Frequency Response ofFrequency Response of Amplifiers (Ch. 6)p

김 영 석김 영 석

충북대학교 전기전자컴퓨터공학부

2013.3.1. .

Email: kimys@cbu.ac.kr

전화: 043-261-3137

전자정보대학 김영석 1

6.1 General ConsiderationsMiller effect

전자정보대학 김영석 2

Association of poles with nodesAssociation of poles with nodes

Cascade of amplifiers

transfer function

전자정보대학 김영석 3

MOSFET Capacitance

C1 = Oxide Capacitance = WLCOX

C2 = Depletion Capacitance = W Lεsi/Wd, Wd=(2εsi *2ΦF /qNsub)1/2

C3, C4 = Overlap Capacitance = Cov*W

C5, C6 = Junction Capacitance = Cj + Cjsw

전자정보대학 김영석 4

MOSFET Resistance

전자정보대학 김영석 5

BJT Resistance

전자정보대학 김영석 6

6.2 Common-Source stageHigh-frequency model of a CS stage(λ= 0)(Using Miller Theorem)

Mid-band Gain:

At the input node:

l iGDvGSin CACC )1( −+=

Dmv RgA −=

• pole is

])1([11

GDDmGSSinSin CRgCRCR

w++

==

At the output node:

• pole is

GDDBGDvDBout CCCACC +≈−+= − )1( 1

11w

T f f ti

][ GDDBDoutDout CCRCR

w+

==

Transfer function

mzDm

out ghwsRg

V−− )1(

)(GD

mz

outin

z

in

out

Cgwwhere

ws

wss

V+=+=

++= zs

)1)(1()(

전자정보대학 김영석 7

Calculation of the zero in a CS stageCalculation of the zero in a CS stage

inoutzin

out VfiniteforVsVVZero 0 ,0)(: =∴=

ZeroPlaneHalfRightCgsVgsCV

nodeoutputatKCL

mzmzGD ) (:

11 RHP+=∴=CGD

전자정보대학 김영석 8

Zero 의미: Feedforward path through CGDZero 의미 Feedforward path through CGD

Main Path 신호 위상 반전

Feedforward Path 신호 위상 변화 없음, 높은 주파수에서 커짐, Main Path 신호와 상쇄되는 주파수가 Zero

RHP Zero로 Stability 문제 일으킴

전자정보대학 김영석 9

RHP(Right-Half-Plane) and LHP(Left-Half-Plane) Zero 의미의미

)/1()/1(:)/1()/1( : RHPzRHPz

wjwwsZeroLHPwjwwsZeroRHP

+=>+−=>−

)/1()/1( : LHPzLHPz wjwwsZeroLHP +=>+

전자정보대학 김영석 10

정확한 Transfer Function 구하기:

Equivalent circuit of CS stage

전자정보대학 김영석 11

전자정보대학 김영석 12

Open-Circuit Time Constant 방법으로 Dominant Pole 구하기

원리:원리:

+++=++=s

ssssD ττττττ )(1)1)(1( 2212121

∑=∴

=≈≈+=++≈p

w

kHzsmsmsgewss πττττ

1

))1(2,1.0,1.,.(1)(1 2121

∑∴

ii

pwτ

전기전자컴퓨터공학부 김영석 13

Open-Circuit Time Constant 방법으로 Dominant Pole 구하기

CGS: Open CGD/CDBCGS: Open CGD/CDB

GSSGSGSGSSX

XGSX CRCRR

IVRR ===== τ,

CGD: Open CGS/CDB

DGSmoutXSGS

RVVVVRVgVIRV

)1( ,

+−==

DmSX

XGDX

DmGSoutGSX

RgRIVRR

RgVVVV

)1(

)1(

+===

+=−=

CDB: Open CGS/CGD

GDDmSGDGDGD CRgRCR )1( +==τ

DBDDBDBDBDX

XDBX CRCRR

IVRR ===== τ,

DBDGDDmSGSSp CRCRgRCR

w+++

=∴)1(

1

전기전자컴퓨터공학부 김영석 14

Input impedance

I

ZsC

Z XGS

in

1

||1=

sCCRVZ

sCRVgI

sCIVZ

DBGDDXX

DBDXmX

GD

XXX

)(1

)1||)(( :

++==∴

−+=

RgsCRandsCCRFreqLowsCRRgsCI

DmDBDDBGDD

DBDDmGDXX

1)1|| 1|)(| ( @

)1(+<<<<+

++

C itiP i il

FreqHighsCRg

ZGDDm

X

@

:)1(

1+

≈ CapacitivePrimarily

sCR

gZ

DBD

mX

1||||1≈

전자정보대학 김영석 15

Output impedanceOutput impedance

If RS is relative large, the effect of RS is neglected.

output pole

11

,GDGS

GDGSeq

GDGS

GDXmeqXX

CCVCC

CCCCC

CVgsCVI+

=+

+=

||11

mGD

GDGS

eq

GDGS

GDmeq

X

XX gC

CCsC

CCCgsCI

VZ +=

++

==

))(||(

1

DBeqmGD

GDGSD

out

CCgCCCR

w+

+=

전자정보대학 김영석 16

6.3 Source followers

Source followerSource follower

Mid Band Gain

mmb ggA /1

mbm

m

mbm

mbv gg

ggg

gA+

=+

=/1/1

Transfer Function

zmout wsgsV /1)( +≈

pmbmin wsggV /1)(

++

전자정보대학 김영석 17

Solving Dominant Pole using open-circuit time constant method

CGD: Open CGS/CLCGD: Open CGS/CL

GDSGDGDGDSX

XGD CRCRR

IVR ==== τ,

CGS: Open CGD/CL

GSX

XmX

CCRVR

VgI =1

CL: Open CGS/CGD

m

GSGSGSGS

mX

XGS g

CCRgI

VR ==== τ,1

LLLL

XL

XmmX

gCCR

gIVR

VgVgI

====

=−=

τ,11

mmX ggI

w =∴1

m

GSLGDS

p

gCCCR

w+

+=∴

전자정보대학 김영석 18

Calculation of the zero in a source follower

)1)((

0)(,0

11 −=

== Lout

VgV

CIV

)0)/1(:(

))(( 11

=+−=−=∴ zzzGS

mz

GSzm

wsZerowCgs

CsVgV

Q

ZeroLHPGSC

전자정보대학 김영석 19

Input impedance

++= )1||1)((

sCgsCIgI

sCIV

CNeglect

XmX

XX

GD

+++==∴

1)1(1sCgsC

gsCI

VZ

sCgsCsC

LmbGS

m

GSX

Xin

LmbGSGS

+=++≈

<<1

)(

11)1(1|:| @

gCgggg

sCZ

gsCFreqLow

bmbbb

m

GSin

mbL

+=−=

+=

+

)()1( .)(

)(

gCACCthatNoteCgC

gsCgg

gggsC

mbGSvGSinGS

mbin

mbGS

mbm

mbmbmbGS

++≈

>>++

11|:|igh @

gZ

gsCFreqHgggg

m

mbL

mbmmbm

Resistance Negative ⇑

++≈ 2sCCsCsCZ

LGSLGSin

전자정보대학 김영석 20

참고

+=+=+=1)11()1()1(

GSmSmSX CssC

gZrgZR πβ

ResistanceNegative⇑

+=1 2

GS

m

CsCg

Cs

ResistanceNegative

+=

⇑

)11(

GSmX Ls

sCgR

ResistancePositive⇑

+= GS

m

CLgLs

s ss⇑

전기전자컴퓨터공학부 김영석 21

Output impedanceOutput impedance

전자정보대학 김영석 22

6.4 Common-gate stageCG stage at high frequencies

Mid Band Gain

DmbmmbmS

mbm

s

out

in

s

in

outv Rgg

ggRgg

vv

vv

vvA )(

)/(1)/(1

+•++

+===

Transfer Function

mbmSsinin

≈ Dout RsV 1)(

+==

++++

SBGSSin

outinmbmSin

CCCCR

w

wswsggRV

,)1||(

1)/1)(/1()/(1

)(

+==

+

DBDGDDD

out

Smbm

S

CCCCR

w

Cgg

R

,1

)||(

Input Impedance

Band WideEffect Miller No =>DD

sCRZ

rggZ

ggZ

DDL

ombm

L

mbmin

1||,)(

1=

++

+=

전자정보대학 김영석 23

6.5 Cascode stage

High-frequency model of a cascode stageHigh frequency model of a cascode stage

Cascode stage = CS stage (input impedance) + CG stage (suppressing the miller effect)

전자정보대학 김영석 24

6.6 Differential pair

Differential pair & Half-circuit equivalent: CS와 동일Differential pair & Half circuit equivalent: CS와 동일

Differential pair with current-source loads

전자정보대학 김영석 25

Differential pair with active current mirror

Mid B d G iMid Band Gain

)||( oPoNmNin

outv rrg

VVA ==

Transfer Function

)/1()(t wsAV +

PoleOutput :)||(

1)/1)(/1(

)/1()(

1

21

p

pp

zv

in

out

Cw

wswswsAs

VV

=

+++

≈

PoleMirror :)/1(

1)||(

2EmP

p

LoPoNp

Cgw

Crr

=

Path(M1,2)Fast and 4)Path(M1,3, Slowby Zero:222p

E

mPz w

Cgw ==

전자정보대학 김영석 26

Zero 구하기

))(1(

0:

zEmPE

out

isCg

V

VZero

−+

=

=

2zEmP

mPEmP

zEmP

gsCg

igVgi

g

+−

==

222pz

E

mPz ww

Cgs −=−=−=

전자정보대학 김영석 27