cmos模拟集成电路设计东南48讲课件及配套chapter3op performance analysis

ogIC

Chapter3OPPerformance Chapter3OP

BodePM&GMUGBPMTransientresponseby1(t)stepNon-idealOL-OPbased

,,

,,

A(j) AV2 V01 1j/ 12

AV

22许

arctg145o4第一个极点频率下，增益衰减-3dB,又称为-3dB带宽，在此极点频率下产生45迟滞相移， 频率特性–

A(j)

jAV0

j V

j/ 1j/

>>p，则 A(j)

AV0p1

1,高频:>>p，则

AV(j)

AV0p1(

p2

PM&GM

:

:只有特定条件的频率特性才带来问题,对应的状态为：,

系统稳定性定量判据PM&闭环收敛:PM/GM达标(充分必要条件)

如PM=45,60UGB(UnitGainBandwidth,orGBW)频率下环路离开正反馈的相位距离，越大越稳定;低频下负反馈连接(必须)，相移为零，提高相位要求在UGB频率下的相移尽可能小。PM与UGB密切相关； 如GM=-10dB，-20dB等

益T=FAV(s)。闭环系统主要环路增益T=1(0dB)时的相移(或PM)。因无源反馈，因此有F1,即FA(j)1 A(j)1 ,, =UGB(orGBW

F0

利用F(s)VFB 1 R1R21s(R1//R2

F1s/z z01s/:

F(s)VFB

F 01s/

no

PM<0对应系统发散条件；系统中存在的极点，很容易使PM降低甚至变性为负,频率补偿

UGB的计算1V开环的单位增益带宽UGB(即单位负反馈环路AV

-

1j/

/

-

f-

-

A(j)

j V(1j/p1)(1j/p2 1j/V1/p1/p22

UGB m

21+4(GBW)2221+4(GBW)22

21+421+4

UGB=GBW m=6.0, m=2.0,大 m=1.0, m=0.5,

误差增大,近似可用;p2太小,误差显著.

PM计算利用1pole&2poles

(1j/PM180oarctg(UGB)180oarctg( )

V1A(j)jGBW 2 1j/2PM180o[90o

)]

arctg2o

A(j)j 1j/

arctg12 1j/2PM

actg(UGB

UGBandPMbyOpenloopGeneral

Open

21+2s+1 2

1()2+j2 UGB

1212221)122V 1(UGB/)2 (UGB/)2 212221)122V2212221)122V221 2V0(UGB/)20 PM&UGBobtainedbyopenloopgeneralModel,butdescribedbyclosedLoopformparameters

V

s s2 2V0 V0 F=1CLconsidered,AV0_CL1/F=1,1/AV00,OL:2separatedrealA(s)0_CL

GBW

p V V

Duetop2effect,UGB<GBW,ifUGBGBWselected,approximatePMPM180o-90o-arctg

2CL0

)arctg

2CL0

)arctg(42

PMevaluationbymoreaccuratemixedButterworthresponsebyCL=1ButterworthresponsebyCL=1IfCL=1/2,orCL2=1/2,thus

PMarctgPMarctg 2p2TheevaluationmodeforPMisonlyvalidforp2>>GBW,orCL>>1/2;ThemodelismorebriefthanOL

x

x(UGB)2 44+1-2222[1+1-1]PMPM2 )4 4

4 1-4 1-425-5-

=1,PM

)o

PM

8-8-

)GeneralExpressionforGBW&

ByClosedLoopQ,(eitherinseparatedpoleor),andGBW=FAV0UGBUGB24)-11 2GBW2PM2 2]411+4Q4]2Slow

Fast

CL 1

1 <22 22UGB 1+Q2

22UGB PM=arctg[1

22

OL

开环和闭环的瞬态响应特性不同,极(零)点变化！

VV

A(s)Vo(s)

AV(s)

1 1s/

1s/

Vin(s)L[1(t)]1/

Vo(s)

1s/

AV0ps(sp)

(1 V0 s

V(t)L1[V(s)]1(t) VV(t)1(t) V(t)1(t) oVz

t1ln[1Vo

Vo(t)AV01(t)从V(

)~V

tttRCln

AV0V2(t2 tRCln(0.9/0.1)差越小，则延迟越短。(线性范围内成立,对闭环更有用)越大，小信号变化的延迟越小。Q:小信号闭环快?

V(s)

1 V V0ssps V

2

s

spV pV

[1(1

)1(1

p2 s s

(1p1)e

z

(1p2)eep2tV(t)1(t) p1t) ep2t V0p p

p

ep1t

p

ep2t

共轭复极点下的瞬态响应-Transientresponseunderstepinputwith

1111p20

p pp

11

0

1

t)j

1

j 1

ep2te0t 12t)j 121p21

V(t)1(t)

ep1t

ep2t

p2p1

1p211(t)A

12t) 12设定

1111

求出

11

Thetransientresponseofoutputvoltagebystepdrivingandunderconjugatepolesconditionswith<1:初始相位与PM -t

1-Vo(t)

0sin(1-0t

arctg( Large,ThemomentwhenLarge,00

1-1-pOvershot&oscillationobservedunderOSVo,peak-

exp(- When1OSSmall!

Twomethodologiesformulti-stage

OLCLMulti-stageOP->AV(s)->Pole,zero,Gain,Freq.CompensationmethodsusedtoadjustPoles/zeroswithinteriorFBorloadeffect,thusopenloopAV(s)ischangedforsufficientPMtoguaranteethestabilityofclosedloopAvf(s);CLOLmethodology,suchasButterworthFilterresponse)CloseLoopstableOPneeded->OpenLoopOP->AV(s)->predictiontheLocationofthepolesandzeros(or&->finallytoestimatetheGain,PMforsystemPolenumberGainstagenumber(+1ormore).Generalgainstages:2 umgainstages:3

OpenloopOP:primitiveforClosedloop

OP->Structure,Parameters->DC,AC,ACpropertiesismostimportant,allpolesshouldbeAllcoefficientofB(s)indenominatorofAV(s)cannotbeRHPzerosshouldbeavoidbypushawayorturnbacktoLHP,forlessPMlost;LoopwithinUGB,onlyonenetpolezerosusedtocompensatepoleforsatisfyingonenetpoledemand;allsecondaryLHPpoles&RHPzerosshouldbefarawayUGB;CL-DFcannotbetoosmall,Qcannotbetoolarge;CLOLPM=60isselectedinbalancespeed&stabilityrequirement.

整形（FrequencySha ）应用。（初-中-高级应用）

一种RC反馈实例–信号处理(t)与控制(f)

如图电压并联负反馈111G(s)

虚地反馈等同负载效应

的极零点，实现某种信号处理(如滤波)，或用于更大的反馈系 ,

反馈网络F简单，不产生附加的极点和零点，解决F=1下的问题可 )

B类应用特点：以反馈环路FB为的闭环应用，FB改造环路系统(传输特性和零极点分布d的控制)，使完整的环路系

系统环路UGB频率下有PM，系统稳定。显然，环路带宽越低，的工作条件和资源约束下，尽量提高增益、带宽和相位，是

H(s)H(s)H(s)11sR 1R1R21s(R1//R2H(s)1H(s)11s(R1R2

fpfpH(s)1s(R1H(s)1H(s)1H(s)1R1R21s(R1//R2C1C21s(R1R2)(C1//C2

2

(先RC并，后RC串H(sH(s)

1s(RCRCRC)s2RRC

1 H(s) zA 1zB/有源H(s)zA z zB调节A,BRC-Block

Lowdropoutregulator

Appendix ButterworthFilter–2order G(s)

QCL121 ) [G(s)/G]1

0_

UGBGBW

arctgUGBarctg1