- 28 -`

AUGUST08,2012|DATASHEET| Rev3.1

IR3894

12AHighlyIntegratedSupIRBuck

Single‐InputVoltage,SynchronousBuckRegulator

PD‐97745

OutputCapacitorSelection

Thevoltagerippleandtransientrequirements

determinetheoutputcapacitorstypeandvalues.

Thecriteriaisnormallybasedonthevalueofthe

EffectiveSeriesResistance(ESR).Howevertheactual

capacitancevalueandtheEquivalentSeriesInductance

(ESL)areothercontributingcomponents.

Thesecomponentscanbe

describedas:

() () ()

()

(16)

8* *

ooESR oESL oC

oESR L

in o

oESL

VV V V

VIESR

VESL

  





















Where:

ΔV

=OutputVoltageRipple

ΔI

=InductorRippleCurrent



Sincetheoutputcapacitorhasamajorroleinthe

overallperformanceoftheconverteranddetermines

theresultoftransientresponse,selectionofthe

capacitoriscritical.TheIR3894canperformwellwith

alltypesofcapacitors.

Asarule,thecapacitormusthavelow

enoughESRto

meetoutputrippleandloadtransientrequirements.

Thegoalforthisdesignistomeetthevoltageripple

requirementinthesmallestpossiblecapacitorsize.

Thereforeitisadvisabletoselectceramiccapacitors

duetotheirlowESRandESLandsmallsize.EightofTDK

C2012X5R0J226M

(22uF/0805/X5R/6.3V)capacitorsis

agoodchoice.

Itisalsorecommendedtousea0.1µFceramiccapacitor

attheoutputforhighfrequencyfiltering.

FeedbackCompensation

TheIR3894isavoltagemodecontroller.Thecont rolloop

isasinglevoltagefeedbackpathincludingerroramplifier

anderrorcomparator.Toachievefasttransient

response

andaccurateoutputregulation,acompensationcircuitis

necessary.Thegoalofthecompensationnetworkisto

provideaclosed‐looptransferfunctionwiththehighest

0dBcrossingfrequencyandadequatephasemargin(greater

than45

).

TheoutputLCfilterintroducesadoublepole,‐40dB/decade

gainslopeaboveitscornerresonantfrequency,andatotal

phaselagof180

.TheresonantfrequencyoftheLCfilteris

expressedasfollows:

(17)



 





Figure25showsgainandphaseoftheLCfilter.Sincewe

alreadyhave180

phaseshiftfromtheoutputfilteralone,

thesystemrunstheriskofbeingunstable.

Phase

Frequency

-180

0dB

-40dB/Decade

-90

Gain



Figure25:GainandPhaseofLCfilter

TheIR3894usesavoltage‐typeerroramplifierwithhigh‐gain

(110dB)andhigh‐bandwidth(30MHz).Theoutputofthe

amplifierisavailableforDCgaincontrolandACphase

compensation.

TheerroramplifiercanbecompensatedeitherintypeIIor

typeIIIcompensation.TypeIIcompensationisshownin

Fig.

26.Thismethodrequiresthattheoutputcapacitorshave

enoughESRtosatisfystabilityrequirements.Iftheoutput

capacitor’sESRgeneratesazeroat5kHzto50kHz,thezero

generatesacceptablephasemarginandtheTypeII

compensatorcanbeused.



- 29 -`

AUGUST08,2012|DATASHEET| Rev3.1

IR3894

12AHighlyIntegratedSupIRBuck

Single‐InputVoltage,SynchronousBuckRegulator

PD‐97745

TheESRzerooftheoutputcapacitorisexpressedas

follows:

(18)

ESR

π *ESR*C

 



OUT

VREF

POLE

E/A

Frequency

Gain(dB)

H(s) dB

Comp



Figure26:TypeIIcompensationnetwork

anditsasymptoticgainplot

Thetransferfunction(V

out

)isgivenby:

( ) (19)

out IN

VsRC

VZsRC



     



The(s)indicatesthatthetransferfunctionvariesasa

functionoffrequency.Thisconfigurationintroducesa

gainandzero,expressedby:



(20)

(21)

2* *



 

 



Firstselectthedesiredzero‐crossoverfrequency(F

):



(22) and F 1/5~1/10 *

oESR s

FF F



UsethefollowingequationtocalculateR3:

** *

(23)

osc o ESR

in LC

VFF R

 



Where:

=MaximumInputVoltage

osc

=AmplitudeoftheoscillatorRampVoltage

=CrossoverFrequency

ESR

=ZeroFrequencyoftheOutputCapacitor

=ResonantFrequencyoftheOutputFilter

=FeedbackResistor



TocanceloneoftheLCfilterpoles,placethezerobeforethe

LCfilterresonantfrequencypole:

75 % *

0.75* (24)

zLC





 



Useequation21tocalculateC3.

OnemorecapacitorissometimesaddedinparallelwithC3

andR3.Thisintroducesonemorepolewhichismainlyused

tosuppresstheswitchingnoise.

Theadditionalpoleisgivenby:

(25)

2* *

POLE



 





Thepolesetstoonehalfoftheswitchingfrequencywhich

resultsinthecapacitorC

POLE

:

(26)

POLE

*R *F



  





Forageneralsolutionforunconditionalstabilityforanytype

ofoutputcapacitors,andawiderangeofESRvalues,we

shouldimplementlocalfeedbackwithatypeIIIcompensation

network.Thetypicallyusedcompensationnetworkfor

voltage‐modecontrollerisshowninFig.27.

- 30 -`

AUGUST08,2012|DATASHEET| Rev3.1

IR3894

12AHighlyIntegratedSupIRBuck

Single‐InputVoltage,SynchronousBuckRegulator

PD‐97745

OUT

REF

Frequency

Gain (dB)

|H(s)| dB

Comp

Figure27:TypeIIICompensationnetwork

anditsasymptoticgainplot

Again,thetransferfunctionisgivenby:

out

 )(



ByreplacingZ

andZ



accordingtoFig.27,thetransfer

functioncanbeexpressedas:





33 4 4 5

52 3 3 44

(1 ) 1

()

()1 (1 )

(27)

sR C sC R R

RC C sR sRC















 















Thecompensationnetworkhasthreepolesandtwo

zerosandtheyareexpressedasfollows:

0(28)

(29)

2* *

(30)

2* *



 

 

  











445 45

(31)

2* *

(32)

2* *( ) 2* *

CRR CR





 

  





Crossoverfrequencyisexpressedas:

* * * (33)

2* *

osc o o

FRC

VLC







Basedonthefrequencyofthezerogeneratedbytheoutput

capacitoranditsESR,relativetocrossoverfrequency,the

compensationtypecanbedifferent.Table3showsthe

compensationtypesforrelativelocationsofthecrossover

frequency.

ABLE3:DIFFERENTTYPESOFCOMPENSATORS

Compensator

Type

ESR

vsF



TypicalOutput

Capacitor

TypeII F

<F

ESR

<F

/2 Electrolytic

TypeIII F

<F

ESR

 SPCap,Ceramic



Thehigherthecrossoverfrequencyis,thepotentiallyfaster

theloadtransientresponsewillbe.However,thecrossover

frequencyshouldbelowenoughtoallowattenuationof

switchingnoise.Typically,thecontrolloopbandwidthor

crossoverfrequency(F

)isselectedsuchthat:





F F * 1/10~1/5





TheDCgainshouldbelargeenoughtoprovidehigh

DC‐regulationaccuracy.Thephasemarginshouldbegreater

than45

foroverallstability.

Forthisdesignwehave:

=12V

=1.2V

osc

=1.8V(ThisisafunctionofVin,pls.seefeedforward

section)

ref

=0.5V

=0.51uH

=8x22uF,ESR≈3mΩeach

Itmustbenotedherethatthevalueofthecapacitanceused

inthecompensatordesignmustbethesmallsignalvalue.

Forinstance,thesmallsignalcapacitanceofthe22ufcapacitor

usedinthisdesignis10ufat1.2Vdcbiasand600kHzfrequency.It

isthisvalue

thatmustbeusedforallcomputationsrelatedtothe

compensation.

Part #	ERJ-3EKF1000V
Description	RES THKFLM 0603 100 OHM 1% 1/10W 100PPM/ C SMD - Cut TR (S
Category	CHIP RESISTOR
Availability	Out of Stock
Qty	0

ERJ-3EKF1000V

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