电源反馈设计速成篇之八建模篇(Peak Current Mode)

电源反馈设计速成篇之八:建模篇(PeakCurrentMode)图1为PeakCurrentMode等效小信号模型.Vg为输入电压,Vo为输出电压,io为输出电流,iL为电感电流,d为占空比,Vc为反馈控制电压.Gvg为Vg到Vo的传递函数,Gvd为d到Vo的传递函数,Gig,Gio,Gid分别为Vg,io,d到iL的传递函数,Zo为开环输出阻抗,Fm为等效调制比(VoltageMode就是三角波幅度倒数,CurrentMode是电压和电流的综合),Kf和Kr是考虑了Vg和Vo的扰动影响,其值很小,一般忽略没有大的影响.Hv是电压反馈环,Hi是电流采样系数,负号表示负反馈.如果是采样电阻的CIC(CurrentInjectionControl)法,Hi就是采样电阻,如果是电感电压的SCM(StandardCurrentMode)法,Hi要根据具体电路求得.CurrentMode的精髓是要知道电感的di/dt.Gvg,Gvd,Zo,Gig,Gid,Gio这些传递函数都可以由VoltageMode得到.不再赘述.GvgGvdFmGigGidGioZoHe-HiKfKr-HvVoVgiLiodVc图1.PeakCurrentMode等效小信号模型He是等效采样保持传递函数1)(−⋅=⋅sTsseeTssHTs为开关周期.对定频后沿调制(ConstantFreqeuncyTrailingEdgeModulation),Kf,Kr如下表:BuckBoostBuck-BoostKf)21(DLRDTis−−LRTis2−)21(DLRDTis−−KrLRTis2LRTDis2)1(2−LRTDis2)1(2−对定频前沿调制(ConstantFreqeuncyLeadingEdgeModulation),Kf,Kr如下表:BuckBoostBuck-BoostKfLRTDis22−LRTis2LRTDis22−KrLRTis2−)211()1(DLRTDis−−⋅−)211()1(DLRTDis−−⋅−Ri为电流取样电阻,即Hi.可以证明,不论Ri去多大,电流内环都一样,因为Fm可以和Ri对消．一般Ri由功耗等决定．定义sensncmTSSTSmF)(11+==,necSSm+=1Ts为开关周期,Se为外加斜坡补偿三角波幅值,Sn为电感电流采样等效三角波幅值.mc为衡量斜坡补偿效果系数,mc=1即Se=0,为纯电流控制，mc1既外加斜坡补偿电感电流采样等效三角波幅值,退化为VoltageMode.一般mc=1.5-2.Hv为设计参数，一般用Type2补偿，零点决定响应快慢，极点补偿ESR零点，ＲＨＰ零点，或1/2开关频率，三者取其低的值.以上为CCMMode,如果为DCMmode,则开环参数为DCMmode下的各个参数,不再赘述.DCMmode每次电流归零,没有采样保持,可认为He=0,Kf,Kr如下表:BuckBoostBuck-BoostKfLRDTis−LRDTis−LRDTis−KrLRDTis00图1为整个系统的信号流图,在推导小信号公式时有很多变量为零,可大大简化.以控制到输出传递函数为例,图2为buck电路,图3为buck小信号模型和控制到输出信号流图.LRLRCCRVincap图2.BuckIc*dd*Vap/D1apcDLRLRRCCFmdvcKrvoHe(s)-Ri图3.Buck小信号模型和控制到输出信号流图可以求得电流内环开环回路增益Ti为)()(sGsHHFTideimi⋅⋅⋅=,电阻取样Hi=Ri,否则要另行计算,和具体电路有关.当电流内环闭环时,控制到输出传递函数Goc为)(1)(sGFKTsGFGvdmrivdmoc⋅⋅−+⋅=电压回路增益Tv为)()(sGsHFTvdvmv⋅⋅=,Hv(s)为要设计的反馈部分.电压外环回路增益T2为ivTTT+=12,根据T2来看相位和幅值裕量.电流环闭合后输出阻抗Zoicl为givdmeivdooiclVTsGFsHHsGsZZ⋅+⋅⋅⋅⋅+=)1()()()()(,Zo(s)为开环输出阻抗.电流环和电压环都闭合后输出阻抗Zovcl为ivdmrvdmvoiclovclTsGFKsGFsHZZ+⋅⋅−⋅⋅+=1)()()(1例子Buck电路:Vg11:=L37.5106−⋅:=Rc0.02:=C400106−⋅:=Fs50103⋅:=Vo5:=R1:=Ri0.33:=SnVgVo−LHi⋅:=Sn5.28104×=Fmmc()1mcSn⋅Ts⋅:=mc设为变量,对Hv零点和极点的选取:选择wzc使Settlingtime为0.5ms,wzc10.5103−⋅:=wzc2103×=选择wpc为ESR零点,RHP零点,1/2开关频率,三者的低频:wZESR1.25105×=ws2π⋅Fs⋅:=0.5ws1.571105×=因没有RHP零点,ESR零点比1/2开关频率低,取wpcwZESR:=wpc1.25105×=Rx103:=Ry103:=Hvswi,()RyRxRy+wis1swzc+1swpc+⋅:=KrTsRi⋅2L⋅:=Kr0.088=KfD−Ts⋅Ri⋅L1D2−⎛⎜⎝⎞⎟⎠⋅:=Kf0.062−=图4为电流内环闭环时,控制到输出传递函数Goc,参变量mc为1,1.2,1.5,2,4.Mc=1.5–2时系统相位和幅值变化平稳.选取mc=1.5.变化wi不会改变Hv相位,选取wi以满足相位和幅值裕量要求.图5给出了T2和wi关系.选取wi=40000,剪切频率fc=13253Hz,相位和幅值裕量55degree,6dB.图6为求得反馈部分电阻,电容值后电流内环闭环时,控制到输出传递函数Goc,mc=1为纯电流控制,mc=1.5为外加斜坡补偿的优化设计.图7为电流环闭合后输出阻抗Zoicl,mc=1为纯电流控制,mc=1.5为外加斜坡补偿的优化设计.图8为电流环和电压环都闭合后输出阻抗Zoicl,mc=1为纯电流控制,mc=1.5为外加斜坡补偿的优化设计.图9-11分别为mc=1时的PSPICE仿真结果,用来验证公式的正确.101001.1031.1041.1051.106604020020gainGoc2iπ⋅fn⋅1,()()gainGoc2iπ⋅fn⋅1.2,()()gainGoc2iπ⋅fn⋅1.5,()()gainGoc2iπ⋅fn⋅2,()()gainGoc2iπ⋅fn⋅4,()()fn101001.1031.1041.1051.106200150100500180−phaseGoc2iπ⋅fn⋅1,()()phaseGoc2iπ⋅fn⋅1.2,()()phaseGoc2iπ⋅fn⋅1.5,()()phaseGoc2iπ⋅fn⋅2,()()phaseGoc2iπ⋅fn⋅4,()()fn图4.电流内环闭环控制到输出传递函数Goc101001.1031.1041.1051.106603003060gainT22iπ⋅fn⋅1.5,10000,()()gainT22iπ⋅fn⋅1.5,20000,()()gainT22iπ⋅fn⋅1.5,40000,()()gainT22iπ⋅fn⋅1.5,100000,()()gainT22iπ⋅fn⋅1.5,200000,()()fn101001.1031.1041.1051.10630025020015010050180−phaseT22iπ⋅fn⋅1.5,10000,()()phaseT22iπ⋅fn⋅1.5,20000,()()phaseT22iπ⋅fn⋅1.5,40000,()()phaseT22iπ⋅fn⋅1.5,100000,()()phaseT22iπ⋅fn⋅1.5,200000,()()fn图5.电压外环回路增益T2和wi关系1101001.1031.1041.1051.10680604020020gainGoc2iπ⋅fn⋅1,()()gainGoc2iπ⋅fn⋅mc,()()fn1101001.1031.1041.1051.106200150100500180−phaseGoc2iπ⋅fn⋅1,()()phaseGoc2iπ⋅fn⋅mc,()()fn图6.电流内环闭环控制到输出传递函数Goc(mc=1,1.5)1101001.1031.1041.1051.106403020100gainZoicl2iπ⋅fn⋅1,()()gainZoicl2iπ⋅fn⋅mc,()()fn1101001.1031.1041.1051.106806040200phaseZoicl2iπ⋅fn⋅1,()()phaseZoicl2iπ⋅fn⋅mc,()()fn图7.电流环闭合后输出阻抗Zoicl(mc=1,1.5)1101001.1031.1041.1051.10680604020gainZovcl2iπ⋅fn⋅1,wi,()()gainZovcl2iπ⋅fn⋅mc,wi,()()fn1101001.1031.1041.1051.1062001000100180−phaseZovcl2iπ⋅fn⋅1,wi,()()phaseZovcl2iπ⋅fn⋅mc,wi,()()fn图8.电流环和电压环都闭合后输出阻抗Zovcl(mc=1,1.5)图9.Pspice结果:电流内环闭环控制到输出传递函数Goc(mc=1)图10.Pspice结果:电流环闭合后输出阻抗Zoicl(mc=1)图11.Pspice结果:电流环和电压环都闭合后输出阻抗Zovcl(mc=1)