EE105 Fall 2007 Lecture 24, Slide 1 Prof. Liu, UC Berkeley

Lecture 24

OUTLINE• MOSFET Differential Amplifiers

Reading: Chapter 10.3-10.6

ANNOUNCEMENTS• The last HW assignment (HW#12) will be due 12/6• Prof. Liu will be away on Tuesday 12/4 (no office hour that

day)

EE105 Fall 2007 Lecture 24, Slide 2 Prof. Liu, UC Berkeley

Common-Mode (CM) Response• Similarly to its BJT counterpart, a MOSFET differential pair

produces zero differential output as VCM changes.

2SS

DDDYX

IRVVV

EE105 Fall 2007 Lecture 24, Slide 3 Prof. Liu, UC Berkeley

Equilibrium Overdrive Voltage• The equilibrium overdrive voltage is defined as VGS-VTH

when M1 and M2 each carry a current of ISS/2.

L

WC

IVV

oxn

SSequilTHGS

EE105 Fall 2007 Lecture 24, Slide 4 Prof. Liu, UC Berkeley

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 VVI

RV 2

EE105 Fall 2007 Lecture 24, Slide 5 Prof. Liu, UC Berkeley

Differential Response

EE105 Fall 2007 Lecture 24, Slide 6 Prof. Liu, UC Berkeley

Small-Signal Response• For small input voltages (+V and -V), the gm values are

~equal, so the increase in ID1 and decrease in ID2 are ~equal in magnitude. Thus, the voltage at node P is constant and can be considered as AC ground.

II

I EED

22

VgIVgI

V

mDmD

P

21 ;

0

II

I EED

21

EE105 Fall 2007 Lecture 24, Slide 7 Prof. Liu, UC Berkeley

Small-Signal Differential Gain• Since the output signal changes by -2gmVRD when the input

signal changes by 2V, the small-signal voltage gain is –gmRD. • Note that the voltage gain is the same as for a CS stage, but

that the power dissipation is doubled.

EE105 Fall 2007 Lecture 24, Slide 8 Prof. Liu, UC Berkeley

Large-Signal Analysis

221121

4

2

12 inin

oxn

SSinoxnDD VV

L

WC

IVV

L

WCII

in

EE105 Fall 2007 Lecture 24, Slide 9 Prof. Liu, UC Berkeley

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 the maximum differential input voltage.

equilTHGSinin VVVV 2max21

EE105 Fall 2007 Lecture 24, Slide 10 Prof. Liu, UC Berkeley

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 in a BJT differential pair that voltage is infinite.

MOSFET Differential Pair BJT Differential Pair

EE105 Fall 2007 Lecture 24, Slide 11 Prof. Liu, UC Berkeley

Effect of Doubling the Tail Current• If ISS is doubled, the equilibrium overdrive voltage for each

transistor increases by , thus Vin,max increases by as well. Moreover, the differential output swing will double.

2 2

EE105 Fall 2007 Lecture 24, Slide 12 Prof. Liu, UC Berkeley

Effect of Doubling W/L• If W/L is doubled, the equilibrium overdrive voltage is lowered

by , thus Vin,max will be lowered by as well. The differential output swing will be unchanged.

22

EE105 Fall 2007 Lecture 24, Slide 13 Prof. Liu, UC Berkeley

Small-Signal Analysis• When the input differential signal is small compared to

4ISS/nCox(W/L), the output differential current is ~linearly proportional to it:

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

212121

4

2

1ininSSoxn

oxn

SSininoxnDD VVI

L

WC

L

WC

IVV

L

WCII

21

2211 0

vv

vgvg mm

PP

inin

vvvv

vv

21

21

EE105 Fall 2007 Lecture 24, Slide 14 Prof. Liu, UC Berkeley

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.

Dmv

P

RgA

v

0

EE105 Fall 2007 Lecture 24, Slide 15 Prof. Liu, UC Berkeley

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 as that of the half circuit’s.

EE105 Fall 2007 Lecture 24, Slide 16 Prof. Liu, UC Berkeley

Example

33,

311

313

3

,

1311,

1

11

1

])/1([

1

DBGDDoutp

SBDBm

mGDGS

m

Yp

GDmmGSSXp

CCR

CCgg

CCg

CggCR

EE105 Fall 2007 Lecture 24, Slide 17 Prof. Liu, UC Berkeley

Half Circuit Example 1

13

31 ||||

1OO

mmv rrg

gA

0 Half circuit for small-signal analysis

EE105 Fall 2007 Lecture 24, Slide 18 Prof. Liu, UC Berkeley

Half Circuit Example 2

21

2

SSm

DDv Rg

RA

Half circuit for small-signal analysis

0

EE105 Fall 2007 Lecture 24, Slide 19 Prof. Liu, UC Berkeley

MOSFET Cascode Differential Pair

Half circuit for small-signal analysis

1331 OmOmv rgrgA

EE105 Fall 2007 Lecture 24, Slide 20 Prof. Liu, UC Berkeley

MOSFET Telescopic Cascode Amplifier

)(|| 7551331 OOmOOmmv rrgrrggA

Half circuit for small-signal analysis

EE105 Fall 2007 Lecture 24, Slide 21 Prof. Liu, UC Berkeley

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.

SSm

CMD

SSDm

DSSDGSCM

Rg

VI

RIg

IRIVV

21

22

21

2

1

DDoutoutout

DDDout

DDout

RIVVV

RRIV

RIV

SSm

D

CM

out

Rg

R

V

V

2/1

EE105 Fall 2007 Lecture 24, Slide 22 Prof. Liu, UC Berkeley

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 output.

EE105 Fall 2007 Lecture 24, Slide 23 Prof. Liu, UC Berkeley

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 therefore node P cannot be viewed as a virtual ground…

EE105 Fall 2007 Lecture 24, Slide 24 Prof. Liu, UC Berkeley

Thevenin Equivalent of the Input Pair

oNThev

ininoNmNThev

rR

vvrgv

2

)( 21

EE105 Fall 2007 Lecture 24, Slide 25 Prof. Liu, UC Berkeley

Simplified Diff. Pair w/ Active Load

)||(21

OPONmNinin

out rrgvv

v