EECE488: Analog CMOS Integrated Circuit Design Set 6 - Courses

EECE488 Set 6 - Frequency Respose of Amplifiers 1SM

EECE488: Analog CMOS Integrated Circuit Design

Set 6

Frequency Response of Amplifiers

Shahriar MirabbasiDepartment of Electrical and Computer Engineering

University of British [email protected]

EECE488 Set 6 - Frequency Respose of Amplifiers 2SM

Simple Pole

sCRsCvv io /1

/1/+

=

11/

+=

sRCvv io

fRCjf

vv

i

o

π211)(

+=

RCf

ffj

fvv

p

p

i

o

π21 ,

)(1

1)( =+

=

iv ovR

C

EECE488 Set 6 - Frequency Respose of Amplifiers 3SM

Miller Effect

Z1 =Z

(1− Av)

)1(12 −

−=

vAZZ

EECE488 Set 6 - Frequency Respose of Amplifiers 4SM

Board Notes

EECE488 Set 6 - Frequency Respose of Amplifiers 5SM

Miller Capacitive Multiplication

C1 = CF(1− Av)

C2 = CF(1− A−1v ) ≈ CF

EECE488 Set 6 - Frequency Respose of Amplifiers 6SM

Applicability of Miller’s Theorem

If the only signal path between X and Y is through impedance Z then Miller’s theorem is typically not applicable.

EECE488 Set 6 - Frequency Respose of Amplifiers 7SM

Applicability of Miller’s Theorem

Miller’s Theorem is typically useful in the cases where there is impedance in parallel with the main signal path.

EECE488 Set 6 - Frequency Respose of Amplifiers 8SM

Poles and Nodes

Interacting Poles

Non-Interacting Poles: One pole associated with each node

EECE488 Set 6 - Frequency Respose of Amplifiers 9SM

Common Source

f p,in =1

2πRS CGS + (1+ gmRD )CGD[ ]

f p,out =1

2π CGD + CDB( )RD[ ]

Neglecting input/output interaction,

EECE488 Set 6 - Frequency Respose of Amplifiers 10SM

Common Source

f p,in =1

2π RS CGS + (1+ gmRD)CGD[ ]+ RD(CGD + CDB )( )

Assume D =s

ω p1

+1⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

sω p2

+1⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟ =

s2

ω p1ω p 2

+s

ω p1

+1 , ω p2 >> ω p1

[ ] 1()1()()(

)2 ++++++++

−=

DBGDDGSSGDDmSDBGDDBGSGDGSDS

DmGD

i

o

CCRCRCRgRsCCCCCCRRsRgsC

vv

EECE488 Set 6 - Frequency Respose of Amplifiers 11SM

Common Source

f p,out =RS (1+ gmRD )CGD + RSCGS + RD (CGD + CDB )

2πRS RD(CGSCGD + CGSCDB + CGDCDB )

GSDBGDD

outp CCCR

f large for , )(2

1, +

≈π

f p,out ≈ gmRS RDCGD

2πRS RD(CGSCGD + CGSCDB + CGDCDB )

≈ gm2π (CGS + CDB )

, for large CGD

EECE488 Set 6 - Frequency Respose of Amplifiers 12SM

Common Source

Right half plane zero, from the numerator of vo/vi

sCGD − gm

. . . → fz =

+gm

2πCGD

vovi

=(sCGD−gm)RD

s2RSRD(CGSCGD +CGSCSB +CGDCDB)+s RS(1+ gmRD)CGD +RSCGS +RD(CGD +CDB)[ ]+1

EECE488 Set 6 - Frequency Respose of Amplifiers 13SM

Common Gate

f pX =1

2π CGS + CSB( ) RS || 1gm + gmb

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

f pY =1

2π CGD + CDB( )RD[ ]

EECE488 Set 6 - Frequency Respose of Amplifiers 14SM

Source Follower (Common Drain)

( ) mGSLGDSmLGDGDGSLGSS

GSm

gCCCRgsCCCCCCRssCg

vivo

+++++++

=)(2

f p1 ≈gm

2π gmRSCGD + CL + CGS( ) , assuming f p2 >> f p1

= 1

2π RSCGD +CL + CGS

gm

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

EECE488 Set 6 - Frequency Respose of Amplifiers 15SM

Source Follower Input Impedance

At low frequencies, gmb >>| sCL |

Zin ≈1

sCGS

1+ gm / gmb( )+1/ gmb

∴ Cin = CGSgmb /(gm + gmb ) + CGD (same as Miller)

LmbGS

m

GSin sCgsC

gsC

Z+⎟⎟

⎠

⎞⎜⎜⎝

⎛++=

111

, GDC Neglecting

EECE488 Set 6 - Frequency Respose of Amplifiers 16SM

Source Follower

LC

|| << s,frequencie high At

GS

m

LGSin

Lmb

Csg

sCsCZ

sCg

2

11++≈

At high frequencies, overall input impedance includes CGD in parallel with series combination of CGS and CLand a negative resistance equal to -gm/(CGSCLω2).

EECE488 Set 6 - Frequency Respose of Amplifiers 17SM

Source Follower Output Impedance

ZOUT =VX / IX

=sRSCGS +1gm + sCGS

≈1/gm , at low frequencies ≈ RS , at high frequencies

EECE488 Set 6 - Frequency Respose of Amplifiers 18SM

Source Follower Output Impedance

R2 =1/ gm

R1 = RS −1/gm

L = CGS

gm

RS −1/gm( )

Output impedance inductance dependent on source impedance, RS!

EECE488 Set 6 - Frequency Respose of Amplifiers 19SM

Source Follower Ringing

Output ringing due to tuned circuit formed with CL and inductive component of output impedance.

EECE488 Set 6 - Frequency Respose of Amplifiers 20SM

Cascode Stage

EECE488 Set 6 - Frequency Respose of Amplifiers 21SM

Cascode Stage

f pA =1

2πRS CGS1 + CGD1 1+ gm1

gm 2 + gmb 2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

( )2211

22

22 GSSBDBGD

mbmpX CCCC

ggf+++

+=

π

f pY =1

2πRD CDB 2 + CL + CGD2( )

EECE488 Set 6 - Frequency Respose of Amplifiers 22SM

Differential Pair

EECE488 Set 6 - Frequency Respose of Amplifiers 23SM

Differential Pair

EECE488 Set 6 - Frequency Respose of Amplifiers 24SM

Differential Pair

f p1 ≈1

2π (roN || roP )CL

f p2 =gmP

2πCE

fZ = 2 f p 2 =2gmP

2πCE