signal Model of CS Stage


Dmv

mD

out

RgA

vgR

v

1

Example: CS Stage

31

33.3300

12

Dmv

Doxnm

RgA

IL

WCg

CH 16 CMOS Amplifiers

0

5.0

/100

12

VV

VAC

mAI

TH

oxn

D

Saturation

VIRVVVV

V

LW

C

IVV

DDDDTHGS

oxn

DTHGS

6.08.0

8.0,6.0

1.12

Example: Faulty CS Stage Design


0

18.05

/100

5.0

5

8.1

1

2

LW

VAC

VV

A

VV

mWPower

oxn

TH

v

DD

28455

56915561

Dv

mD

RA

gAImWPower

However, no solution exists since M1 is out of the saturation region (VDD-IDRD<VGS-VTH).

CS Stage I/O Impedance Calculation

x

xin i

vR


Dx

xout R

i

vR

CS Stage Including Channel-Length Modulation


ODout

ODmv

rRR

rRgA

||

||

xAv

Example: ½ Gain

2xAv


No Channel-Length Modulation With Channel-Length Modulation

DD

DD

O

RI

RI

r

1

1

Example: RD → ∞


D

oxn

D

oxn

v

Omv

I

WLC

ILW

CA

rgA

2

2

CS Stage with Current Source Load


21

211

||

||

OOout

OOmv

rrR

rrgA

Example: CS Stage with Current Source Load


211 || OOmv rrgA

CS Stage with Diode-Connected Load


122

122

1

||||1

||||1

OOm

out

OOm

mv

rrg

R

rrg

gA

Example: CS Stage with Diode-Connected PMOS


12

12 ||||

1OO

mmv rr

ggA

CS Stage with Source Degeneration


Sm

Dv

Rg

RA

1

Example: CS Stage with Source Degeneration


21

11

mm

Dv

gg

RA

Example: Degeneration Resistor

8

2001

v

m

A

g

4

2001

v

m

A

g


200141

6.18

mSSm

Dm

DDm

gRRg

Rg

KRRg

Without Degeneration With Degeneration

Effective Transconductance


Sm

m

in

outm Rg

g

v

iG

1

Effect of Transistor Output Resistance


SmOout

SOmOout

RgrR

RrgrR

1

1

Stage with Explicit Depiction of rO


Sometimes, the transistor’s output resistance is explicitly drawn to emphasize its significance.

Example: NMOS Current Source Design

VV

V

VAC

KR

mAI

DS

oxn

out

D

3.0

25.0

/100

20

1

min

1

2


578

201

150

12

3.0min

S

SOSm

THGS

Dm

THGSDS

R

KRrRg

VV

Ig

VVV

Example: Output Resistance of CS Stage with Degeneration I


121

2211

2

111

Ooutmmm

mmmOout

rRggg

gggrR

Example: Output Resistance of CS Stage with Degeneration II


211

12111

OOmout

OOOmout

rrgR

rrrgR

Example: Failing Microphone Amplifier


No Amplification!!

Because of the microphone’s small low-frequency output resistance (100Ω), the bias voltage at the gate is not sufficient to turn on M1.

mVVKK

KVX 5.25.2

50||100100

50||100

Capacitive Coupling


To fix the problem in the previous example, a method known as capacitive coupling is used to block the DC content of the microphone and pass the AC signal to the amplifier.

Capacitive Coupling: Bias Analysis


Since a capacitor is an open at DC, it can be replaced by an open during bias point analysis.

2

21

2

2

1

THDDoxnD VV

RR

R

L

WCI

Capacitive Coupling: AC Analysis


Since a capacitor is a short at AC, it can be replaced by a short during AC analysis.

ODmin

out rRgv

v||

Capacitive Coupling: I/O Impedances

212

1

|| RRR

R

in

in


ODout rRR ||

Example: Amplifier with Direction Connection of Speaker


This amplifier design still fails because the solenoid of the speaker shorts the drain to ground.

Example: Amplifier with Capacitive Coupling at I/O


This amplifier design produces very little gain because its equivalent output resistance is too small.

08.0||

8||

spDmv

spDeq

RRgA

RRR

Source Degeneration with Bypass Capacitor


It is possible to utilize degeneration for biasing but eliminate its effect on the small-signal by adding a bypass capacitor.

DmG

v RgRRR

RRA

21

21

||

||

Example: Source Degeneration with Bypass Capacitor Design

mVV

VV

VV

VAC

mWPower

KR

A

SR

DD

TH

oxn

in

v

400

8.1

0

5.0

/100

5

50

5

2


KRKR

R

LW

g

R

D

m

S

225,3.64

2463

864

3.461

148

21

Concept Summary


Common-Gate Stage


In a common-gate stage, the input is applied at the source while the output is taken at the drain.

Small Signal Analysis of Common-Gate Stage


Dmv RgA

Example: Common-Gate Stage Design

VV

VV

VAC

LW

mAI

DD

TH

oxn

D

8.1

5.0

/100

50

5.0

2


06.64471

71.2

vm

DTHbDDDD

Ag

kRVVRIV

Input Impedance of Common-Gate Stage


min g

R1

The Use of Low Input Impedance


The low input impedance of a common-gate stage can be used to impedance match a 50-Ω transmission line.

Output Impedance of Common-Gate Stage


DOout RrR ||

Example: Alternate Av Expression of CG Stage


in

outv R

RA

CG Stage in the Presence of Finite Source Resistance


Sm

D

in

out

Rg

R

v

v

1

Output Impedance of a General CG Stage


SOSmDout RrRgRR 1||

CG and CS Stages Output Impedance Comparison


SOSmDoutCSoutCG RrRgRRR 1||

Since when calculating the output impedance, the input voltage source of the CG stage is grounded, the result will be identical to that of a CS stage if the same assumptions are made for both circuits.

Example: AV and Rout


Smm

Dm

in

out

Rgg

Rg

v

v

21

1

1

λ = 0

DOSm

Omout RrRg

rgR ||||1

12

11

λ > 0

Example: CG Stage Lacking Bias Current


Although the capacitor C1 isolates the DC content of the signal source, it also blocks the bias current of M1, hence turning it OFF.

Example: CG Stage with Source Shorted to Ground


Although there is now a path for bias current to flow to ground, the signal current also goes with it, hence producing no gain.

CG Stage with Proper Bias Circuitry


R1 is used to provide a path for bias current to flow without directly shorting the source to ground.

However, it also lowers the input impedance of the circuit

1||1

Rg

Rm

in DmSm

v RgRRg

A

111

1

Input Current Flowing Paths


To maximize the useful current i2, R1 needs to be much larger than 1/gm.

mgR

11

Example: CG with Complete Bias Network


VV

mWPower

g

RR

A

VV

VAC

DD

m

S

v

TH

oxn

8.1

2

50/1

500,0

5

0

5.0

/100

1

2

kRkR

R

VVIg

LW

VV

GG

D

THGSDm

GS

135,45

682

4.136/2

244

8.0

21

1

Example: Min W/L


VV

mWPower

g

RR

A

VV

VAC

DD

m

S

v

TH

oxn

8.1

2

50/1

500,0

5

0

5.0

/100

1

2

2

1

1

1

22

22

v

RDDoxn

D

RTHGSTHGSv

DD

THRGSDDDD

AVV

C

I

L

W

VVVVVA

V

VVVRIV

Source Follower


Source follower sense the input at the gate and produces the output at the source.

Source Follower’s Response to an Input Change


As the input changes by a small amount, the output will follow the input and changes by a smaller amount, hence the name source follower.

Small-Signal Model and Voltage Gain for Source Follower


mS

S

in

out

gR

R

v

v1

Example: Source Follower with Current Source


AV

1vA

Source Follower Acting as a Voltage Divider


mS

S

in

out

gR

R

v

v1

Complete Small-Signal Model with rO


mSO

SO

in

out

gRr

Rr

v

v1

||

||

Example: Source Follower with a Real Current Source


mOO

OOv

grr

rrA

1||

||

21

21

Example: Source Follower with a Real Current Source


VV

VV

VAC

mWPower

A

R

DD

TH

oxn

v

S

8.1

0

5.0

/100

10

5.0

50

2

36050

1

5.01

LW

g

Rg

RA

m

Sm

Sv

Output Resistance of Source Follower


SOm

out Rrg

R ||||1

Example: Source Follower with Biasing


kR

VV

VV

VAC

A

mAI

G

DD

TH

oxn

v

D

50

8.1

0

5.0

/100

8.0

1

2

107

933.0

867

2

LW

VRIVV

RR

I

VVR

A

SDDDGS

S

SD

THGS

Sv

Source Follower with Current Source Biasing


In IC technology, source follower is often biased by a current source to avoid the bias current’s dependence on the supply voltage.

Summary of MOS Amplifier Topologies


Example: Common Source Stage I


3213

3213

1

||||||1

||||||1

OOOm

out

OOOm

mv

rrrg

R

rrrg

gA

Example: Common Source Stage II


331

2

||11

Omm

Ov

rgg

rA

Example: CS and CG Stages


Sm

OvCG

OOSOmmvCS

Rg

rA

rrRrggA

1

2

11112

1

||1

Example: Composite Stage I


21

11

mm

Dv

gg

RA

Example: Composite Stage II


221

4332

12

2

221

||11

||||1

1||

1

||1

Omm

OOm

in

out

mO

m

Om

in

out

rgg

rrg

v

v

gr

g

rg

v

v

Chapter Summary


The impedances looking into the gate, drain, and source of a MOS are equal to ∞, rO and 1/gm respectively (under proper conditions).

The transistor has to be properly biased before small-signal can be applied.

Resistive path between the supply rails establishes the gate bias voltage.

Only three amplifiers topologies are possible. CS stage provides moderate AV, high Rin and moderate Rout.

Source degeneration improves linearity but lower AV.

Source degeneration raises the Rout of CS stage considerably.

CG stage provides moderate AV, low Rin and moderate Rout.

AV for CS and CG stages are similar but for a sign.

Source follower provides AV less than 1, high Rin and low Rout, serving as a good voltage buffer.

Chapter 16 CMOS Amplifiers 16.1 General Considerations 16.2 Operating Point Analysis and Design ...

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Transcript of Chapter 16 CMOS Amplifiers 16.1 General Considerations 16.2 Operating Point Analysis and Design ...