Lecture 24 - University of California, Berkeleyee105/sp08/lectures/lecture24_2.pdf · Lecture 24 OUTLINE • MOSFET Differential Amplifiers • Reading: Chapter 10.3‐10.6 EE105

5/6/2008

EE105 Fall 2007 1

Lecture 24

OUTLINE• MOSFET Differential Amplifiers

• Reading: Chapter 10.3‐10.6

EE105 Spring 2008 Lecture 24, Slide 1 Prof. Wu, UC Berkeley

Common‐Mode (CM) Response

• Similarly to its BJT counterpart, a MOSFET differential pair produces zero differential output as V changesas VCM changes.

2SS

DDDYXIRVVV −==


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EE105 Fall 2007 2

Equilibrium Overdrive Voltage

• The equilibrium overdrive voltage is defined as VGS‐VTH when M1 and M2 each carry a current of ISS/2.ISS/2.

( ) WIVV SS

equilTHGS =−


( )

LWCoxn

equilTHGS

μ

Minimum CM Output Voltage

• In order to maintain M1 and M2 in saturation, the common‐mode output voltage cannot fall below VCM‐VTH.

• This value usually limits voltage gain.

THCMSS

DDD VVIRV −>−2


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EE105 Fall 2007 3

Differential Response


Small‐Signal Response

• For small input voltages (+ΔV and ‐ΔV), the gm values are ~equal, so the increase in ID1 and decrease in ID2are ~equal in magnitude Thus the voltage at node Pare ~equal in magnitude. Thus, the voltage at node P is constant and can be considered as AC ground.

( )

1

2

2

2

EED

EED

II I

II I

= + Δ

= −Δ


( )( )

1

2

1 2

0

D m P

D m P

D D

P

I g V V

I g V VI I

V

Δ = Δ −Δ

Δ = −Δ −Δ

Δ = −Δ

⇒ Δ =

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EE105 Fall 2007 4

Small‐Signal Differential Gain

• Since the output signal changes by ‐2gmΔVRD when the input signal changes by 2ΔV, the small‐signal voltage gain is –g RD.voltage gain is gmRD.

• Note that the voltage gain is the same as for a CS stage, but that the power dissipation is doubled.


Large‐Signal Analysis


( ) ( )2211214

21

2 inin

oxn

SSinoxnDD VV

LWC

IVVLWCII

in−−−=−

μμ

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EE105 Fall 2007 5

Maximum Differential Input Voltage

• There exists a finite differential input voltage that completely steers the tail current from one transistor to the other This value is known as thetransistor to the other. This value is known as the maximum differential input voltage.

2

2

If all current flows through M :

2

0

SSGS TH

n ox

IV V WCL

I V V

μ= +

⇒


( )

1 1

1 2 max

0

2

2

D GS TH

SSin in

n ox

GS TH equil

I V V

IV V WCL

V V

μ

= ⇒ =

− =

= −

MOSFET vs. BJT Differential Pairs

• In a MOSFET differential pair, there exists a finite differential input voltage to completely switch the current from one transistor to the other whereas incurrent from one transistor to the other, whereas in a BJT differential pair that voltage is infinite.

MOSFET Differential Pair BJT Differential Pair


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EE105 Fall 2007 6

Effect of Doubling the Tail Current

• If ISS is doubled, the equilibrium overdrive voltage for each transistor increases by , thus ΔVin,maxincreases by as well Moreover the

22increases by as well. Moreover, the

differential output swing will double. 2


Effect of DoublingW/L

• If W/L is doubled, the equilibrium overdrive voltage is lowered by , thus ΔVin,max will be lowered by as well The differential output swing will be unchanged

22well. The differential output swing will be unchanged.


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EE105 Fall 2007 7

Small‐Signal Analysis

• When the input differential signal is small compared to 4ISS/μnCox(W/L), the output differential current is ~ linearly proportional to it:linearly proportional to it:

• We can use the small‐signal model to prove that the change in tail node voltage (vP) is zero:

( ) ( )2121214

21

ininSSoxn

oxn

SSininoxnDD VVI

LWC

LWC

IVVLWCII −=−≈− μ

μμ


21

2211 0vv

vgvg mm

−=⇒=+

( )1 2

1 2

in in

P P

v vv v v v= −

⇒ + = − +

Virtual Ground and Half Circuit

• Since the voltage at node P does not change for small input signals, the half circuit can be used to calculate the voltage gain.the voltage gain.


Dmv

P

RgAv

−== 0

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EE105 Fall 2007 8

MOSFET Diff. Pair Frequency Response

• Since the MOSFET differential pair can be analyzed using its half‐circuit, its transfer function, I/O impedances, locations of poles/zeros are the same asimpedances, locations of poles/zeros are the same as that of the half circuit’s.


Example

1311,

1])/1([

1

GDmmGSSXp CggCR ++=ω

( )33,

311

313

3

,

1

11

DBGDDoutp

SBDBm

mGDGS

m

Yp

CCR

CCggCC

g

+=

⎥⎦

⎤⎢⎣

⎡++⎟⎟

⎠

⎞⎜⎜⎝

⎛++

=

ω

ω


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EE105 Fall 2007 9

Half Circuit Example 1

0≠λ Half circuit for small-signal analysis


⎟⎟⎠

⎞⎜⎜⎝

⎛−= 13

31 ||||1

OOm

mv rrg

gA

Half Circuit Example 2Half circuit for small-signal analysis

0=λ


( ) ( )212

SSm

DDv Rg

RA+

−=

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EE105 Fall 2007 10

MOSFET Cascode Differential Pair

Half circuit for small-signal analysis


1331 OmOmv rgrgA −≈

MOSFET Telescopic Cascode AmplifierHalf circuit for small-signal analysis


( )[ ])(|| 7551331 OOmOOmmv rrgrrggA −≈

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EE105 Fall 2007 11

CM to DM Conversion Gain, ACM‐DM

• If finite tail impedance and asymmetry are both present, then the differential output signal will contain a portion of the input common‐mode signal.contain a portion of the input common mode signal.

SSm

CMD

SSDm

DSSDGSCM

Rg

VI

RIgIRIVV

21

22

+

Δ=Δ⇒

Δ+Δ

=Δ+Δ=Δ

( )2

1

DDDout

DDout

RIVVVRRIV

RIV

ΔΔΔΔΔΔ+Δ−=Δ

Δ−=Δ


21 DDoutoutout RIVVV ΔΔ−=Δ−Δ=Δ

( ) SSm

D

CM

out

RgR

VV

2/1 +Δ

=ΔΔ

MOS Diff. Pair with Active Load

• Similarly to its BJT counterpart, a MOSFET differential pair can use an active load to enhance its single ended outputits single‐ended output.


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EE105 Fall 2007 12

Asymmetric Differential Pair

• Because of the vast difference in magnitude of the resistances seen at the drains of M1 and M2, the voltage swings at these two nodes are different and thereforeswings at these two nodes are different and therefore node P cannot be viewed as a virtual ground…


Thevenin Equivalent of the Input Pair


oNThev

ininoNmNThev

rRvvrgv

2)( 21

=−−=

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EE105 Fall 2007 13

Simplified Diff. Pair w/ Active Load

( ) 3

3

1

1m

A out Thev

Thevm

out Thev

gv v vR

gv v

= ++

+


3

44

3

2

KCL at : 01

out Thev

m oN

out out Thevout m A

oThev

m

g rv v vv g vr R

g

≈⋅

++ + =

+ 1 2

( || )outmN ON OP

in in

v g r rv v

=−

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Lecture 24 - University of California, Berkeleyee105/sp08/lectures/lecture24_2.pdf · Lecture 24 OUTLINE • MOSFET Differential Amplifiers • Reading: Chapter 10.3‐10.6 EE105