On the Operation of CMOS Active-Cascode Gain StageVictor Lu, William Eisenhower, Yun Chiu

Illinois Center forWireless Systems

Active Cascode

Benefits:• High DC gain• High bandwidth• Low power implementation

Issues:• Pole-Zero Doublet• Settling Issues

Pole-Zero Doublet

• Closely spaced pole and zero near unity gain bandwidth of auxiliary amplifier• Zero is from auxiliary amplifier shorting out reducing output resistance• Pole is from cascode output

Settling Concerns

• Pole-Zero doublet can cause slow settling• Rapid settling until regular cascode gain• Slow from there until final value•Rate Depends on relative spacing of doublet•Wider the spread slower the settling•If no doublet, amplifier settles rapidly to final value

Modeling Doublet

ωo= AA dominate pole ωa= AA unity gain bandwidth ωu= cascode unity gain bandwidth x= ω3/ ωo

Canceling Doublet

• It is possible to cancel doublet exactly• Requires ration of unity gain bandwidths so that the cancel out the slow settling component

Simulation Model

Small-signal linear model including some second-order effects

Simulation Results Simulation Results

Closed loop settling behavior for auxiliary amplifier bandwidth of 10 kHz, 100 kHz, 1 MHz, 5 MHz, 9 MHz, 10.95 MHz, 20 MHz, 30 MHzDashed curves are for first-order model

Vo

V2

V1

X

Y

ro2Cgs2

ro1

gm2V2

gm1V1

Co

Cgd2

Cgd1

Cm

-Aa(s)

Cgs1

|Aa(jω)|

ω(log)

|Atot|(log)

~Aa

Ao

At

ωo ωaω3 ω1ω2 ωu

~A1

~A2Doublet

Atot(jω) = Gm,eff(jω)·Ztot(jω)

Out

VB

In

M2

M1

Aa(s)

X

IB

Co

Y

Auxiliary Amp (AA)

ω(log)

|Ztot|(log)

~Aa

ro1

ro

Ro

ωo ωaω3 ω1ω2 ωu

Ztot(jω) = Zo(jω) // (jωCo)-1

|Zo(jω)|

(ωCo)-1

A B

ro

Co/xCo

Co/xCoAaro

A

B

22 2 1

22 2

2 2 1 1 1 1 2 21 1

2 1 2

11

1 1 1

0

om o o a a

uo oam o m o m o m oo o

um oa

rg r r Ak

r rg r g r A g r g rr r

k g r