哈工大模拟coms第10章-stability and FrenComp

DesignofAnalogIntegratedCircuitsStabilityandFrequencyCompensation1/15/20231Outline1.GeneralConsiderations2.Multi-PoleSystems3.PhaseMargin4.FrequencyCompensation5.FrequencyCompensationofTwo-StageOpAmps1/15/202321.GeneralConsiderationsThecircuitmayoscillateinfeedbacksystems.Oscillationconditions(Barkhausen’sCriteria,巴克豪森判据)1.Atω1,thephaseshiftaroundtheloopissomuchthatthefeedbackbecomespositive;2.Theloopgainisstillenoughtoallowsignalbuildup.1/15/20233GainCrossoverPhaseCrossover在一般反馈电路的处理中，β小于或等于1，且与频率无关；当β<1，幅值曲线会下移，增益交叉点会向原点方向移动，系统更易稳定。因此，常分析βH=H（β=1）的相位图和幅值图。1/15/20234BodePlots(波特图)1.Theslopeofthemagnitudechangesby＋20dB/decateveryzerofrequencyandby-20dB/decateverypolefrequency.

2.Forapole(zero)frequencyωmofatLHP,thephasebeginstofall(rise)atapproximately0.1ωm,experiencesatchangeof-45°(+45)atωm,andapproachesachangeof-90°(+90°)at10ωm.ThatofRHP,changeinversely.LHP:lefthalf-planeatcomplexfrequencyplane;RHP:righthalf-planeatcomplexfrequencyplane1/15/20235波特（Bode）图1、在每个零点频率处，幅值曲线的斜率按20dB/dec变化；在每个极点频率处，其斜率按－20dB/dec变化。2、对一个在左半平面的极点（零点）频率ωm，相位约在0.1ωm处开始下降（上升），在ωm处经历－45°（＋45）的变化，在大约10ωm处达到－90°（＋90°）的变化。右半平面的情况，反之。右半平面的零点对反馈系统的稳定性更加有害，因为它提高增益，但延迟相位。1/15/20236Time-domainresponseofaclosed-loopsystemversusthepositionofpolesExpressingeachpolefrequencyassp=jωP

+σp,theimpulseresponseofthesystemincludesatermexp(jωP

+σP),具有位于右半平面的极点的闭环系统是不稳定的；1/15/20237Feedbacksystemwithone-polefeedforwardamplifierThesystemisunconditionallystableforallnon-negativevaluesofβ1/15/202382.Multi-PoleSystemsTwo-polesystemThesystemisstable,butsmallmargin.1/15/20239Three-polesystemThesystemisnotstable.↓βAdditionalpoles(andzeros)impactthephasetoamuchgreaterextenttheydothemagnitude.1/15/2023103.PhaseMarginHowfarshouldPXbefromGX?letusconsidera“marginal”case,e.g.AtGX,phase=-175°WehavePhaseMargin(PM):definedas

PM=180°+∠βH(ω=ω1)其中，ω1为增益交点频率1/15/202311Howmuchphasemarginisadequate?ForPM=45°，ForPM=60°，ForPM=90°，1/15/2023124.FrequencyCompensationMethodsofincreasingPM减少极点数,PX往外推减小带宽,GX往里推1/15/202313Frequencycompensation:TelescopiccascodeopampshowninFig.belowPoles:Out，A，N，X（Y）1/15/202314FrequencycompensationBodeplot,forβ＝11/15/202315FrequencycompensationMethods:Increaseloadcapacitance,i.e.adjustdominantpole(firstpole).Avoidmirrorpole.Thefirstnon-dominantpolemustbefarfromorigin.(equaltoormorethanunity-gainbandwidth)1/15/202316Frequencycompensation↑Rout→AV↑，虽然ωp，out=(RoutCL)-1降低,由于不影响GX和PX，因此，增大Rout并不能对运放进行补偿IncreasingRoutdoesnotcompensationtheopamp.1/15/202317FrequencycompensationFulldifferentialopamps:Avoidmirrorpole.Onedominantpole(output)

andnon-dominantpole(XorY)atrelativelyhighfrequenciesdueto“shield”ofcommon-gatetransistors.stable1/15/2023185.FrequencyCompensationofTwo-StageOpAmpsPoles:AddapoleforeverystageampilifierX(Y)，E（F），A（B）Twodominantpoles:

E(F),A(B)closetoorigin.Notstable,requiringcompensation.1/15/202319Millercompensation(密勒补偿)增加密勒电容以一个中等电容建立一个低频极点形成“极点分裂”效应当CL>

CC>>CE(gmII=gm9)(millerpole)(outputpole)Weget（补偿前(Cc=0)：）1/15/202320Millercompensation(cont.)密勒补偿中，零点的影响不可忽略右平面的零点减缓增益的下降（增益交点外推），延迟相位（相位交点向原点移动）考虑零点的影响，CC的选取：PM=60°时，GB频率（即近似等于单位增益带宽）处若PM>60°,p2>2.2GB，并由z=10GB令z=10GB时1/15/202321Millercompensation(cont.)消除密勒补偿中零点的方法增加与补偿电容串联的电阻切断补偿电容的前馈通路将零点移到右平面无穷远处，或者左平面并抵消第一非主极点AV=1,Rout=1/gm2

CCAv=-gmIIR21/15/202322SlewofopampswithcompensationPositiveslewrate(红色),whenI1≥ISSNegativeslewrate(青色),whenI1≥

ISSWhenI1<ISSWhenI1<ISS1/15/202323Summary反馈系统存在潜在不稳定性单极点系统是稳定的双极点系统是稳定的，但相位裕度不大三极点（以上）系统是不稳定的，需要相位补偿相位裕度PM＝60deg，可以兼顾稳定性和瞬态反应速度补偿方法：减少极点数减小带宽密勒补偿：需要考虑RHZ1/15/202324二级运放设计实例（optional）约束条件电源电压工艺温度设计描述小信号增益频率响应，增益带宽积GB相位裕度PM输入共模范围（ICMR）输出摆幅转换速率功耗负载电容CL1/15/202325关系方程60degPM要求p2>2.2GB

，else>10GB1/15/202326设计步骤0.确定正确的电路偏置，保证所有晶体管处于饱和区。为保证良好的电流镜，并确保M4处于饱和区（Sx=Wx/Lx）I6=I71/15/202327设计步骤（续）1.根据需要的PM＝60deg求Cc（假定z>10GB）2.由已知的Cc并根据转换速率的要求（或功耗要求）选择ISS（I5）的范围；3.由计算得到的电流偏置值(I5/2),设计W3/L3（W4/L4）满足上ICMR（或输出摆幅）要求，即饱和区条件；4.验证M3处镜像极点是否大于10GB5.设计W1/L1（W2/L2）满足GB的要求6.设计W5/L5满足下IC