3. Fundamental amplifier configurations & Elementary R forms

Sedra & Smith Sec. 5.6

(S&S 5th Ed: Sec. 4.7)

ECE 102, Fall 2012, F. Najmabadi

Voltage Amplifier Model

F. Najmabadi, ECE102, Fall 2012 (2/23)

Input Resistance: Ri = vi/ii Voltage gain: Av = vo/vi with load Open-loop gain: Avo = vo/vi with no load Output resistance: Ro (resistance seen between output terminals with vi= 0 )

sigi

i

sig

i

RRR

vv

+=

oL

Lvov

i

o

RRRAA

vv

+⋅==

oL

Lvo

sigi

i

sig

o

RRRA

RRR

vv

+⋅⋅

+=

Fundamental MOS Amplifier Configurations

F. Najmabadi, ECE102, Fall 2012 (3/23)

We are considering only signal circuit here!

There are only FOUR single-transistor MOS Amplifier Configuration

Possible MOS amplifier configurations

F. Najmabadi, ECE102, Fall 2012 (4/23)

Same as Common Gate (vi does not change)

Common-Source Common-Gate Common-Drain

Common-Source with Rs Not Useful

PMOS configurations are the same as NMOS

F. Najmabadi, ECE102, Fall 2012 (5/23)

Common-Source Common-Gate Common-Drain

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

Textbook includes RD in its analysis

F. Najmabadi, ECE102, Fall 2012 (6/23)

Small Signal Circuit for a Common Source Amplifier

Textbook is inconsistent. It includes RD for common source and common gate but does not include RS in common drain.

Note RD is parallel to RL.

To avoid confusion, I am using only one resistor, R’L, which is the equivalent of all resistors in the drain circuit (e.g., for the above circuit, R’L = R L || RD )

Textbook:

Lecture:

Common Source Configuration (Gain)

F. Najmabadi, ECE102, Fall 2012 (7/23)

Signal Circuit:

Small Signal Circuit with MOS SSM

omvo

Lomi

ov

Logsmo

rgA

RrgvvA

Rrvgv

−=

′−==

′−=

)||(

)||(

Relevant circuit for Gain calculation

By KCL

Common Source Configuration (Ri)

F. Najmabadi, ECE102, Fall 2012 (8/23)

0

∞==

=

i

ii

i

ivR

i

Small Signal Circuit with MOS SSM

Relevant circuit for Ri calculation

Common Source Configuration (Ro)

F. Najmabadi, ECE102, Fall 2012 (9/23)

oo rR = Current source becomes open circuit

Small Signal Circuit with MOS SSM

Relevant circuit for Ro calculation (set vi = 0)

Common Source with Source Resistor

F. Najmabadi, ECE102, Fall 2012 (10/23)

0 ∞==⇒=i

iii i

vRiInput Resistance

Signal Circuit:

Small Signal Circuit with MOS SSM

Common Source with Source Resistor (Gain*)

F. Najmabadi, ECE102, Fall 2012 (11/23) * Text book ignore ro

omvo

oLSm

Lmv

LSomo

Lom

i

ov

rgArRRg

RgA

RRrgrRrg

vvA

−=

′++′

−≈

′+++′

−==

/1

)1(

0)(

0)(

=−+−

+′

=−−−

+

−=

Simo

So

L

o

Simo

oS

S

S

Sigs

vvgr

vvRv

vvgr

vvRv

vvv

Node voltage method:

Node vS

Node vo

Relevant circuit for Gain calculation

Common Source with Source Resistor (Ro*)

F. Najmabadi, ECE102, Fall 2012 (12/23) * Text book ignore ro

)1( Somoo RrgrR ++=

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 vx and compute ix

Ro = vx /ix

Somo

x

S

Sx Rrgr

vRvi

)1( ++==

Somox

x

o Rrgrvi

R )1(11++

=≡

Common Gate Configuration

F. Najmabadi, ECE102, Fall 2012 (13/23)

Signal Circuit:

Small Signal Circuit with MOS SSM

Common Gate Configuration (Gain*)

F. Najmabadi, ECE102, Fall 2012 (14/23)

omvo

Lomv

Loo

om

i

ov

rgARrgA

Rrr

rgvvA

≈

′≈

′+==

)||(

)||(1

io

om

Lo

o

imo

io

L

o

igs

vr

rgRr

v

vgr

vvRv

vv

+=

′

=−+−

+′

−=

1||

0)(

Node voltage method:

Node vo

Common Gate Configuration (Ri and Ro*)

F. Najmabadi, ECE102, Fall 2012 (15/23)

om

L

mi

om

Lo

i

ii

rgR

gR

rgRr

ivR

′+≈

+′+

==

1

1

)()1(

)(

Loiomi

Liogsmii

RrirgvRirvgiv′+=+

′++=KVL:

* Text book ignore ro

oo rR =

Current source becomes open circuit

Output Resistance (set vi = 0)

Input Resistance

Common Drain Configuration (Source Follower)

F. Najmabadi, ECE102, Fall 2012 (16/23)

11

)||(1

)||(

≈+

=

′+′

=

om

omvo

Lom

Lomv

rgrgA

RrgRrgA

omLo

oim

oimo

o

L

o

oigs

vgRr

vvg

vvgrv

Rv

vvv

+′

=

=−−+′

−=

||

0)(

Node voltage method:

Node vo

Gain

Common Drain Configuration (Source Follower)

F. Najmabadi, ECE102, Fall 2012 (17/23)

m

x

o

xgsm

o

xx g

vrvvg

rvi

/1+=−=

Input Resistance

Output Resistance (set vi = 0)

1||1 m

om

o gr

gR ≈=

0=ii

∞==i

ii i

vR

MOS Fundamental Amplifier Configurations (PMOS circuits are identical)

F. Najmabadi, ECE102, Fall 2012 (18/23)

Common Source with RS oLSm

Lmv rRRg

RgA/1 ′++

′−=

Common Drain/Source Follower

)||(1)||(

Lom

Lomv Rrg

RrgA′+

′=

Common Source )||( Lomv RrgA ′−=

Common Gate )||( Lomv RrgA ′=

F. Najmabadi, ECE102, Fall 2012 (19/23)

Elementary R Forms

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

F. Najmabadi, ECE102, Fall 2012 (20/23)

oo rR =Set vi = 0, current source becomes open circuit

Ex: Output resistance of a CS Amplifier

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.

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

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

F. Najmabadi, ECE102, Fall 2012 (21/23)

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

signals. o In fact, one or two MOS terminals have to be connected to bias power supply

to ensure that MOS is in saturation (there is an exception, see next page)

Signal Circuit Real Circuit

A)

No Signal circuit MOS is NOT in saturation

B)

MOS Elementary R Forms (PMOS circuits are identical)

F. Najmabadi, ECE102, Fall 2012 (22/23)

∞

Input resistance of 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

Diode-connected Transistor Always in saturation! m

om g

rg

1||1≈

or

F. Najmabadi, ECE102, Fall 2012 (23/23)

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

using fundamental amplifiers configurations

and elementary R forms