Datasheet

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ƒ
Z1
+
1
2pR3C6
(19)
ƒ
Z2
+
1
2pR1C8
(20)
ƒ
P1
+
1
2pR5C8
(21)
ƒ
P2
+
1
2pR3C7
(22)
ƒ
INT
+
1
2pR1C6
(23)
ƒ
LC
+
1
2p L
OUT
C
OUT
Ǹ
(17)
R2 +
R1 0.891
V
OUT
* 0.891
(18)
TPS54550
SLVS623A–MARCH2006–REVISEDAPRIL2006
UseoftheSWIFTDesignerSoftwareis
recommendedfordesignswithunusuallyhighclosed
loopcrossoverfrequencies,lowvalue,lowESR
outputcapacitorssuchasceramics,orifthe
designerisunsureaboutthedesignprocedure.
Whendesigningcompensationnetworksforthe
TPS54550,anumberoffactorsneedtobe
considered.Thegainofthecompensatederror
amplifiershouldnotbelimitedbytheopen-loop
Additionally,thereisapoleattheorigin,whichhas
amplifiergaincharacteristicsandshouldnotproduce
unitygainwiththefollowingfrequency:
excessivegainattheswitchingfrequency.Also,the
closedloopcrossoverfrequencyshouldbesetless
than1/5oftheswitchingfrequency,andthephase
marginatcrossovermustbegreaterthan45
Thispoleisusedtosettheoverallgainofthe
degrees.Thegeneralprocedureoutlinedhere
compensatederroramplifieranddeterminesthe
producesresultsconsistentwiththeserequirements
closedloopcrossoverfrequency.
withoutgoingintogreatdetailaboutthetheoryof
ThereareanumberofpopularwaystodesignType
loopcompensation.
3compensationnetworks.Thetheorybehindthese
First,calculatetheoutputfilterLCcornerfrequency
calculationsisbeyondthescopeofthisdocument.It
usingEquation17:
isalwaysbesttotouseanycalculatedcompensation
valuesasthebasisforaninitialdesign,andthen
verifytheactualclosedloopresponse.Theinitial
valuesmaythenbeadjustedtosuittheindividual
designrequirements.TheSWIFTsoftwaredesign
Forthedesignexample,f
LC
=4315Hz.
toolcanalsobeusedtoprovideanintialcircuit
design.
Theclosedloopcrossoverfrequencyshouldbe
greaterthanf
LC
andlessthan1/5oftheswitching
Inthiscircuit,thefirstcompensationzerowassetat
frequency.Also,thecrossoverfrequencyshouldnot
approximately1/2theLCcornerfrequency,withthe
exceed50kHz,astheerroramplifiermaynot
secondzeroslightlybelowthattoincreasethephase
providethedesiredgain.Forthisdesign,acrossover
gainpriortothedoublepoleoftheLCoutputfilter.At
frequencyof13kHzwaschosen.Thisvalueis
theLCcornerfrequency,theoverallphaseresponse
chosenforcomparativelywideloopbandwidthwhile
rapidlydropsby180degrees,soitisimprtantto
stillallowingforadequatephaseboosttoinsure
increasetheinitialphaseof90degreespriortothe
stability.
LCcorner.
Next,calculatetheR2resistorvaluefortheoutput
Thetwocompensationpolesaresethighenoughto
voltageof3.3VusingEquation18:
tonotcauselossofphasemarginattheclosedloop
crossoverandlowenoughtonotcausetheerror
amplifiergaintoexceedtheunitygainbandwidth
limitoftheinternaloperationalamplifier.The
ForanyTPS54550design,startwithanR1valueof
integratorfrequencyisthenchosentosettheoverall
1.0kΩ.R2isthen374Ω.
gainandcrossoverfrequency.
Nowthevaluesforthecompensationcomponents
Thisresultsinthefollowingpoleandzero
thatsetthepolesandzeroesofthecompensation
frequencies:
networkcanbecalculated.AssumingthatR1>R5
f
Z1
=2340Hz
andC6>C7,thepoleandzerolocationsaregiven
byEquation19throughEquation22:
f
Z2
=1591Hz
blank
f
P1
=120kHz
blank
f
P2
=159kHz
blank
f
INT
=234Hz
blank
21
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