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1、ControlLoopCookbookLloydH.DixonINTRODUCTION:KEA(S)ErroramplifierwithcompensationSwitchingpowersuppliesuseclosed-loopKMODPulsewidthmodulatorfeedbacktoachievedesignobjectivesforlineandloadregulationanddynamicresponse.KPWRPowerswitchingtopologyFortunately,theclosed-loopsystemsusedinKLC(S
2、)Outputpowerfilterswitchingpowersuppliesareusuallynotverycom-plicated,permittingtheuseofsimpleanalyticalKFBFeedbacktechniquestoachieveloopstabilization.Asimpli-AlthoughthepulsewidthmodulatorandpowerfiedversionoftheNyquiststabilitycriteriacanbeswitchingcircuitarereallynotlinearelements
3、,theirusedbecauseunitygaincrossoveroccursonlystate-spaceaveragedlinearequivalentscanonceinthegainvs.frequencycharacteristic.Bodebeusedatfrequenciesbelowtheswitchingplotsprovideasimpleandpowerfulmethodofdis-frequency,fS.playingandcalculatingtheloopgainparametersOpen-loopandclosed-loopg
4、ain:(seeAppendixB).ThispaperbeginswithaquickTheopen-loopgain,T,isdefinedasthetotalreviewofbasiccontrollooptheory.gainaroundtheentirefeedbackloop(whethertheLinearControlLoopTheoryloopisactuallyopen,forpurposeofmeasurement,AsshowninFigure1,apowersupplyfeedbackorclosed,innormaloperation)
5、.loopcanbedescribedintermsofsmall-signallin-T(s)=KEA•KMOD•KPWR•KLC•KFB(1)earequivalentgainblocks.The(s)appendedtocertaingainblocksindicatesthatthegainvariesasClosed-loopgain,G,definestheoutputvs.afunctionoffrequency.controlinputrelationship,withtheloopclosed:Figure1.-FeedbackLoop5-1Co
6、ntrolLoopCookbook1T“Gain”elementsasshowninFigure1neednotG(s)=(2)KFB1+Thavethesameunitsfortheiroutputandinput(suchasVolts/Volt).IfFig.1isacurrentmodecon-Atlowfrequencies,open-loopgainTisnor-trolloop,“Output”isacurrentsource,andKFBismallyverymuchgreaterthan1,sothatclosed-loopmostlikelya
7、currentsenseresistor.KFB“gain”isgainGapproachestheideal1/KFB.Athigherfre-thenexpressedinVolts/Amp,andclosedloopgainquencies,Tdiminishes,mostlybecauseoftheG(s)isactuallyatransconductance(Amps/Volt).low-passfiltercharacteristicKLC(S).ThefrequencyPulsewidthmodulatorKMODhasitsgainwhereTha
8、sdimi
