3. Fundamental MOS Configurations and

Discrete MOS Amplifiers

ECE 102, Winter 2011, F. Najmabadi

Reading: Sedra & Smith: Secs. 5.6 & 5.7

Voltage Amplifier Model

Voltage Amplifier Model

Input Resistance: Ri = vi/iiOpen-loop gain: Avo = vo/vi with no loadOutput resistance: Ro (resistance seen between

output terminals with vi= 0 )

We focus on Unilateral amplifiers (i.e., Ri is independent of Load)

sigi

i

S

i

RRR

vv

+=

oL

Lvov

in

o

RRRAA

vv

+⋅==

oL

Lvo

sigi

i

S

out

RRRA

RRR

vv

+⋅⋅

+=

Rsig

Cascaded Amplifiers

91.0100k1M

1M

1

11 =+

=+

=sigi

i

S

i

RRR

vv

9.91k100k

100k10

11

11,

1

21 =

+⋅=

+⋅==

oL

Lvo

i

iv RR

RAvvA100k 2121 === iLio RRvv

9.901k10k

10k100

22

22,

2

32 =

+⋅=

+⋅==

oL

Lvo

i

iv RR

RAvvA10k 3232 === iLio RRvv

909.010100

1001

33

33,

33 =

+⋅=

+⋅==

oL

Lvo

i

Lv RR

RAvvA

8183211

=⋅⋅== vvvi

Lv AAA

vvA 74491.0 x 8181 ==⋅=

s

iv

s

L

vvA

vv

MOS Fundamental Configurations

MOS fundamental amplifier configurations

Common-Source Common-Gate Common-Drain

Since PMOS has the same signal model, configurations and results are exactly the same

Common Source Configuration

Small Signal Circuit:

Small Signal Circuit with MOS SSM

Common Source Configuration (Gain)

)||(

)||||(

)||||(

Domvo

LDomin

ov

LDogsmo

RrgA

RRrgvvA

RRrvgv

−=

−==

−=

Small Signal Circuit with MOS SSM

Relevant circuit forGain calculation

Common Source Configuration (Ri)

∞==

=

i

ii

i

ivR

i 0

Small Signal Circuit with MOS SSM

Relevant circuit forRi calculation

Common Source Configuration (Ro)

Doo RrR ||=Current source becomes open circuit

Small Signal Circuit with MOS SSM

Relevant circuit forRo calculation (set vi = 0)

Common Source with Source Resistor

∞==⇒=i

iii i

vRi 0Input Resistance

Small Signal Circuit:

Small Signal Circuit with MOS SSM

Common Source with Source Resistor (Gain*)

* Text book ignore ro

oDSm

Dmvo

oLDSm

LDmv

LDSomo

LDom

i

ov

rRRgRgA

rRRRgRRgA

RRRrgrRRrg

vvA

/1

/)||(1)||(

)||()1()||(

++−=

++−≈

+++−==

0)(||

0)(

=−+−

+

=−−−

+

−=

Simo

So

LD

o

Simo

oS

S

S

Sigs

vvgr

vvRR

v

vvgr

vvRv

vvv

Node voltage method:

Node vs

Node vo

Relevant circuit forGain calculation

Common Source with Source Resistor (Ro*)

* Text book ignore ro

DSomoo RRrgrR ||])1([ ++=

Somo

x

S

s

Smo

xS

S

S

Sgs

Rrgrv

Rv

vgr

vvRv

vv

)1(

0)(

++=

=−−−

+

−=

Node voltage method:

Node vs

set vi = 0 Attach ix and compute vx

D

x

Somo

x

o

xx

D

x

S

Sx

Rv

Rrgrv

Rvi

Rv

Rviii

+++

==

+=+=

)1(

21

2121 ||111 :Noting

RRRR=+

Common Gate Configuration

Small Signal Circuit:

Small Signal Circuit with MOS SSM

Common Gate Configuration (Gain*)

)||()||||(

)||||(1

Domvo

LDomv

LDoo

om

i

ov

RrgARRrgA

RRrr

rgvvA

≈≈

+==

io

om

LDo

o

imo

io

LD

o

igs

vr

rgRRr

v

vgr

vvRR

vvv

+=

=−+−

+

−=

1||||

0)(||

Node voltage method:

Node vo

Relevant circuit forGain calculation

Common Gate Configuration (Ri and Ro*)

om

LD

mi

om

LDo

i

ii

rgRR

gR

rgRRr

ivR

||11

||

+≈

++

==

)||()1(

)||()(

LDoiomi

LDiogsmii

RRrirgvRRirvgiv

+=+

++=KVL:

* Text book ignore ro

Doo RrR ||=

Current source becomes open circuit

Output Resistance (set vi = 0)

Input Resistance

Common Drain Configuration (Source Follower)

11

)||(1)||(

≈+

=

+=

om

omvo

Lom

Lomv

rgrgA

RrgRrgA

Note: This circuit needs a load as it is really a current amplifier.

omLo

oim

oimo

o

L

o

oigs

vgRr

vvg

vvgrv

Rv

vvv

+=

=−−+

−=

||

0)(

Node voltage method:

Node vs

Gain

Common Drain Configuration (Source Follower)

m

x

o

xgsm

o

xx g

vrvvg

rvi

/1+=−=

Input Resistance

Output Resistance (set vi = 0)

mo

mo g

rg

R 1||1≈=

0=ii

∞==i

ii i

vR

Summary of MOS Amp. Fundamental Forms(PMOS circuits are identical)

Common Source with RS

oLDSm

LDmv rRRRg

RRgA/)||(1

)||(++

−=

Common Drain/Source Follower

)||(1)||(

Lom

Lomv Rrg

RrgA+

=

Common Source

)||||( LDomv RRrgA −=

Common Gate

)||||( LDomv RRrgA =

Transistor can be configured to act as a resistor for small signals!

Doo RrR ||=Set vi = 0, current source becomes open circuit

Ex: Output resistance of a CS Amplifier

Do Rr ||

or

If we connect any two terminals of a MOS, we get a two-terminal device.o For Small Signals, this two terminal device can be replaced with its

Thevenin equivalent circuit.o As there is NO independent sources present, the Thevenin

equivalent circuit is reduced to a resistor.

Transistor can be configured to act as a resistor for small signals!

But, MOS should be in saturation for small signal model to work!o Connection between MOS terminals are, therefore, made through

ground for small signals.o In fact, one or both MOS terminals have to be connected to bias power

supplies to ensure that MOS is in saturation

Notation: ro is the small-signal resistance between the point and ground

Small Signal CircuitReal Circuit

A)

No Small Signal circuitMOS is NOT in saturation

B)

Elementary Configuration for MOS resistance(PMOS circuits are identical)

∞

Input resistanceof CS Amp

Above configurations are for Small Signal. Typically one or both grounds are connected to bias voltage sources to ensure that MOS is in saturation!

Output resistance of CS Amp with Rs

)1()1(Rgr

RRgr

mo

mo

+≈++

Input resistance of CG Amp

ommom

o

rgR

grgRr

+≈++ 1

1

or Diode-connectedTransistorAlways in saturation!m

om g

rg

1||1≈

Gain, input and output resistances of MOS amplifiers can be found

usingthe fundamental amplifiers and

elementary R configurations

Discrete MOS Amplifiers(Analysis using the fundamental Amplifiers

and elementary R configurations)

Stable Bias circuits for discrete MOS amplifiers

Drain Feedback

Will Discuss later

Identical small-signal circuit if

21 || RRRG =

One power supply

DSGGS IRVV −=

Two power supplies

DSSSGS IRVV −=

We will do analysis for this configuration

Signal is typically coupled to discreteamplifiers via coupling capacitors

We assume that the small signals of interest are at sufficiently high frequencies, such that the (large) capacitors can be approximated as shorts.o A lower cut-off frequency for Amplifier

These capacitors can be added at input, output, and between amplifier stages.

These capacitor can also be used to “by-pass” resistors needed for bias but not for small-signal.

Discrete CS Amplifier

Real Circuit

Test book uses current source for biasing(not a practical discrete circuit)

Fundamental CS form

Derivation of small-signal circuit for Discrete CS Amplifier

Real Circuit

Short capsZero bias supplies

Rearrange

Discrete CS Amplifier

)||||( LDomv RRrgA −=

Fundamental CS form

Elementary R Configuration

Gi RR =

∞

Elementary R Configuration

Doo RrR ||=

or

Discrete CS Amplifier with RS

Real Circuit

Small Signal Circuit

Discrete CS Amplifier with RS

Fundamental CS form with RS

∞

Elementary R Configuration

Gi RR =

∞

Elementary R Configuration

DSmoo RRgrR ||)]1([ +=)1( smo Rgr +

oLDSm

LDmv rRRRg

RRgA/)||(1

)||(++

≈

Discrete CG Amplifier

Real Circuit

Small Signal Circuit

Discrete CG Amplifier

Fundamental CSGform

Doo RrR ||=

Elementary R Configuration

Elementary R Configuration

om

LD

mom

LDo

rgRR

grgRRr ||1

1||

+≈++

++

=om

LDoSi rg

RRrRR1

|| ||

)||||( LDomv RRrgA =

Discrete CD Amplifier (Source Follower)

Real Circuit

Small Signal Circuit

Discrete CD Amplifier (Source Follower)

Fundamental CD form

Gi RR =

Elementary R Configuration

∞

Elementary R Configuration

Sm

o Rg

R ||1=

mg/1

mg/1

)||||(1)||||(

LSom

LSomv RRrg

RRrgA+

=