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Fabrication and characterization of multiple flexible magnetic windings


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FABRICATION AND CHARACTERIZATION OF MULTIPLE FLEXIBLE MAGNETIC WINDINGS By MOHAMMED S. ALAM A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2001

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ii ACKNOWLEDGMENTS Iwouldliketothankmyadvisor,Dr.KhaiD.T.Ngoforhisinterestand patienceduringtheworkforthisthesis.Hisapproachtoproblemsolvingand knowledgeofpracticalissuesmadethisworkpossible.Hehelpedmetounderstand theprocessofengineering.IwouldalsoliketothankDr.AlexanderDomijanandDr. VladimirA.Rakovforalloftheirsuggestionsandforbeingonmyadvisory committee.IwouldalsoliketothankDr.CharlieKorman,Dr.JohnAMallick, RichardJSaia,andSriramRamakrishnanofGeneralElectricCorporationfortheir fundinginthisresearch.ThanksarealsoduetoPaiboonNakmahachalasint,June Chen,andMehulShahfortheirhelpandcamaraderie.Iwouldliketoplaceonrecord myappreciationandgratitudetotheBangladeshUniversityofEngineering& Technology,Dhakafortheopportunitytostudyandlearninanenvironmentthat made it all fun. Finally, I thank my family for their love and support.

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iii TABLE OF CONTENTS Page ACKNOWLEDGMENTS. . . . . . . . . . . . . . . . . . . . . . . . .ii LIST OF TABLES. . . . . . . . . . . . . . . . . . . . . . . . . . . .v LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . .vi ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vii i CHAPTERS 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . .1 1.1 Background. . . . . . . . . . . . . . . . . . . . . . . . . . .1 1.2 Thesis Chapter Synopses . . . . . . . . . . . . . . . . . . . . .3 2 FLEX MANUFACTURING. . . . . . . . . . . . . . . . . . . . . . .5 2.1 Types of Flex Circuits. . . . . . . . . . . . . . . . . . . . . . .5 2.2 Some Process Rules. . . . . . . . . . . . . . . . . . . . . . . .6 2.2.1 Material Sizes in Flex Circuits. . . . . . . . . . . . . . . . .6 2.2.2 Design Rules . . . . . . . . . . . . . . . . . . . . . . .6 2.2.3 Improving Flexibility and Bend Radius. . . . . . . . . . . . .7 2.2.4 Tear Stops . . . . . . . . . . . . . . . . . . . . . . . .7 2.2.5 Circuit Pattern . . . . . . . . . . . . . . . . . . . . . .8 2.3 Flex Circuit Fabrication Process . . . . . . . . . . . . . . . . . .8 2.3.1 Computer Aided Design Translation. . . . . . . . . . . . . .8 2.3.2 Etching. . . . . . . . . . . . . . . . . . . . . . . . . .9 2.3.3 Solder Masking . . . . . . . . . . . . . . . . . . . . . .9 2.3.4 Alignment and Lamination . . . . . . . . . . . . . . . . .10 2.3.5 Drilling. . . . . . . . . . . . . . . . . . . . . . . . .10 2.4 Definition of Terms . . . . . . . . . . . . . . . . . . . . . .10 2.4.1Small Rectangle. . . . . . . . . . . . . . . . . . . . . .10 2.4.2 Large Rectangle. . . . . . . . . . . . . . . . . . . . . .11

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iv 3 LAYOUT DESCRIPTION AND FABRICATION OF THE FIVE-WINDING TRANSFORMER . . . . . . . . . . . . . . . . . . . . . . . . . .12 3.1 Description of Layout . . . . . . . . . . . . . . . . . . . . . .12 3.2 Folding Sequence. . . . . . . . . . . . . . . . . . . . . . . .22 4 MODELLING OF THE TRANSFORMER AND EXPERIMENTAL RESULTS. .26 4.1 Modelling. . . . . . . . . . . . . . . . . . . . . . . . . . .27 4.1.1 Basic Measurement Methodology. . . . . . . . . . . . . . .28 4.1.2 Why Use the Four-point Measurement System? . . . . . . . .32 4.1.3 The Measurement Board: Layout and Interconnections . . . . . .33 4.2 Effect of Nonzero Current Sense Impedances. . . . . . . . . . . . .35 4.3 Experimental Results. . . . . . . . . . . . . . . . . . . . . . .39 5 CONCLUSION. . . . . . . . . . . . . . . . . . . . . . . . . . .47 5.1 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . .47 5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . .47 APPENDIX: MATLAB SCRIPT TO CALCULATE THE REAL AND IMAGINARY PARTS OF THE IMPEDANCES . . . . . . . . . . . . . . . . . . . . .49 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . .53 BIOGRAPHICAL SKETCH. . . . . . . . . . . . . . . . . . . . . . . .55

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v LIST OF TABLES Table page 2-1 Material sizes used in the flex circuit. . . . . . . . . . . . . . . . . . .6 2-2 Some design rules. . . . . . . . . . . . . . . . . . . . . . . . . . .6 3-1 Specification of the transformer. . . . . . . . . . . . . . . . . . . . .13 4-1 Summary of the dc resistance measurement. . . . . . . . . . . . . . . .39 4-2 Summary of the ECM parameters measurement . . . . . . . . . . . . . .41

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vi LIST OF FIGURES Figure Page 1-1A fabricated flex circuit for a five-winding transformer. . . . . . . . . .2 1-2A 5/6-turn winding pattern.. . . . . . . . . . . . . . . . . . . . . .3 2-1 Types of flex. . . . . . . . . . . . . . . . . . . . . . . . . . . .6 2-2 Good and bad copper pattern to prevent broken conductor. . . . . . . . . . .8 2-3 Small rectangle . . . . . . . . . . . . . . . . . . . . . . . . . . .9 2-4 Large rectangle . . . . . . . . . . . . . . . . . . . . . . . . . .1 0 3-1 Planar core (E/18/10). . . . . . . . . . . . . . . . . . . . . . . .13 3-2First small rectangle. . . . . . . . . . . . . . . . . . . . . . . . .14 3-3 Holes and folding lines for. . . . . . . . . . . . . . . . . . . ..15 3-4Width of the large rectangles . . . . . . . . . . . . . . . . . . . .16 3-5Hole dimensions in cm. . . . . . . . . . . . . . . . . . . . . . . .17 3-6Large rectangle dimensions in cm . . . . . . . . . . . . . . . . . .18 3-7Layout of the twelve-turn primary winding. . . . . . . . . . . . . . .19 3-8 L ayout of the reset winding. . . . . . . . . . . . . . . . . . . . . .20 3-9Layout of the nine-turn winding. . . . . . . . . . . . . . . . . . . .20 3-10 L ayout of the five-turn winding . . . . . . . . . . . . . . . . . . .21 3-11 Layout of the six-turn winding. . . . . . . . . . . . . . . . . . . .21 3-12V ertical drawing. . . . . . . . . . . . . . . . . . . . . . . . . .22 3-13 First flex folded along folding lines 1 and 2.. . . . . . . . . . . . . .22

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vii 3-14 Second flex folded along folding lines 1 and 2. . . . . . . . . . . . .23 3-15 First flex folded along folding lines. . . . . . . . . . . . . . . . .23 3-16 Second flex folded along folding lines . . . . . . . . . . . . . . . .24 3-17 First flex placed on top of second flex and folded along folding lines. . .24 3-18 Complete transformer. . . . . . . . . . . . . . . . . . . . . . . .25 4-1Extended cantilever model for a five-winding transformer.. . . . . . . .27 4-2Basic measurement setup.. . . . . . . . . . . . . . . . . . . . . .29 4-3Measuring leakage impedances. . . . . . . . . . . . . . . . . . . .30 4-4Turn ratio measurement.. . . . . . . . . . . . . . . . . . . . . . .31 4-5Reference waveform being sampled at the terminal . . . . . . . . . . .32 4-6 Four-point measurement system. . . . . . . . . . . . . . . . . . . . .33 4-7 Circuit diagram indicating the testing terminals for the transformer . . . . . .34 4-8 Layout diagram of the bottom of the test fixture showing interconnects .. . . . .35 4-9 Layout diagram of the top of the test fixture showing the BNC terminations.. . .36 4-10 Leakage impedance measurement referred to the primary node. . . . . .36 4-11 Norton equivalent of leakage impedance measurement circuit. . . . . . .38 4-12T ransformer implemented on a test fixture. . . . . . . . . . . . . . .40 4-13 The bottom view of the test fixture. . . . . . . . . . . . . . . . . .42 4-14 Ideal transformer. . . . . . . . . . . . . . . . . . . . . . . . . .43 4-15 Extended cantilever model schematic implemented in PSPICE. . . . . .44 4-16T ransformer winding voltage waveforms simulated in PSPICE. . . . . .45 4-17 Experimental voltage waveforms across the windings. . . . . . . . . . . .46

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viii Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science FABRICATION AND CHARACTERIZATION OF MULTIPLE FLEXIBLE MAGNETIC WINDINGS By Mohammed S. Alam December 2001 Chairman: Khai D. T. Ngo Major Department: Electrical and Computer Engineering Flexiblecircuitsareusedformagneticcomponentstoreducesizeandweight andtoincreasepowerdensity.Theflexfoilsarebasicallybuiltusingconductorand insulatormaterials.Amongtheconductormaterials,probablythebestsolutionis copperbecauseitpresentsagoodtrade-offbetweenelectricalcharacteristicsand cost.Becausetheinsulatormaterialneedsgoodmechanicalcharacteristics,itshould bechosencarefully.Whendesigningflexcircuits,manyfactorsmustbeconsidered, suchasmechanicalperformanceandelectricalperformance.Thebendradiusisthe most important mechanical characteristic for this particular application. Thisthesispresentsthedesign,fabrication,andcharacterizationofafivewindingtransformerusingaflexcircuit.Thisdesigntechniquedealswiththetradeoffamongcoresize,coreloss,easeofmanufacturingandfolding;theminimum numberoflayers;andthewindingassemblysothattheterminationsoftheprimary andsecondaryfallonbothsidesofthecore.Thismethodvirtuallyeliminates

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ix externalsolderingorconductivevias,thusreducingdcresistanceandcostand increasingreliability.Thedesignedtransformerhastwelveturnsintheprimary windingandtwelveturnsintheresetwinding.Thesecondarywindingshavenine, five,andsixturns.Beforefabrication,thelayoutofthetransformerwasdonein AutoCADandthedetailsofthelayoutwerepresented.AplanarEcore(E18/4/10) wasusedtodesignthetransformer.Thedcresistancesof91m W,1210 m W,125 m W 49m W ,and108m W wereobtainedfortheprimary,reset,nine-,five-,andsix-turn windings,respectively.ThetransformerismodeledbyusingtheExtendedCantilever Model (ECM) approach.

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1 CHAPTER 1 INTRODUCTION 1.1. Background Magneticcomponentsareoftenfabricatedusingplanarwindingsonprinted circuitboards[1],flexcircuits[2],andhybridcircuits[3]becauseofthetrendtoward miniaturizationofelectroniccomponents.Comparedtotheconventional transformers/inductors,planartransformers/inductorshavelowerpackagingprofiles andhigherpowerdensities[4].PlanarwindingsusingmultilayerPCB(ML-PCB) havebeenreportedin[5],butthenumberofturnsofwindingsthatcanbeplacedin seriesislimitedandisdeterminedbythecoretype.Thisapproachisnotsuitablefor windings with a large number of turns and a high degree of interleaving. Theflexcircuitispresentedasamethodtofabricateawindingassemblywith alargenumberofconductiveandinsulatinglayers[6-12].However,nodetailed schemeispresentedusing2D-foldingformultiwindingmagneticcomponentswhere severaltrade-offsexistincludingcoresize,coreloss,easeofmanufacturingand foldingofflexcircuits,andtheminimumnumberoflayers.Thisthesisdealswith these issues.A v e-winding transformer is laid out, fabricated, and modeled. Two-dimensional(2D)foldingisdefinedasthefoldingpatterninwhichthe flexcircuitisfoldedbothalongthex-axisandy-axis.Afabricatedflexcircuitfora five-windingtransformerisshowninFigure1-1.Figure1-1showsthattogetthe

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2 requirednumberofturns,theflexcircuitshouldbefoldedbothalongthex-axisand y-axis; that is, the folding is two-dimensional (2D). The advantages of 2D folding are as follows: Itavoids longflex circuitsthatusuallyresultiftheturnsareconstrainedtoa1D layout. Itavoidsalargenumberofseparateflexcircuitsthatneedtobeassembled.Infact, it might be possible to lay out all the windings on a single flex circuit. Itminimizesthenumberofviasused.Infact,allthepatternsshowninFigure1-1 requirenovia.Aviaisusedtoconnecttheisolatedcopperpatternthatwillbein series. F igure1-1.Afabricatedflexcircuitforafive-windingtransformer.(a)Primary and reset windings; (b) Secondary windings (a) (b)

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3 Inordertoreducethemanufacturingcost,thenumberoflayersshouldbekeptata minimum.Onewaytoaccomplishthisistoputseveralwindingsonthesamelayeras showninFigure1-1.Inaddition,severalhalf-turns(orfractionalturns,ingeneral)ofthe same winding can be put in the same layer. Anotherwaytoreducethenumberoflayersinawindingstackistoincreasethe numberoffractionalturnsoneachlayer.Forinstance,ifa5/6turnisputoneachlayer,the 5/6turnwindingpatternshowninFigure1-2results.Thispatternusesspacemoreefciently.Thatis,itcoversmostofthewindingareaoneachsideoftheexcircuitwithcopper.Thus,foragivennumberofseriesturns,thenumberof5/6-turnlayerswouldbe almosthalfofthenumberhalf-turnlayers.Sixfoldingedgesarehexagonallydistributed alongthecircumferenceofthewindingstack.Copperbuild-upalongthefoldingedges would be less than in the half-turn patterns, and planarization would be less of a problem. 1.1. Thesis Chapter Synopses DifferenttypesofflexcircuitsarediscussedinChapter2.Alsodiscussedare someprocessrulesandtheiradvantagesandlimitationsinkeepingwiththeaimof thisstudy.Layoutandfabricationofafive-windingprototypetransformerare detailed in Chapter 3. The folding sequence is also described. Figure 1-2. A 5/6-turn winding pattern

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4 Amodelofthetransformer[13]andexperimentalresultsarepresentedin Chapter 4.TheproceduretoimplementtheECMinacircuitsimulatorisalsobriefly described.Chapter5drawsconclusionsfromtheresultsanddiscussesinsights obtainedfromthiswork.Finally,itproposespossiblefuturedirectionsthatmaybe explored.

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5 CHAPTER 2 FLEX MANUFACTURING Theflexcircuitsbasicallyarebuiltusingconductorandinsulatormaterials. Amongtheconductormaterials,theuseofcopperprobablyisthebestsolution becauseitpresentsagoodtrade-offbetweenelectricalcharacteristicsandcost. Becausetheinsulatormaterialneedsgoodmechanicalcharacteristicsinorderto allowfoldingwithnocrackingproblems,itsselectionismorecomplicated.Usually kapton,whichischemicallyapolymide,isusedastheinsulatorbecauseofitsgood electrical, thermal, and mechanical properties. 2.1. Types of Flex Circuits Therearetwotypesofflexcircuits:single-sidedflexandmulti-sidedflex.The single-sidedflexcircuithasoneconductivelayeronaflexibleinsulatinglayerand canbefabricatedwithorwithoutcoverlayers.Single-sidedflexcircuitsareless expensive. The single-sided flex circuit is shown in Figure2-1(b). Themulti-sidedflexcircuithastwoormoreconductivelayerswithaflexible insulatinglayerbetweentwoconductivelayersandcanbefabricatedwithorwithout coverlayers.Connectionsbetweenconductivelayersareprovidedbyplattedthroughholes.Accessholesorexposedpadswithoutcoversmaybeoneitherorbothsides. The multilayer flex circuit is shown in Figure2-1(a).

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6 2.2. Some Process Rules Buildingaflex-circuitgenerallyinvolvesemployingthesamestepsfrom circuittocircuit.However,certaincircuitdesigncanaddcost.Accessholesand supplementarylayersaddcost.Usuallythecostiscomparabletothenumberof layers.Thehigherthenumberoflayers,thehigherthecost.Forexample,twodoublesidedcircuitscouldpotentiallybelessexpensivethanonefour-layermulti-sided circuit. Circuits can also be folded in order to save space and layers. 2.2.1. Material Sizes in Flex circuits Material sizes [14] used in flex circuits are listed in Table2-1. 2.2.2. Design Rules Some design rules [14] are given in Table2-2. Table 2-1. Material sizes used in the ex circuit MaterialSizes (milli inch) Insulator0.5, 1, 2, 3, 5 Conductor0.7, 1.4, 2.8, 4.2 Adhesive0.5, 1, 3, 4 Table 2-2. Some design rules FunctionMinimum Value (mili inch) Conductor width/ spacing5 for 1 ounce copper, 7 for 2 ounce copper Trace to edge spacing5 Inner radius for holes or slots12.5 Conductor width5 times greater than the thickness (a) (b) Figure 2-1. Types of flex (a) double-sided; (b) single-sided

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7 2.2.3. Improving Flexibility and Bend Radius Single-sidedcircuitsareprobablythebestchoicefordynamic(flex-in-use) applications.Generally,mutilayercircuitsarebettersuitedtostaticapplications wherethecircuitisfoldedonlyduringinstallation.Theminimumallowablebend radiusofamulti-sidedflexissixtimestheoverallthickness.Roughly,thecircuit thicknessisslightlysmallerthanthesumoftheinsulator,adhesive,andcoverlayers. Some possibilities to improve flexibility include: Circuitswithtwolayersormoreselectivelyplattedtoimprovedynamicflexibility Keeping the number of bends to a minimum ConductorsstaggeredtoavoidanI-beameffect,androutedconductorsperpendicular to a bend Pads or through-holes not be placed in bend areas Factoryformingasaconsideredoption.Mostconstructionscanbefactoryformed dependingonthegeometry.Becausecircuitsareflexible,formedcircuitswillrelax in time. Form tolerances apply only to the part in the constrained position. Preferablenottoplaceconductor,discontinuitiesinthecoverorotherstressconcentrating features near any bend location. Unbondedlayersinarelativelythickmultilayerorrigid-flexcircuitareanoption in order to improve flexibility, but this may be more expensive. 2.2.4. Tear Stops Polymidepresentsahighinitialtearstrength,butonceatearstarts,it propagateseasily.Allinsidecornersmustberadiused.Thelargertheinsideradius, thegreaterthetearstrength.Iftearingisaconcern,polymide-insulatedcircuitscan bedesignedattheinnercornersforcornersof120oorless.Internalorexternal

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8 polymideorTeflontearstopscanbeincorporated.PolymideorTeflontearstopswill add to circuit cost. 2.2.5. Circuit Pattern Foreaseofmanufacturing,flaringoflinesintopadsisnecessarywhenthepad isunsupportedbythecoverlay.Thisisdonetoprovidestrainreliefatthepad/line intersectiontopreventbrokenconductors.Foreaseofmanufacturing,sudden expansionorreductioninconductorwidthisnotrecommended.Acuteanglecopper pattern is also not recommended, as shown in Figure2-2. 2.3. Flex Circuit Fabrication Process Flexcircuitfabricationprocesscanbebrokendownintofiveseparate production steps [15,16]. Each is described separately. 2.3.1. Computer Aided Design Translation TheflexcircuitcanbemanufactureddirectlyfromCADdata(usuallyGerber files).APCbasedsoftwaretranslatesGerberdataintoaplotfile.Thisplotfileis Figure 2-2. Good and bad copper pattern to prevent broken conductor

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9 electronicallysenttothePlotter/Etcher.InthePlotter/Etcher,ahighprecisioninkjet print head images the circuit onto a flex circuit material. 2.3.2. Etching Afterthecircuitdesignhasbeenimagedontotheflexmaterial,thefilmisthen forwardedusingapositivedrivemotioncontrolsystemintoacascadingetchtankin frontofthePlotter/Etcher.Oncethefilmhasbeenloadedintotheetchtank,the Potter/Etcherautomaticallystartsapresetetchcycle.Theflexcircuitissprayedwith sodiumpersulfate.Thesodiumpersulfate,etchesawayalloftheexposedcopper, leavingonlytheprotectedcircuitdesignonthefilm.Aftertheetchcycleiscomplete, thefilmissprayedwithafreshwaterrinse.Thisrinseremovesanyactiveetchantstill deposited on the circuit. The flex circuit is then forwarded out of the Plotter/Etcher. 2.3.3. Solder Masking AftertheflexcircuithasbeenremovedfromthePlotter/Etcher,acoverlayer is used to protect the circuit from bridging or electrical gaps. Figure 2-3. Small rectangle (in cm)

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10 2.3.4. Alignment and Lamination Aftersoldermasking,thelayersarealignedwiththealignmentpunch.Once aligned, the layers are then laminated in heat seal press. 2.3.5. Drilling Thelaminatedboardisthenplacedinhighperformancedrillerforthrough hole drilling and final board routing. 2.4. Definition of Terms 2.4.1. Small Rectangle: A small rectangle contains only one hole as shown in Figure2-3. Figure 2-4. The large rectangle

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11 2.4.2. Large Rectangle: A large rectangle contains three vertical rectangles as shown in Figure2-4.

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12 CHAPTER 3 LAYOUT DESCRIPTION AND FABRICATION OF THE FIVE-WINDING TRANSFORMER Beforethelayoutofthetransformer,thecoreshouldbeselectedaccordingto therequirementssuchaspower,numberofturns,powerloss,dutyratioofthe converter,operatingfrequency,powercarriedbydifferentwindings,voltageand currentofdifferentwindings,andsoforth.Thespecificationsofthetransformerare showninTable3-1.The primaryandresetwindingsarereferredtoaswindingsW1and W2,respectively,andthenine-,ve-,andsix-turnsecondarywindingsarereferredtoas W3,W4,andW5,respectively.Sincethetransformerfabricatedissupposedtobeusedina multipleoutputforwardconverter,theresetwindingwillbeusedtoresettheconverter. Accordingtothespecifications,coreE18/4/10[17],whichisaplanarEcore,was selectedbyusingMathcad[18],andbyusingequationsfrom[19].Thematerialof thecoreis3F3ferrite.Thecross-sectionalviewofthecoreE18/4/10isshownin Figure3-1 3.1. Description of Layout ThelayoutofthetransformerwasdonebyAutoCAD[20].Thelayoutofthe primaryandtheresetwindingwasdoneinoneflexandthelayoutofthesecondary windingswasdoneinanotherflex.Thetwoflexescanbefabricatedeitherinsinglesidedflexorindouble-sidedflex.Fortherestofthethesis,thefirstflexwillbe

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13 referredtoasprimaryandresetwindingsandthesecondflexwillbereferredtoas secondary windings. Aftertryingindifferentmethods,itwasdecidedtouse24smallrectangles whereasmallrectangleisdefinedinSection2.4.1.Theholesandfoldinglinesofthe firstandsecondflexesareshowninFigure3-3.Theholedimensionsoftheflexesare determinedbythesizeofthecore.Figure3-1showsthedimensionsofthemiddle legofthecoreas10mmx4mm.SinceitwasdeterminedthattheKaptonandthe copper,shouldnottouchthecore,aclearanceof0.15mmwaschosenbetweenthe Kaptonandthecore.Ifthecoppertouchesthecore,itmightshortthecore.Sothe Table 3-1.Specification of the Transformer WindingsTurnsError in number of turns Peak Voltage (Volt), wave shape (rectangle) Peak Current (Amp) wave shape (rectangle W1 12 0.12 38 1.538 W2 12 0.12 W3 9 0.12 10 0.30 W4 5 0.04 5 2.10 W5 6 0.12 12 0.41 Operating frequency 300 KHz Output Power 20 Watt Power loss 1 Watt F igure 3-1. Planar core (E18/4/10). (a) Top view (b) Bottom view

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14 holedimensionswerechosenas10.3mmx4.3mm.Figure3-1showsthatthe cornersofthelegofthecorearerounded.Sothecornersoftheholewerealso rounded.AccordingtoSection2.2.2,theminimumroundradiusshouldbe12.5mils. Soaroundradiusof31milswaschosen.Thezoom-inviewoftheholewithits dimensionsisshowninFigure3-5.Todeterminethedimensionsofthesmall rectangles,thedimensionsofthefirstrectangleshouldbedeterminedfirst.The dimensionsofthefirstrectanglearedeterminedbythesizeofthecore,too.Figure 3-1showsthatthemaximumdimensionsofasmallrectanglecanbe14mmx20mm. Tomakesurethereisaclearanceof0.15mmbetweentheKaptonandthecore,the dimensionsofthefirstsmallrectanglewerechosenas13.7mmx19.7mm.Figure 3-3showsthatthoughthereare24smallrectangles,eachofthethreeverticalsmall rectanglescanbegroupedasonelargerectangle.Sothereareeightlargerectangles ineachoftheflex,andthedimensionsofthefirstlargerectangleshouldbe13.7mm x3*19.7mm,thatis,thewidthandheightare13.7mmand3*19.7mm.Thefirst largerectangleisshowninFigure3-6withitsdimensions.Toaligntheholesafter F igure 3-2. First small rectangle (in cm)

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15 thefoldingoftheflex,theheightofalllargerectanglesshouldbesame.Thewidth ofthelargerectanglescanbedifferent,butthisshouldnotaffectthealignmentofthe holes. There are folding lines between all small rectangles. Thewidthofthelargerectanglesismadeinalong-shortpatternsothat,uponfolding,twoconsecutivefoldingedgesdonotfallontopofeachother.Bydoingthis,thejamFigure3-3.Holesandfoldinglinesfor(a)Firstflex.(b)Secondflex(dimensionsin cm ) 1 2 1 2 3 4 5 6 7 8 9

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16 mingofcopperalongthefoldingedgescanbeavoided.Thewidthofeachlargerectangle is determined by the following equations: n=1,2,6,10(3.1) n=3,5,7(3.2) n=4,8,12(3.3) wherewnisthewidthofthenthlargerectangle,aisthewidthoftherstlargerectangle, andbisthelength,whichisshorterthanthewidthoftherstlargerectangle.Forthe designed transformer, a and b are shown in Figure3-4. Figure3-3showsthatthewidthofthelargerectanglesaredeterminedby equations3.1to3.3,andtheseequationscanbeappliedforanynumberoflarge rectangles.Forexample,forn=3,thewidthofthe3rdlargerectangleis12.7mm w n a = w n ab = w n a2b = Figure 3-4. Width of the large rectangles 8th large rectangle 7th6th5th4th3rd 2nd 1st

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17 (13.7mm-1mm)byusingtheEquation(3.2).Inthedesignofthetransformer,the value of b was chosen to be 1 mm. Aspreviouslydiscussed,therearetwoflexcircuitries.Thefirstflexcircuit containsprimaryandresetwindings,andthesecondflexcircuitcontainsnine-, five-,andsix-turnsecondarywindings.Tounderstandthecopperpatternofthe windings clearly, each is described separately. AsshowninFigure3-7,theprimarywindingstartsatterminalP+andends atterminalP-.Theserpentinecopperpatternfollowsaround24aperturestomake twelveturns,accordingtothespecificationsasshowninTable3-1.Figure3-8shows thelayoutoftheresetwindingwhichstartsatterminalR+andendsatterminalR-. Theserpentinecopperpatternfollowsaround24aperturestomake12turns, according to specification. Thenine-turnsecondarywindingstartsatterminal9+andendsatterminal 9-,andtheserpentinepathfollows12aperturestomakenineturnsasshownin Figure 3-5. Hole dimensions in cm

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18 Figure3-9.Thefive-turnsecondarywindingstartsatterminal4+andendsat terminal4-,andtheserpentinepathfollows10aperturestomakefiveturnsasshown inFigure3-10.Duringthelayout,aneffortwasmadetoincreasethewidthofthis five-turnwindingbecauseitcarriesmorecurrent.Thesix-turnsecondarywinding startsatterminal6+andendsatterminal6-,andtheserpentinepathfollowstwelve apertures to make six turns as Figure3-11. Thecopperrunsperpendicularlyalongthefoldinglinestomakethefolding easierandthecopperissplitalongthefoldinglinesinordertomaketheinter-layer Figure 3-6. Large rectangle dimensions in cm

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19 capacitancelessandalsotofoldmoreeasily.Thecopperpatternisextendedoutside atthebeginningandendofthewindingstoformpadsfortheterminations.Atthe terminations, it is necessary to see the spacing between the copper. Otherwise,onemightshortthecopper.Soatleast2mmspacingwasensured. Figure3-7andFigure3-8werecombinedtoformthefirstflex,asshownFigure11(a)andFigure3-9-Figure3-11werecombinedtoformthesecondflex,asshownin Figure1-1(b).Sincetwoormorewindingswerefabricatedinoneflex,aminimum copperspacingof0.3mmwaschosen,asshowninSection2.2.2Forallthewindings, thecopperthicknesswas1.4milsbutthewidthofcoppervaries.Sincethecopper widthoftheresetwindingcanbesmaller,aminimumcopperwidthof0.3mmwas chosenaccordingto.Aneffortwasmadetouseallareasoftherectanglesforcopper so that minimum winding copper loss occurs. Thelayoutwasdoneinawaysuchthat,afterfolding,theterminationsoftheprimaryandresetwindingsfellononesideofthetransformercore,andtheterminationsof allthesecondarywindingsfellontheothersideofthetransformercore.Itwasalso Figure 3-7. Layout of the twelve-turn primary winding P+ P-

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20 ensuredthattwoterminationsofanysecondarywindingwerenexttoeachotherupon folding.Bydoingthis,thelengthofthewirewasreducedduringtestingofthetransformer,anditalsomadethewindingeasiertoshortduringthemeasurement.Aprimary benet of this layout is that there are no vias or soldering. AsshowninFigure3-12,therstexhasKaptononbothsidesexceptwherethe terminationsare.Thesecondary-windingexhasKaptonononesideexceptwherethe terminationsare;theothersidehasexposedcopper.ItisobviousthattheexesaresingleFigure 3-8. The layout of the reset winding R+ RFigure 3-9. Layout of the nine-turn winding 9+ 9-

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21 sidedandnotdouble-sided.Thesingle-sidedexwasfabricatedratherthandouble-sided becausethedouble-sidedexismorecostly.Forallwindings,thecopperattheterminationsiscoveredbysoldersothattheterminationsdonotoxidize.ItisalsoseeninFigure 3-12showsthattheKaptonandadhesivethicknessareboth0.5mils.TheKaptonand adhesivethicknessof1milscouldbeusedwithlesscost;howeverinordertottwoexes intothewindowheightofthecore(4mmtotalfortwocores),theKaptonandadhesive thickness of 0.5 mils were chosen. Figure 3-10. Layout of the five-turn winding 5+ 5Figure 3-11. Layout of the six-turn winding 6+ 6-

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22 Afterfolding,thetotalheightofboththeexeswerecalculatedfromFigure3-12 and was 3.536 mm []. 3.2. Folding Sequence TherstandsecondexofthetransformershowninFigure1-1shouldbefolded alongthefoldinglinesaccordingtothesequences.Otherwise,theprimaryandsecondary windingexescannotbeinterleaved.Therstandsecondexofthetransformeralong withfoldinglinesareshowninFigure3-3.InFigure3-3,thedottedlinesarethefolding lines,andtheyarenumberedfrom1to9tomaintainafoldingorder.Forboththerstand secondex,theyarerstz-foldedalongfoldinglines1and2,asshowninFigure3-13and Figure3-14, respectively. Thentheyarez-foldedalongthefoldinglines3,4,5,6,7,8,and9,respectively,as showninFigure3-15andFigure3-16.Thetwoexesarefoldedalongfoldinglines1 F igure 3-12. Vertical drawing. (a) First flex. (b) Second flex (a) (b) 1.420.56 + () 2410 3 25.4 3.536mm = Figure 3-13. First flex folded along Folding Lines 1 and 2 =folding line 2 1

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23 and2rstbecauseiftheyarefoldedalongfoldinglines3,4,5,6,7,8,and9rst,it wouldbedifculttofoldexalongthefoldinglines1and2becauseofthethickcopperstack.Afterfoldingalongthefoldinglines,thetwoexesareunfolded,andthesecond exisplacedontopoftherstex,tointerleavetheprimaryandsecondarywindingsas showninFigure3-17.Theyarethenfoldedagainalongfoldinglines1and2rst.Then the folded rst small rectangle is inserted in the E18/4/10 core, and then the two coupled windingsarez-foldedalongthefoldinglines3,4,5,6,7,8,and9,andtheninserted intothecore.Thiswasdonesothattheaperturesofthewindingsbecomealigned. The complete transformer is shown in Figure3-18. Figure 3-14. Second flex folded along Folding Lines 1 and 2 =folding line 1 2 Figure3-15.FirstflexfoldedalongFoldingLines1and2first,andthenFolding Lines 3, 4, 5, 6, 7, 8, and 9 =folding line 1 2 3 4 5 6 7 8 9

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24 Figure3-16.SecondflexfoldedalongFoldingLines1and2firstandthenFolding Lines 3, 4, 5, 6, 7, 8, and 9 =folding line 1 9 8 7 6 5 4 3 Figure3-17.Firstflexplacedontopofthesecondflex,andFoldedalongfoldin g Lines 1 and 2 first, then Folding Lines 3, 4, 5, 6, 7, 8, and 9 =foldin g line 2 second ex rst ex

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25 Figure 3-18. Complete transformer 5+ 56+ 69+ 9R+ p+ PR-

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26 CHAPTER 4 MODELING OF THE TRANSFORMER Modelingofmultiwindingmagneticcomponentsisdifficultinviewofthe cross-couplingamongthewindings.Analyticalexpressionsareinvariablycomplex anddifficulttoobtainforsuchcases.Additionally,suchanapproachislimitedto specificgeometriesand/ornumberofwindings.Modelingamagneticcomponent fromterminalportmeasurementsisnecessaryinmanycasesforverifyingor predictingconverterdynamics.Forapplicability,themodelhastobesufficiently broad-bandtodealwiththehighfrequencynonsinusoidalwaveformspresentin present-day converters. TheExtendedCantileverModelin[13],modifiedin[15],[21],and[22]is usedtomodelthetransformer.However,themeasurementsetupitselftendstohave parasiticelementsthatcanaltertheobservedfrequencyresponseoftheDeviceUnder Test(DUT).Thefour-pointmeasurementsystemispreferredforitsabilitytoreduce theeffectsofparasiticelements.MeasurementofleakageimpedancesintheECM requiressensingshort-circuitcurrents.Thisisanextremelystringentcondition.In fact,non-idealitiesinmeasurementofshort-circuitcurrentscanaffectthevery topologyoftheimpedancebeingmeasured.Itisimportanttounderstandthe requirement of a good short with respect to the ECM.

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27 4.1. Modeling Anequivalentcircuitmodelisdevelopedthatisusefulforthesimulationofthe converterintowhichthetransformerisembedded.Theproceduredescribedin[21]is employedtomeasurethemodelparametersforthefrequencyofinterestwhichis300 KHz. Themodeltopology,anextendedcantilevermodel(ECM)[13],isshownin Figure4-1.InECM,N(N+1)/2independentparametersarerequiredtomodelatransformercontainingNwinding.EachparameteroftheECMcanbedirectlymeasured.The self-impedanceZ11canbemeasuredbyopen-circuitingW2,W3,...,andmeasuringthe impedance of winding W1. The self-impedance Z11 is given by, Figure 4-1. Extended cantilever model for a five-winding transformer W1W2W3W4W51:n21:n31:n4n5:1

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28 ,,(4.1) Tomeasuretheeffectiveturnsratiosn2,n3,...,avoltageisappliedtowindingW1with other windings open-circuited. The effective turns ratio nk is given by, for,(4.2) A negative value of nk indicates that the winding polarity marks should be reversed. TomeasuretheeffectiveleakageimpedanceZjk,windingWjisdrivenwithvoltage sourcevj,whileallotherwindingsareshort-circuited.Itisimportantthatgoodlowimpedanceshort-circuitsbeused.ThecurrentikinwindingWkismeasured.Theeffective leakage impedance is Zjk is given by, ,;,(4.3) 4.1.1. Basic Measurement Methodology Themeasurementoftheratiooftheappliedvoltagetotheoutputcurrent/ voltageisthefirststepindeterminingthedesiredtransferfunction.Theactual transferfunctionismeasuredasaratiooftheappliedandmeasuredwaveformsusing anImpedance/Gain-Phaseanalyzer(Figure4-2).AHewlett-Packard4194A Impedance/Gain-Phaseanalyzerwasusedtocharacterizethedeviceundertest (DUT).Thequantitiesrequiredforthemodelhavedimensionsofresistance(Ohms) fortheselfandleakageimpedancesoraredimensionlessfortheturnsratios.Inother words,theappliedstimulusisalwaysavoltage,andtheobservedstimulusisa currentformeasuringtheimpedancesoravoltagefortheturnsratios.Measurement ofthecurrentisaccomplishedusingcurrentsenseresistorsinserieswiththewinding Z 11 v 1 i 1 ----=i k 0 =2k5 n k v k v 1 ----=k1 2k5 Z jk v j n j n k i k ------------------=kj v n 0 =nj

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29 beingmeasured.Thistransformsthemeasurementofcurrenttoameasurementof voltage.Foreachleakageimpedance,acurrentsenseresistorisusedtoshortthe windingin ordertosensethecurrentintheshort-circuitedwinding,asshownin Figure4-3. Allotherwindingsbeingexcitedhavetrueshortsacrosstheirterminals.The effectsofusingcurrentsenseresistorsinplaceofatrueshortisdiscussedin Section4.2.Thetwovoltagesarethenfedtothe4194A,andtheratiobetweenthe twovoltagesisscaledbythevalueofthecurrentsenseimpedancetoobtainthe impedancebeingmeasured.Fortheselfimpedance,thecurrentsenseresistoris DUT SweptFrequency Source Source Ref Test 4194A Impedance Gain/ Phase Analyzer Figure 4-2. Basic measurement setup

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30 simplyplacedinserieswiththewindingtoobtainthecurrentthroughit.These relations can be formally written as follows: (4.4) where is the ratio measured by the 4194A. Theturnsratiosaredirectlymeasuredasthevaluesrecordedbythe4194A (Figure4-4). i2v2 + n2 n3 n4 i3i4 n5 i5 vp+ 1 F igure 4-3. Measuring leakage impedances vappvSense,1ZsenseZ ij v appj v Sensei n i n j ----------------------------------Z Sense = vSensej ,vapp i ,----------------

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31 (4.5) Itshouldbenotedthatallthesevaluesaremeasuredacrossafrequencyrangeof10KHzto 1.01 MHz. Then these data were post-processed for 300 KHz. Theself-impedanceoftheprimarywinding, Z11, ismeasuredusingthe impedanceanalyzer,asthiswouldavoidanyparasiticeffectsbyusingtheother measuringsystems.Because Z11islargeathighfrequencies,parallelcable capacitancescancauseproblemsifitismeasuredinasimilarfashiontotheleakage impedances. Figure 4-4. Turn ratio measurement. i2v2 + n2 n3 n4 i3i4 n5 i5 vp+ 1 vp+ vappvSense,1n jk v Sensek v appj ----------------------=

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32 4.1.2. Why Use the Four-point Measurement System? Inthissection,theadvantagesofthefour-pointmeasurementsystemare illustratedusingthecaseofself-impedancemeasurement.Theoscillatorofthe 4194Atypicallysourcesoutasinewaveofpresetmagnitudeintotheterminalsofthe DUT.Duringthismeasurement,thereferenceandthetestinputsofthe4194Aareset toahighimpedancelevelof1M W .Thereferenceandtestwaveformsarefedbackto the4194AfromtheDUT.ForthecaseshowninFigure4-5,thereferencewaveformisfed backtothe4194AthroughaT-connectoratthesamepointthesourcewaveformisbeing appliedtotheDUT.Inthiscase,theterminatingimpedanceis1M W inparallelwitha28 pFCapacitance.Hence,thecurrentinthecablesconnectingthereferenceandtest potentialstothe4194Awillbesmall.Again,theparasiticdropsacrossthecablewillbe small.However,thedropacrosstheexcitingcableanditsinterconnectswillbesubstantial asthecablecarriesthesourcingcurrent,whichcouldbelarge.Infact,the Zpar(s)isrcvoltagedropshowninFigure4-5isnowbeingerroneouslyfedbackaspartofthereference voltage vref, instead of the actual voltage vp. Figure4-5.Referencewaveformbeingsampledattheterminalwherethesourc e waveform is applied Zparisrc Zparvref+ DUT vp+ vapp

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33 Thefour-pointmeasurementsystemavoidsthisproblembyusingseparate pointsforthesourcingandreferencevoltages(Figure4-6).Thisensuresthatthe referencevoltagedoesnotincludetheparasiticscausedbytheinterconnectsasthe currentinthiscaseislow.Whileseriesparasiticeffectsareavoided,parallelparasitic effects, such as the cable capacitance, can still affect the measurement. 4.1.3. The Measurement Board: Layout and Interconnections ThemeasurementboardwasfabricatedonadoublelayerFR4copperboard usingaT-Techcircuitboardmillingmachine.Itsdimensionsare4x4.Theboard layoutisbasedonthefour-pointmeasurementsystemwithanemphasisonkeeping thereferenceandtestpointsclosetotheactualwindingsand/orcurrentsense resistors(Figure4-7).Thesourcinginputsarelocatedfartherfromthetestand referencepoints.Figure4-8detailstheactuallayoutofthebottomofthetestboard. AlltheBNCconnectionsandtransformerwindingsaresolderedonthebottomofthe board.Thecurrentsenseimpedancesorshortsforvarioustestconfigurationsare solderedonthetopoftheboard.Theviasontheboardconnectthewindingsdirectly Figure 4-6. Four-point measurement system Zparisrc Zparvp+ DUTvappvref

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34 totheshortsorcurrentsenseimpedances.Theconnectionsonthetopoftheboard are shown in Figure4-9. TheBNCterminationsshownonthetopoftheboardareconnectedtothe 4194Athroughspeciallymadeshortcoaxialcablestoreduceparasitics.Caddock10 m W currentsenseresistors(PartNo.MP916,[23])with5%precisionwereusedforthe measurementofleakageimpedances.Theinductancewasestimatedinthemanufacturers datasheetsat7.5nH.A10cm coaxialcable(17pFcapacitance)wasusedtosensethe appliedvoltage,anda13cmcoaxialcable(21pFcapacitance)wasusedtosensethe voltage across the current sensor. Figure 4-7. Circuit diagram indicating the testing terminals for the transformerBNC_in_pri BNC_sen_pr BNC_sen_5t BNC_sen_6t BNC_sen_rst BNC_sen_9ti2rst + n2 n3 n4 i3i4 n5 i5 vp+ 1 9t + 5t + 6t + BNC_sen_pri BNC_in_5t BNC_in_6t BNC_in_rst BNC_in_9t P+

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35 4.2. Effect of Nonzero Current Sense Impedances Therearethreekindsofmeasurementstobeperformed.Fortheturnsratio measurements,nocurrentsensorsareneeded.Themeasurementoftheselfimpedance Zpp(s) isperformedontheimpedanceanalyzeranddoesnotneeda currentsensor.However,currentsensorsareneededforthemeasurementofleakage impedances,andEquation(4.3)requiresshortcircuitconditionsatthewinding where the current is sensed. Figure4-10showstheactualmeasurementsetupreferredtotheprimary node. If Zsc(s) is to be a good short, at all frequencies, Figure4-8.Layoutdiagramofthebottomofthetestfixtureshowinginterconnects betweentheBNCconnectorsandthevariousportsofthetransformer. BNC_sen_rst BNC_sen_pri BNC_in_pri BNC_in_rst BNC_in_5t BNC_sen_5t BNC_in_6t BNC_sen_6t BNC_in_9t BNC_sen_9t White= Cu Black= Isolation

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36 Figure4-9.LayoutdiagramofthetopofthetestfixtureshowingtheBNC terminations. BNC_sen_rst BNC_in_rst BNC_in_5t BNC_sen_5t BNC_in_6t BNC_sen_6t BNC_in_9t BNC_sen_9t BNC_sen_pri BNC_in_pri White= Cu Black= Isolation Figure 4-10. Leakage impedance measurement referred to the primary node 1:nj(s) + WjZij(s) Zsc(s) isc,j Z2j(s) ZNj(s) Z1j(s) vapps () nis () -----------------

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37 where(4.6) Atlowfrequencies,theright-handsideoftheinequalitywillbeextremely small,anditisdifficulttouseextremelysmallcurrentsensors.Also,thisis impracticalathighfrequenciesbecauseoftheparasiticinductanceofthecurrent senseresistor.For instance,a0.1 W surfacemountprecisionresistorwouldrealistically haveaseriesinductanceofabout5nH.At10MHz,theimaginarypartcurrentsense impedanceisapproximately30m W. Thiswouldseverelydistortthemeasuredphaseand magnituderesponse. Hence,wehavetochangethemeasurementproceduresuitablyin order to avoid this problem. ThequantitybeingmeasuredinFigure4-10istheleakageimpedance Zij(s) The measured leakage impedance Zij,mea(s) is given by, where(4.7) Arelationbetweenthemeasuredandactualimpedancescanbederivedeasilybyusingthe admittanceequivalentofthemeasurementcircuitinFigure4-10.TheNortonequivalentof the circuit is shown in Figure4-11. Theshortcircuitcurrent isc(s) isrelatedtotheinputcurrent iapp(s) bythe following relation: (4.8) where. Zsc's ) () Z1js () Z2js () Zijs () |||| ZNjs () |||||| () Zsc's () Zscs () njs ()2----------------= Zlmmea ,s () v'apps () iscj ,nj* s () -----------------------=v'apps () vapps () nis () ----------------= iscs () Y'scs () Yijs () Y'scs () Ynjs ()n1nj = N++ --------------------------------------------------------------------------------iapps () = iapps () Ylms () v'apps () =

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38 The measured leakage impedance Ylm,mea(s) is given by (4.9) Combining Equation (4.8) and Equation (4.9), we get (4.10) Simplifying the equation, (4.11) Equation (4.11) can be rewritten as (4.12) iapps () = Figure 4-11. Norton equivalent of leakage impedance measurement circuit Yij(s) Ysc(s) isc(s) Y1js () Y2js () YNjs () +++ () v' app s () Yijs ()Ylmmea ,s () iscs () v'apps () -----------------= Ylmmea ,s () Y'scs () Yijs () Yijs () Y'scs () Ynjs ()n1nj = N++ --------------------------------------------------------------------------------= Yijmea ,s () 1 Ylijs () Y'scs () ---------------Ynjs ()n1nj = NY'scs () -----------------------------------++ Yijs () =Yljs () 1 Yijmea, s () Y sc 's () ---------------------------- Y 1js () Y 2js () Y Njs () +++ () Yijmea, s () Y sc 's () ---------------------------- Yijmea, s () =

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39 Equation(4.12)representsasetoflinearequationswithoneequationformed byeachmeasurementofaleakageimpedance.Hence,thenumberofunknowns (leakageimpedances)isequaltothenumberofequations.Thesystemis,therefore, uniquelydeterminable.Bysolvingthissetoflinearequations,wecancompensate forthenon-idealityofthecurrent-senseresistor.Foran idealshort(), Equation(4.12)reducestotheidealcaseasdenedintheECM,i.e.,. 4.3. Experimental Results Thetransformerconstructedhasvewindings,includingtheresetone.TheprimaryandresetwindingsarereferredtoaswindingW1,W2,respectively,andthenine-, ve-,andsix-turnsecondarywindingsarereferredtoasW3,W4,andW5,respectively. Thetransformerwasdesignedfora20W,300KHzforwardconverter.Thelengthand widthofthewindingsvaryindifferentsegmentsofthelayout.So,thelengthandwidthat differentsegmentsarecalculatedfromthelayout,andthenthedcresistancesarecalculatedandsummeduptogetthetotalresistance.Thedcresistancesarecalculatedfromthe design Equation (4.13), (4.13) whereRdcisthedcresistanceofthewinding, r istheresistivityofcopper,listhelength of the winding, w is the width of the winding, and t is the thickness of the winding. Table 4-1 Summary of the dc resistance measurement Windings Thickness, t (cm) Average width, w (cm) Total length (cm) Measured (m W ) Calculated (m W ) W10.00360.27855.488 91 97 W20.00360.02055.488 1210 1230 W30.00360.18241.616 125 111 W40.00360.24423.120 49 46 W50.00360.13527.744 108 100 Y sc 's() Yijs () Yijmea ,s () = Rdcr l wt ----=

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40 Afterfabrication,thedcresistancewasmeasuredbyaKeithley2001multimeter. ThedcresistancesaresummarizedinTable4-1,indicatinggoodagreementbetweenthe measured and calculated values. TomeasuretheECMparameters,thetransformerwasimplementedinatest fixture,asshowninFigure4-12,whichisthetopofthetestfixture.Thebottomview ofthetestfixtureisshowninFigure4-13.Themeasurementboardwasfabricatedon adoublelayerFR4copperboardusingaT-Techcircuitboardmillingmachine.Its dimensionsare4x4.Theboardlayoutisbasedonthefour-pointmeasurement systemwithanemphasisonkeepingthereferenceandtestpointsclosetotheactual windingsand/orcurrent-senseresistors.Thesourcinginputsarelocatedfartherfrom Figure4-12.TransformerimplementedonatestfixturetomeasureECMparameters (top view of the test fixture)

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41 thetestandreferencepoints.Measurementsoftheextendedcantilevermodel parametersweremade,asdescribedinSection4.1.Hewlett-Packard4194A Impedance/Gain-Phaseanalyzer[24]wasusedtomeasurealltheparameters.The turnsratiosweremeasuredusingtheGain-PhasefunctionoftheHP4194A.The magnetizingimpedanceZ11wasmeasuredusingtheImpedancefunctionoftheHP 4194A. Table 4-2 Summary of the ECM parameters measurement at 300 KHz TomeasureleakageimpedanceZjk,thecurrent-senseresistorwasusedto shortwindingkinordertosensethecurrentintheshort-circuitedwindingk.The otherwindingsj,excepttheexcitedwindingk,hadtrueshortsacrosstheirterminals. TheratioofthevoltagesacrossthewindingskandjisthenmeasuredbytheGainPhaseanalyzer.Thiswasscaledbythecurrent-senseadmittanceandtheturnsratios njandnk*tocomputeZjk.Allvoltagesweremeasuredatthewindingterminalsto avoidinterconnectandcableparasitics.Itisnecessarytomentionthatthevalueof thecurrentsenseresistoris10m W with5%-precisionandapackageinductanceof ParametersMeasured Real Measured Imaginary Extracted Real Extracted imginary n21.0100.00001.010.000 n30.7600.00000.760.000 n40.4200.00000.420.000 n50.5100.00000.510.000 Z11( W ) 7.3570651.357.36651.3 Z12( W ) 3.383-1.05003.36-1.060 Z13( W ) 0.2630.09700.270.100 Z14( W ) 0.4250.35300.410.360 Z15( W ) 0.4590.17100.440.175 Z23( W )2.2060.52002.210.510 Z24( W )6.0473.17106.053.170 Z25( W )9.2872.48109.282.475 Z34( W )1.1700.99401.170.992 Z35( W )1.9300.68001.920.680 Z45( W )1.2682.18001.272.170

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42 7.5nH(CaddockpartnumberMP916[23].Itisshownin[21]thatthemeasured parameterswithcurrentsensorof50m W +15nH,theextractedparametersdonotvary muchstartingat100KHz.Sincetheoperatingfrequencyofthedesignedtransformer is300KHz,10m W +7.5nHwasconsideredasufficientlygoodshort.Themodel parameters are summarized in Table4-2. ToverifythemeasuredECMparameters,thetransformermodelwas generatedinPSPICE[25].Alltheimpedancesweremodeledasresistanceinseries withinductanceexceptZ12becauseithasanegativeimaginarycomponent.Since PSPICEcannotusenegativeinductance,L12isimplementedbyusinganinductance F igure 4-13. The bottom view of the test fixture

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43 block.AninductanceblockisgeneratedusingaVoltage-Current G(s) block (Glaplace,Figure4-14). TheidealtransformerinFigure4-14wasimplementedbyusingavoltage controlledvoltagesource(VCVS)andacurrentcontrolledcurrentsource(CCCS) connectedinanantiparallelsense.Thevoltagecontrolledvoltagesourcetransforms theprimaryvoltagetothesecondary,andthecurrentcontrolledcurrentsource transformsthesecondarycurrenttotheprimary.Sincethetransformerterminals cannotbeshortedtoreproducemeasurementresults,asthiswouldleadtotopological andconvergenceerrors,thetransformerwasshortedbyusinga10n W resistorwhen needed.Thegainmultiplierwassettotheturnsratio.Toverifytheimplemented ECM,15virtualexperimentswereperformedonPSPICE.Theschematicgenerated onPSPICE,alongwiththeECMparameters,isshowninFigure4-15.Allvirtual experimentsgeneratevirtuallythesamedataastheactualexperiments,shownon Table4-2 Figure 4-14. Ideal transformer

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44 AtransientsimulationwasperformedinPSPICEusingtheschematicas showninFigure4-15.Asquarewaveof300KHzwasappliedattheinputofthe primarywinding.Allotherwindingswereopen-circuitedexceptthesix-turn secondarywinding.A0.5 W loadwasconnectedacrossthesix-turnwinding.Tomake theopencircuit,a1e9 W resistancewasconnectedacrossthereset,nine-,andfiveturnwindings.Thesimulationwaveformsofthevoltagesacrossallwindingsare showninFigure4-16inwhichVin,V3,V4,andV5arethevoltagesacrossthe primary,nine-,five-,andsix-turnwindings,respectively.Asseenfromthe waveforms,thevoltagerisetimeandovershootattheprimarywindingare7.35ns and110%,respectively.Therisetimeofthevoltageatthesix-turnwindingis37.6 ns,andthereisnoripple.Sinceallotherwindingsareopen-circuited,thevoltages basicallyfollowthevoltageattheprimarywinding.Theovershootisdefinedbythe Figure 4-15. Extended cantiliver model schematic implemented in PSPICE

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45 followingequation:wherey1isthemaximumvalueofawaveformandy2isthefinal value of a waveform. (4.14) Figure4-16.PSPICEtransformerwindingvoltagewaveforms.(a)ECMmodel (dotted lines). (b) Ideal PSPICE model (solid lines) Ideal PSPICE model Overshoot y 1 y 2 () y 2 ---------------------100 =

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46 Thetransformerwastested,asshowninFigure4-12,toreproducethesimulated voltagewaveforms.ItwasexactlythesamesetupasthesimulationshowninFigure4-15. TheexperimentalwaveformsareshowninFigure4-17inwhichch1,ch2,ch3,andch4 arethevoltagesacrosstheprimary,nine-,ve-,andsix-turnwindings.Therisetimeand therippleatvoltageoftheprimarywindingwere8nsand110%,respectively,whichare consistentwiththesimulatedvalues.Therisetimeofthevoltageatthesix-turnwindingis 38 ns and there is no ripple. This value is also consistent with the simulated values. Figure 4-17. Experimental voltage waveforms across the windings VpriV3V5V4

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47 CHAPTER 5 CONCLUSION 5.1. Summary Thepracticaldesignissuesofmultipleexiblemagneticwindingsformagnetic componentsandtheirfabricationtechniqueswerestudied.Aexibleve-winding transformerwasfabricated,andthedcresistancesandtheECMparametersweremeasured. Itisveryimportanttousethecorrectvaluesoftheresistanceandparasiticinductance valuestomeasureECMparameters,otherwiseonemightgetunreliablevaluesofECM parameters. The key results are summarized as follows: Thedcresistancesofprimary,reset,nine-,five-,andsix-turnwindingswere97 m W 1230 m W 111 m W 46 m W and 100 m W respectively. ThetransformerwasmodeledbyECMparameters.Turnratiosof1.01,0.76,0.42, and 0.51 was obtained for the reset, nine-, five-, and six-turn windings. ToverifythemeasuredECMparameters,thetransformermodelwasgeneratedin PSPICE,and15virtualexperimentswereperformed.Allvirtualexperiments generate virtually the same data as the actual experiment. 5.2. Future Work Thefollowingtopicsrequirefurtherinvestigationtounderstandcompletely the proposed method of frequency domain modeling: Amoreefficientuseofcopperascomparedtoitsutilizationinthehalf-turncopper pattern. Evolvingatopologicalorproceduralprocedureinmodelgenerationtotakecareof nonsymmetricalcases,thatis,forthecaseswhentheimpedancesarenotbilateral in nature. Incorporating large signal core loss and hysteresis dependencies in the model.

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48 Effectofnon-idealgroundsduetothetestfixtureparasitcsathighfrequencieson the measured parameters. Obtainingaphysicalcircuitrepresentationorbasisfromthemeasuredparameters. Validation of simulation results with actual hardware testing.

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49 APPENDIX MATLAB SCRIPT TO CALCULATE THE REAL AND IMAGINARY PARTS OF THE IMPEDANCES % Load the measurement data clear all; V2=loadasc(N2.txt); V3=loadasc(N3.txt); V4=loadasc(N4.txt); V5=loadasc(N5.txt); V11=loadasc(Z11.txt); V12=loadasc(Y12.txt); V13=loadasc(Y13.txt); V14=loadasc(Y14.txt); V15=loadasc(Y15.txt); V23=loadasc(Y23.txt); V24=loadasc(Y24.txt); V25=loadasc(Y25.txt); V34=loadasc(Y34.txt); V35=loadasc(Y35.txt); V45=loadasc(Y45.txt); % Defining frequency data f=100e3:2.5e3:1.01e6; f=f; % Creating Vectors for Magnitude and Phase of the measured data N2g=V2(37:401); N2p=V2(438:802); %N2p=N2p-180; N3g=V3(37:401); N3p=V3(438:802); N4g=V4(37:401); N4p=V4(438:802); N5g=V5(37:401); N5p=V5(438:802); Z11g=V11(37:401); Z11p=V11(438:802); Y12g=V12(37:401); Y12p=V12(438:802); Y13g=V13(37:401); Y13p=V13(438:802);

PAGE 59

50 Y14g=V14(37:401); Y14p=V14(438:802); Y15g=V15(37:401); Y15p=V15(438:802); Y23g=V23(37:401); Y23p=V23(438:802); Y24g=V24(37:401); Y24p=V24(438:802); Y25g=V25(37:401); Y25p=V25(438:802); Y34g=V34(37:401); Y34p=V34(438:802); Y35g=V35(37:401); Y35p=V35(438:802); Y45g=V45(37:401); Y45p=V45(438:802); I=sqrt(-1); % Defining the current sense resistor Zsk=.01+f.*2*pi*7.5e-9*I; Ysk=1./Zsk; % Obtain magnitde and phase of magnetizing impedance Z11g=(abs(Zsk))./Y11g; Z11p=(180/pi)*angle(Zsk)-Y11p; % Obtain magnitde and phase of leakage impedance Z12g=1./(Y12g.*N2g.*abs(Ysk)); Z12p=-(Y12p-N2p+180/pi*angle(Ysk)); Z13g=1./(Y13g.*N3g.*abs(Ysk)); Z13p=-(Y13p-N3p+180/pi*angle(Ysk)); Z14g=1./(Y14g.*N4g.*abs(Ysk)); Z14p=-(Y14p-N4p+180/pi*angle(Ysk)); Z15g=1./(Y15g.*N5g.*abs(Ysk)); Z15p=-(Y15p-N5p+180/pi*angle(Ysk)); Z23g=1./(Y23g.*N2g.*N3g.*abs(Ysk)); Z23p=-(Y23p+N2p-N3p+180/pi*angle(Ysk)); Z24g=1./(Y24g.*N2g.*N4g.*abs(Ysk)); Z24p=-(Y24p+N2p-N4p+180/pi*angle(Ysk)); Z25g=1./(Y25g.*N2g.*N5g.*abs(Ysk)); Z25p=-(Y25p+N2p-N5p+180/pi*angle(Ysk)); Z34g=1./(Y34g.*N3g.*N4g.*abs(Ysk)); Z34p=-(Y34p+N3p-N4p+180/pi*angle(Ysk)); Z35g=1./(Y35g.*N3g.*N5g.*abs(Ysk)); Z35p=-(Y35p+N3p-N5p+180/pi*angle(Ysk)); Z45g=1./(Y45g.*N4g.*N5g.*abs(Ysk)); Z45p=-(Y45p+N4p-N5p+180/pi*angle(Ysk));

PAGE 60

51 % Compute real and imaginary parts N2=N2g.*exp(I*N2p*pi/180); N3=N3g.*exp(I*N3p*pi/180); N4=N4g.*exp(I*N4p*pi/180); N5=N5g.*exp(I*N5p*pi/180); Z11=Z11g.*exp(I*Z11p*pi/180); Z12=Z12g.*exp(I.*Z12p1*pi/180); Z13=Z13g.*exp(I.*Z13p*pi/180); Z14=Z14g.*exp(I.*Z14p*pi/180); Z15=Z15g.*exp(I.*Z15p*pi/180); Z23=Z23g.*exp(I.*Z23p*pi/180); Z24=Z24g.*exp(I.*Z24p*pi/180); Z25=Z25g.*exp(I.*Z25p1*pi/180); Z34=Z34g.*exp(I.*Z34p*pi/180); Z35=Z35g.*exp(I.*Z35p*pi/180); Z45=Z45g.*exp(I.*Z45p*pi/180); R11=real(Z11); L11=imag(Z11); R12=real(Z12); L12=imag(Z12); R13=real(Z13); L13=imag(Z13); R14=real(Z14); L14=imag(Z14); R15=real(Z15); L15=imag(Z15); R23=real(Z23); L23=imag(Z23); R24=real(Z24); L24=imag(Z24); R25=real(Z25); L25=imag(Z25); R34=real(Z34); L34=imag(Z34); R35=real(Z35); L35=imag(Z35); R45=real(Z45); L45=imag(Z45); % Compute transfer function coefficients for Z12 [B12,A12]=invfreqs(Z12,f*2*pi,3,2); hc12=freqs(B12,A12,f*2*pi); % Print real and imaginary parts of impedances at 300 KHz k=81; f(k)

PAGE 61

52 [R11(k) L11(k);R12(k) L12(k);R13(k) L13(k);R14(k) L14(k);R15(k) L15(k);... R23(k) L23(k);R24(k) L24(k);R25(k) L25(k);R34(k) L34(k);R35(k) L35(k);... R45(k) L45(k)]

PAGE 62

53 REFERENCES [1]A.Estrov,-MHZResonantConverterPowerTransformerisSmall,Efcient, Economical,Power Conversion, and Intelligent Motion, pp. 14-24, Aug. 1986. [2]A.F.Goldberg,J.G.Kassakian,andM.F.SchlechtIssuesRelatedTo1-10MHzTransformerDesign, IEEEPowerElectronicsSpecialistConferenceRecord ,pp.379-386, 1987. [3]P.M.GradzkiandF.C.Lee,DesignofHigh-FrequencyHybridPowerTransformer, Proceedings of Applied Power Electronics Conference pp. 319-326, 1988. [4]A.Estrov,IntegratingPlanarMagneticsinHigh-densityPowerConverters, Power Magnetics Magazine, pp. 18-21, Oct. 1990. [5]D.V.D.Linde,C.A.M.Boon,andJ.BKlaassens,DesignaHigh-FrequencyPlanar PowerTransformerinMultilayerTechnology, IEEETransactionsonIndustrialElectron ics, Vol. 38, pp. 135-141, Apr. 1991. [6]A.J.Yerman,High-FrequencyTransformer,U.S.PatentNo.4,959,630,September 25th, 1990. [7]K.D.T.Ngo,R.P.Alley,andA.J.Yerman,FabricationMethodforaWindingAssemblywithaLargeNumberofPlanerLayers, ProceedingsofAppliedPowerElectronics Conference pp. 543-549, 1991. [8]K.D.T.Ngo,R.P.Alley,andA.J.Yerman,R.J.Charles,andM.H.Kuo,Evaluationof Trade-offsinTransformerDesignforVery-Low-VoltagePowerSupplywithVery HighEfciency,andPowerDensity, ProceedingsofAppliedPowerElectronicsConference, pp. 344-353, 1990. [9]K.KSumandE.Herbert,NovelLow-ProleMatrixTransformersforHighDensity PowerConversion, PowerConversion,andIntelligentMotion, pp.102-104,Sept. 1988. [10]M.P.Perry,MultipleLayersSeriesConnectedWindingDesignforMinimumLoss, IEEETransactionsonPowerApparatus,andSystems ,PAS-98,No.1,pp.116-123, Jan. 1979. [11]Y.Q.Hu,D.K.W.Cheng,andY.S.Lee,NewFabricationMethodforPlanarMultilayerWindingsUsedinLow-ProleMagneticComponents, IEEETransactionson Magnetics, Vol. 35, No. 2, pp. 1056-1059, Mar. 1999.

PAGE 63

54 [12]Y.Q.Hu,D.H.He,andT.Y.Jin,Design,andApplicationofHigh-FrequencyLowProlePowerTransformers, IEEEInternationalConferenceonPowerElectronics, and Drive Systems PEDS, pp.40-45, July 1999. [13]R.W.EricsonandD.Maksimovic,AMultiple-windingMagneticsModelHaving DirectlyMeasurableParameters, IEEEPowerElectronicsSpecialistConference Record pp. 1472-1478, May 1987. [14]Flex-CircuitDesignGuide,ApplicaionAid#24,MincoProductsInc.,Minneapolis, MN. [15]K.D.T.NgoandS.Srinivas,BroadbandExtendedCantileverModelforMagnetic ComponentWindings, IEEETransactionsonPowerElectronics ,Vol.16,Issue6,pp. 551-557, July 2001. [16]W.SchillhammerandC.Forman,AdvancesinFlex/RigidFlexPrototypingTechnology, Idea/MicroelectronicsConferenceRecord ,WESCON,pp282-285,Sept. 1994. [17] SoftFerrites ,DataHandbookMA01,PhillipsComponents,1996,RockvilleCenter, NY. [18] Mathcad 2000 Professional Mathsoft Inc, Cambridge, MA. [19]R.W.Ericson,FundamentalsofPowerElectronics, Edition1997,Chapman&Hall, Boca Raton, Fl. [20] AutoCAD 2000 Education Version Autodesk Inc., San Rafael, CA. [21]M.ShahandK.D.T.Ngo,ParameterExtractionfortheExtendedCantiliverModel ofMagneticComponentWindings, IEEETransactionsonaerospaceandElectronic Systems Vol. 36, Issue 1, pp. 260-266, Sept. 1999. [22]S.Srinivas,Frequency-DomainModellingofMulti-WindingMagneticsBasedon theExtendedCantiliverModel, MastersThesis ,UniversityofFlorida,Gainesville, FL, 1999. [23] CaddockFilmResistorsCatalog ,26thEd.,1997,CaddockElectronicsInc.,Riverside, CA. [24]HP4194AImpedance/Gain-PhaseAnalyzerOperationManual,Hewlett-Packard Ltd., Kobe, Hyogo, Japan. [25] PSPICE student version 9.1, Cadence Inc., San Jose, CA. .

PAGE 64

55 BIOGRAPHICAL SKETCH MohammedS.AlamwasbornonAugust30,1973,inRangpur,Bangladesh. HerecievedaBSdegreeinElectricalandElectronicsEngineeringwithanemphasis inCircuitDesignfromtheBangladeshUniversityofEngineering&Technology, Dhaka(Bangladesh),inAugust1997.SinceJanuary1999,hehasbeenpursuingan MSinElectricalandComputerEngineeringattheUniversityofFloridaintheareas ofPowerElectronicsandCircuitDesign.HeisalsointerestedinRFICDesign.Other interests include photography and listening to music.


Permanent Link: http://ufdc.ufl.edu/UFE0000301/00001

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Title: Fabrication and characterization of multiple flexible magnetic windings
Physical Description: Mixed Material
Copyright Date: 2008

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Material Information

Title: Fabrication and characterization of multiple flexible magnetic windings
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

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Holding Location: University of Florida
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FABRICATION AND CHARACTERIZATION OF MULTIPLE FLEXIBLE
MAGNETIC WINDINGS











By

MOHAMMED S. ALAM


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2001















ACKNOWLEDGMENTS

I would like to thank my advisor, Dr. Khai D. T. Ngo for his interest and

patience during the work for this thesis. His approach to problem solving and

knowledge of practical issues made this work possible. He helped me to understand

the process of engineering. I would also like to thank Dr. Alexander Domijan and Dr.

Vladimir A. Rakov for all of their suggestions and for being on my advisory

committee. I would also like to thank Dr. Charlie Korman, Dr. John A Mallick,

Richard J Saia, and Sriram Ramakrishnan of General Electric Corporation for their

funding in this research. Thanks are also due to Paiboon Nakmahachalasint, June

Chen, and Mehul Shah for their help and camaraderie. I would like to place on record

my appreciation and gratitude to the Bangladesh University of Engineering &

Technology, Dhaka for the opportunity to study and learn in an environment that

made it all fun. Finally, I thank my family for their love and support.















TABLE OF CONTENTS

Page

ACKN OW LEDGM EN TS ................... ............................ ii

LIST OF TABLES ......... ............................................. v

LIST OF FIGURES .............................................. vi

ABSTRACT ......... .... .................................... viii

CHAPTERS

1 INTRODUCTION ................................. ............. 1

1.1 Background ............................................. 1
1.2 Thesis Chapter Synopses ......... ....................... ..... 3

2 FLEX MANUFACTURING .......... .................................. 5

2.1 Types of Flex Circuits ............... ......................... 5
2.2 Some Process Rules................ .................... ........ 6
2.2.1 Material Sizes in Flex Circuits. ............................ 6
2.2.2 Design Rules ....... ....... ................... ......... 6
2.2.3 Improving Flexibility and Bend Radius.................... ..... 7
2.2.4 Tear Stops .......... ............................ ......... 7
2.2.5 Circuit Pattern ............... ......................... 8
2.3 Flex Circuit Fabrication Process ................ ................. 8
2.3.1 Computer Aided Design Translation ........................... 8
2.3.2 Etching ................ ........................... 9
2.3.3 Solder Masking ............... ......................... 9
2.3.4 Alignment and Lamination .............................. 10
2.3.5 Drilling .................................... ........... 10
2.4 Definition of Terms ................ ......................... 10
2.4.1 Small Rectangle ....................................... 10
2.4.2 Large Rectangle ............... ....................... 11









3 LAYOUT DESCRIPTION AND FABRICATION OF THE FIVE-WINDING
TRAN SFORM ER ......... .............................. 12

3.1 D description of Layout ........................................... 12
3.2 Folding Sequence. ............................................ 22

4 MODELLING OF THE TRANSFORMER AND EXPERIMENTAL RESULTS. 26

4.1 M odelling .................................. ...... ...... .. 27
4.1.1 Basic Measurement Methodology ............................ 28
4.1.2 Why Use the Four-point Measurement System? ................ 32
4.1.3 The Measurement Board: Layout and Interconnections ........... 33
4.2 Effect of Nonzero Current Sense Impedances ......................... 35
4.3 Experimental Results ......................................... 39

5 CONCLUSION ..................................................47

5.1 Summary ................................................47
5.2 Future Work ................ ............................. 47

APPENDIX: MATLAB SCRIPT TO CALCULATE THE REAL AND IMAGINARY
PARTS OF THE IMPEDANCES .........................................49

REFERENCES ....... ............................................... 53

BIOGRAPHICAL SKETCH ........................................... 55















LIST OF TABLES

Table

2-1 Material sizes used in the flex circuit .................................. 6


2-2 Some design rules ................ .............................. 6


3-1 Specification of the transformer ................. ................. .. 13


4-1 Summary of the dc resistance measurement. .......................... 39


4-2 Summary of the ECM parameters measurement ........................... 41

















LIST OF FIGURES


Figure

1-1 A fabricated flex circuit for a five-winding transformer

1-2 A 5/6-turn winding pattern ........................

2-1 Types of flex .............. ..................

2-2 Good and bad copper pattern to prevent broken conductor.


2-3 Small rectangle


Large rectangle ...................

Planar core (E/18/10) ..............

First small rectangle ...............

Holes and folding lines for .........

Width of the large rectangles .......

Hole dimensions in cm.............

Large rectangle dimensions in cm ...

Layout of the twelve-turn primary wir

Layout of the reset winding.........

Layout of the nine-turn winding .....

Layout of the five-turn winding ....

Layout of the six-turn winding .....


3-12 Vertical drawing


. 14

S.15

. 16

. 17

..18


hiding. .......... ......... ......... 19

. . . . . . . . 2 0

. . . . . . . . 2 0

. . . . . . . . . 2 1

. . . . . . . . . 2 1

. . . . . . . . 2 2


3-13 First flex folded along folding lines 1 and 2.


Page

. 2

. 3


2-4

3-1

3-2

3-3

3-4

3-5

3-6

3-7

3-8

3-9

3-10

3-11


. .. .. ........









3-14 Second flex folded along folding lines 1 and 2. ................... .. .23

3-15 First flex folded along folding lines .............................. 23

3-16 Second flex folded along folding lines ............................ 24

3-17 First flex placed on top of second flex and folded along folding lines ..... 24

3-18 Complete transformer. ........................................... 25

4-1 Extended cantilever model for a five-winding transformer ................ 27

4-2 Basic measurement setup. ......................................... 29

4-3 Measuring leakage impedances. .................................... 30

4-4 Turn ratio measurement. .......................................... 31

4-5 Reference waveform being sampled at the terminal ................... 32

4-6 Four-point measurement system. .................................... 33

4-7 Circuit diagram indicating the testing terminals for the transformer ........... 34

4-8 Layout diagram of the bottom of the test fixture showing interconnects ......... 35

4-9 Layout diagram of the top of the test fixture showing the BNC terminations ..... 36

4-10 Leakage impedance measurement referred to the primary node ........... 36

4-11 Norton equivalent of leakage impedance measurement circuit ............ 38

4-12 Transformer implemented on a test fixture ............................ 40

4-13 The bottom view of the test fixture. ................................ 42

4-14 Ideal transformer. ................. ................................ 43

4-15 Extended cantilever model schematic implemented in PSPICE ........... 44

4-16 Transformer winding voltage waveforms simulated in PSPICE ........... 45

4-17 Experimental voltage waveforms across the windings ................... .. 46















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

FABRICATION AND CHARACTERIZATION OF MULTIPLE FLEXIBLE
MAGNETIC WINDINGS

By

Mohammed S. Alam

December 2001

Chairman: Khai D. T. Ngo
Major Department: Electrical and Computer Engineering

Flexible circuits are used for magnetic components to reduce size and weight

and to increase power density. The flex foils are basically built using conductor and

insulator materials. Among the conductor materials, probably the best solution is

copper because it presents a good trade-off between electrical characteristics and

cost. Because the insulator material needs good mechanical characteristics, it should

be chosen carefully. When designing flex circuits, many factors must be considered,

such as mechanical performance and electrical performance. The bend radius is the

most important mechanical characteristic for this particular application.

This thesis presents the design, fabrication, and characterization of a five-

winding transformer using a flex circuit. This design technique deals with the trade-

off among core size, core loss, ease of manufacturing and folding; the minimum

number of layers; and the winding assembly so that the terminations of the primary

and secondary fall on both sides of the core. This method virtually eliminates









external soldering or conductive vias, thus reducing dc resistance and cost and

increasing reliability. The designed transformer has twelve turns in the primary

winding and twelve turns in the reset winding. The secondary windings have nine,

five, and six turns. Before fabrication, the layout of the transformer was done in

AutoCAD and the details of the layout were presented. A planar E core (E18/4/10)

was used to design the transformer. The dc resistances of 91 mQ, 1210 mQ, 125 mQ,

49 mQ, and 108 mQ were obtained for the primary, reset, nine-, five-, and six-turn

windings, respectively. The transformer is modeled by using the Extended Cantilever

Model (ECM) approach.















CHAPTER 1
INTRODUCTION

1.1. Background

Magnetic components are often fabricated using planar windings on printed

circuit boards [1], flex circuits [2], and hybrid circuits [3] because of the trend toward

miniaturization of electronic components. Compared to the conventional

transformers/inductors, planar transformers/inductors have lower packaging profiles

and higher power densities [4]. Planar windings using multilayer PCB (ML-PCB)

have been reported in [5], but the number of turns of windings that can be placed in

series is limited and is determined by the core type. This approach is not suitable for

windings with a large number of turns and a high degree of interleaving.

The flex circuit is presented as a method to fabricate a winding assembly with

a large number of conductive and insulating layers [6-12]. However, no detailed

scheme is presented using 2D-folding for multiwinding magnetic components where

several trade-offs exist including core size, core loss, ease of manufacturing and

folding of flex circuits, and the minimum number of layers. This thesis deals with

these issues. A five-winding transformer is laid out, fabricated, and modeled.

Two-dimensional (2D) folding is defined as the folding pattern in which the

flex circuit is folded both along the x-axis and y-axis. A fabricated flex circuit for a

five-winding transformer is shown in Figure 1-1. Figure 1-1 shows that to get the












t


t


Figure 1-1. A fabricated flex circuit for a five-winding transformer. (a) Primary
and reset windings; (b) Secondary windings
required number of turns, the flex circuit should be folded both along the x-axis and

y-axis; that is, the folding is two-dimensional (2D).

The advantages of 2D folding are as follows:
* It avoids longflex circuits that usually result if the turns are constrained to a 1D
layout.

* It avoids a large number of separate flex circuits that need to be assembled. In fact,
it might be possible to lay out all the windings on a single flex circuit.

* It minimizes the number of vias used. In fact, all the patterns shown in Figure 1-1
require no via. A via is used to connect the isolated copper pattern that will be in
series.


(a)














i (b)
i:; v






















Figure 1-2. A 5/6-turn winding pattern


In order to reduce the manufacturing cost, the number of layers should be kept at a

minimum. One way to accomplish this is to put several windings on the same layer as

shown in Figure 1-1. In addition, several half-turns (or fractional turns, in general) of the

same winding can be put in the same layer.

Another way to reduce the number of layers in a winding stack is to increase the

number of fractional turns on each layer. For instance, if a 5/6 turn is put on each layer, the

5/6 turn winding pattern shown in Figure 1-2 results. This pattern uses space more effi-

ciently. That is, it covers most of the winding area on each side of the flex circuit with cop-

per. Thus, for a given number of series turns, the number of 5/6-turn layers would be

almost half of the number half-turn layers. Six folding edges are hexagonally distributed

along the circumference of the winding stack. Copper build-up along the folding edges

would be less than in the half-turn patterns, and planarization would be less of a problem.

1.1. Thesis Chapter Synopses

Different types of flex circuits are discussed in Chapter 2. Also discussed are

some process rules and their advantages and limitations in keeping with the aim of

this study. Layout and fabrication of a five-winding prototype transformer are

detailed in Chapter 3. The folding sequence is also described.






4


A model of the transformer [13] and experimental results are presented in Chapter

4. The procedure to implement the ECM in a circuit simulator is also briefly

described. Chapter 5 draws conclusions from the results and discusses insights

obtained from this work. Finally, it proposes possible future directions that may be

explored.















CHAPTER 2
FLEX MANUFACTURING

The flex circuits basically are built using conductor and insulator materials.

Among the conductor materials, the use of copper probably is the best solution

because it presents a good trade-off between electrical characteristics and cost.

Because the insulator material needs good mechanical characteristics in order to

allow folding with no cracking problems, its selection is more complicated. Usually

kapton, which is chemically a polymide, is used as the insulator because of its good

electrical, thermal, and mechanical properties.

2.1. Types of Flex Circuits

There are two types of flex circuits: single-sided flex and multi-sided flex. The

single-sided flex circuit has one conductive layer on a flexible insulating layer and

can be fabricated with or without coverlayers. Single-sided flex circuits are less

expensive. The single-sided flex circuit is shown in Figure 2-1(b).

The multi-sided flex circuit has two or more conductive layers with a flexible

insulating layer between two conductive layers and can be fabricated with or without

coverlayers. Connections between conductive layers are provided by platted through-

holes. Access holes or exposed pads without covers may be on either or both sides.

The multilayer flex circuit is shown in Figure 2-1(a).














(a)


LEGEND
* Copper
E] Kapton
O Adhesive
71\------


(b)
Figure 2-1. Types of flex (a) double-sided; (b) single-sided

2.2. Some Process Rules

Building a flex-circuit generally involves employing the same steps from

circuit to circuit. However, certain circuit design can add cost. Access holes and

supplementary layers add cost. Usually the cost is comparable to the number of

layers. The higher the number of layers, the higher the cost. For example, two double-

sided circuits could potentially be less expensive than one four-layer multi-sided

circuit. Circuits can also be folded in order to save space and layers.

2.2.1. Material Sizes in Flex circuits

Material sizes [14] used in flex circuits are listed in Table 2-1.

Table 2-1. Material sizes used in the flex circuit
Material Sizes (milli inch)
Insulator 0.5, 1, 2, 3, 5
Conductor 0.7, 1.4, 2.8, 4.2
Adhesive 0.5, 1, 3, 4


2.2.2. Design Rules

Some design rules [14] are given in Table 2-2.

Table 2-2. Some design rules
Function Minimum Value (mi
Conductor width/ spacing 5 for 1 ounce copper
7 for 2 ounce copper
Trace to edge spacing 5
Inner radius for holes or slots 12.5
Conductor width 5 times greater than


li inch)




the thickness









2.2.3. Improving Flexibility and Bend Radius

Single-sided circuits are probably the best choice for dynamic (flex-in-use)

applications. Generally, mutilayer circuits are better suited to static applications

where the circuit is folded only during installation. The minimum allowable bend

radius of a multi-sided flex is six times the overall thickness. Roughly, the circuit

thickness is slightly smaller than the sum of the insulator, adhesive, and cover layers.

Some possibilities to improve flexibility include:

* Circuits with two layers or more selectively platted to improve dynamic flexibility

* Keeping the number of bends to a minimum

* Conductors staggered to avoid an I-beam effect, and routed conductors perpendic-
ular to a bend

* Pads or through-holes not be placed in bend areas

* Factory forming as a considered option. Most constructions can be factory formed
depending on the geometry. Because circuits are flexible, formed circuits will relax
in time. Form tolerances apply only to the part in the constrained position.

* Preferable not to place conductor, discontinuities in the cover or other stress con-
centrating features near any bend location.

* Unbonded layers in a relatively thick multilayer or rigid-flex circuit are an option
in order to improve flexibility, but this may be more expensive.

2.2.4. Tear Stops

Polymide presents a high initial tear strength, but once a tear starts, it

propagates easily. All inside corners must be radiused. The larger the inside radius,

the greater the tear strength. If tearing is a concern, polymide-insulated circuits can

be designed at the inner corners for corners of 1200 or less. Internal or external
















44 1






Good Bad

Figure 2-2. Good and bad copper pattern to prevent broken conductor


polymide or Teflon tear stops can be incorporated. Polymide or Teflon tear stops will

add to circuit cost.

2.2.5. Circuit Pattern

For ease of manufacturing, flaring of lines into pads is necessary when the pad

is unsupported by the coverlay. This is done to provide strain relief at the pad/line

intersection to prevent broken conductors. For ease of manufacturing, sudden

expansion or reduction in conductor width is not recommended. Acute angle copper

pattern is also not recommended, as shown in Figure 2-2.

2.3. Flex Circuit Fabrication Process

Flex circuit fabrication process can be broken down into five separate

production steps [15,16]. Each is described separately.

2.3.1. Computer Aided Design Translation

The flex circuit can be manufactured directly from CAD data (usually Gerber

files). A PC based software translates Gerber data into a plot file. This plot file is









electronically sent to the Plotter/Etcher. In the Plotter/Etcher, a high precision inkjet

print head images the circuit onto a flex circuit material.

2.3.2. Etching

After the circuit design has been imaged onto the flex material, the film is then

forwarded using a positive drive motion control system into a cascading etch tank in

front of the Plotter/Etcher. Once the film has been loaded into the etch tank, the

Potter/Etcher automatically starts a preset etch cycle. The flex circuit is sprayed with

sodium persulfate. The sodium persulfate, etches away all of the exposed copper,

leaving only the protected circuit design on the film. After the etch cycle is complete,

the film is sprayed with a fresh water rinse. This rinse removes any active etchant still

deposited on the circuit. The flex circuit is then forwarded out of the Plotter/Etcher.

2.3.3. Solder Masking

After the flex circuit has been removed from the Plotter/Etcher, a cover layer

is used to protect the circuit from bridging or electrical gaps.


C 1370
0,470


1,030 1,970


0,470 .

0,470-- I...
0.430 L0.470


Figure 2-3. Small rectangle (in cm)









2.3.4. Alignment and Lamination

After solder masking, the layers are aligned with the alignment punch. Once

aligned, the layers are then laminated in heat seal press.

2.3.5. Drilling

The laminated board is then placed in high performance driller for through

hole drilling and final board routing.





1,970







1,970



-----I



1.970




1,370-
Figure 2-4. The large rectangle

2.4. Definition of Terms

2.4.1. Small Rectangle:

A small rectangle contains only one hole as shown in Figure 2-3.






11


2.4.2. Large Rectangle:

A large rectangle contains three vertical rectangles as shown in Figure 2-4.















CHAPTER 3
LAYOUT DESCRIPTION AND FABRICATION OF THE FIVE-WINDING
TRANSFORMER

Before the layout of the transformer, the core should be selected according to

the requirements such as power, number of turns, power loss, duty ratio of the

converter, operating frequency, power carried by different windings, voltage and

current of different windings, and so forth. The specifications of the transformer are

shown in Table 3-1. The primary and reset windings are referred to as windings W1 and

W2, respectively, and the nine-, five-, and six-turn secondary windings are referred to as

W3, W4, and W5 respectively. Since the transformer fabricated is supposed to be used in a

multiple output forward converter, the reset winding will be used to reset the converter.

According to the specifications, core E18/4/10 [17], which is a planar E core, was

selected by using Mathcad [18], and by using equations from [19]. The material of

the core is 3F3 ferrite. The cross-sectional view of the core E18/4/10 is shown in

Figure 3-1 .

3.1. Description of Layout

The layout of the transformer was done by AutoCAD [20]. The layout of the

primary and the reset winding was done in one flex and the layout of the secondary

windings was done in another flex. The two flexes can be fabricated either in single-

sided flex or in double-sided flex. For the rest of the thesis, the first flex will be










referred to as primary and reset windings and the second flex will be referred to as

secondary windings.




I I ~





--4m

'igure 3-1. Planar core (E18/4/10). (a) Top view (b) Bottom view

Table 3-1. Specification of the Transformer
Windings Turns Error in num- Peak Voltage Peak Current
ber of turns (Volt), wave (Amp)
shape (rectan- wave shape
gle) (rectangle
W1 12 0.12 38 1.538
W2 12 0.12
W3 9 0.12 10 0.30
W4 5 0.04 5 2.10
W5 6 0.12 12 0.41
Operating frequency 300 KHz
Output Power 20 Watt
Power loss 1 Watt


After trying in different methods, it was decided to use 24 small rectangles

where a small rectangle is defined in Section 2.4.1. The holes and folding lines of the

first and second flexes are shown in Figure 3-3. The hole dimensions of the flexes are

determined by the size of the core. Figure 3-1 shows the dimensions of the middle

leg of the core as 10 mm x 4 mm. Since it was determined that the Kapton and the

copper, should not touch the core, a clearance of 0.15 mm was chosen between the

Kapton and the core. If the copper touches the core, it might short the core. So the











11 1
0,470


1,030 1,970


0,470

0,47 0- 1 ..
0.430 L0.470
Figure 3-2. First small rectangle (in cm)
hole dimensions were chosen as 10.3 mm x 4.3 mm. Figure 3-1 shows that the

corners of the leg of the core are rounded. So the corners of the hole were also

rounded. According to Section 2.2.2, the minimum round radius should be 12.5 mils.

So a round radius of 31 mils was chosen. The zoom-in view of the hole with its

dimensions is shown in Figure 3-5. To determine the dimensions of the small

rectangles, the dimensions of the first rectangle should be determined first. The

dimensions of the first rectangle are determined by the size of the core, too. Figure

3-1 shows that the maximum dimensions of a small rectangle can be 14 mm x 20 mm.

To make sure there is a clearance of 0.15 mm between the Kapton and the core, the

dimensions of the first small rectangle were chosen as 13.7 mm x 19.7 mm. Figure

3-3 shows that though there are 24 small rectangles, each of the three vertical small

rectangles can be grouped as one large rectangle. So there are eight large rectangles

in each of the flex, and the dimensions of the first large rectangle should be 13.7 mm

x 3*19.7 mm, that is, the width and height are 13.7 mm and 3*19.7 mm. The first

large rectangle is shown in Figure 3-6 with its dimensions. To align the holes after










4-&H /NI




*---
I


~Q


T
--4-


I


- -I -I- --I-


I I I
--- -I----


I I


- -I--- -t+- --





I I
---------
t _ _


-1. 37 30 0-.1.270- 1.170- 27 0-1.370 1.270- 1.270-
3 4 5 6 7 8 9


Figure 3-3. Holes and folding lines for (a) First flex. (b) Second flex (dimensions in
cm)
the folding of the flex, the height of all large rectangles should be same. The width

of the large rectangles can be different, but this should not affect the alignment of the

holes. There are folding lines between all small rectangles.

The width of the large rectangles is made in a long-short pattern so that, upon fold-
ing, two consecutive folding edges do not fall on top of each other. By doing this, the jam-


1.970

1


2


E.800



1.970


1,970


I 0.430 0.370 0.370









ming of copper along the folding edges can be avoided. The width of each large rectangle

is determined by the following equations:

n = a n=1,2,6,10 (3.1)

wn a b, n=3,5,7 (3.2)


wn a 2b, n=4,8,12 (3.3)

where wn is the width of the nth large rectangle, a is the width of the first large rectangle,

and b is the length, which is shorter than the width of the first large rectangle. For the

designed transformer, a and b are shown in Figure 3-4.

8th large rectangle

7th

6th

5th

4th


3rd .

{ ____ 2nd h -

1st




Figure 3-4. Width of the large rectangles

Figure 3-3 shows that the width of the large rectangles are determined by

equations 3.1 to 3.3, and these equations can be applied for any number of large

rectangles. For example, for n=3, the width of the 3rd large rectangle is 12.7 mm


















RO,800
0.87
1.03






0.804


Figure 3-5. Hole dimensions in cm

(13.7 mm-1 mm) by using the Equation (3.2). In the design of the transformer, the

value of 'b' was chosen to be 1 mm.

As previously discussed, there are two flex circuitries. The first flex circuit

contains primary and reset windings, and the second flex circuit contains nine-,

five-, and six-turn secondary windings. To understand the copper pattern of the

windings clearly, each is described separately.

As shown in Figure 3-7, the primary winding starts at terminal P+ and ends

at terminal P-. The serpentine copper pattern follows around 24 apertures to make

twelve turns, according to the specifications as shown in Table 3-1. Figure 3-8 shows

the layout of the reset winding which starts at terminal R+ and ends at terminal R-.

The serpentine copper pattern follows around 24 apertures to make 12 turns,

according to specification.

The nine-turn secondary winding starts at terminal 9+ and ends at terminal

9-, and the serpentine path follows 12 apertures to make nine turns as shown in













1,970







1,970



--- --I



1.970




^1,370-

Figure 3-6. Large rectangle dimensions in cm

Figure 3-9. The five-turn secondary winding starts at terminal 4+ and ends at

terminal 4-, and the serpentine path follows 10 apertures to make five turns as shown

in Figure 3-10. During the layout, an effortwas made to increase the width of this

five-turn winding because it carries more current. The six-turn secondary winding

starts at terminal 6+ and ends at terminal 6-, and the serpentine path follows twelve

apertures to make six turns as Figure 3-11.

The copper runs perpendicularly along the folding lines to make the folding

easier and the copper is split along the folding lines in order to make the inter-layer


























Figure 3-7. Layout of the twelve-turn primary winding


capacitance less and also to fold more easily. The copper pattern is extended outside

at the beginning and end of the windings to form pads for the terminations. At the

terminations, it is necessary to see the spacing between the copper.

Otherwise, one might short the copper. So at least 2 mm spacing was ensured.

Figure 3-7 and Figure 3-8 were combined to form the first flex, as shown Figure 1-

l(a) and Figure 3-9 -Figure 3-11 were combined to form the second flex, as shown in

Figure 1-1(b). Since two or more windings were fabricated in one flex, a minimum

copper spacing of 0.3 mm was chosen, as shown in Section 2.2.2 For all the windings,

the copper thickness was 1.4 mils but the width of copper varies. Since the copper

width of the reset winding can be smaller, a minimum copper width of 0.3 mm was

chosen according to. An effort was made to use all areas of the rectangles for copper

so that minimum winding copper loss occurs.

The layout was done in a way such that, after folding, the terminations of the pri-

mary and reset windings fell on one side of the transformer core, and the terminations of

all the secondary windings fell on the other side of the transformer core. It was also



























Figure 3-8. The layout of the reset winding

ensured that two terminations of any secondary winding were next to each other upon

folding. By doing this, the length of the wire was reduced during testing of the trans-


Figure 3-9. Layout of the nine-turn winding

former, and it also made the winding easier to short during the measurement. A primary

benefit of this layout is that there are no vias or soldering.

As shown in Figure 3-12, the first flex has Kapton on both sides except where the

terminations are. The secondary-winding flex has Kapton on one side except where the

terminations are; the other side has exposed copper. It is obvious that the flexes are single-


























Figure 3-10. Layout of the five-turn winding


Figure 3-11. Layout of the six-turn winding

sided and not double-sided. The single-sided flex was fabricated rather than double-sided

because the double-sided flex is more costly. For all windings, the copper at the termina-

tions is covered by solder so that the terminations do not oxidize. It is also seen in Figure

3-12 shows that the Kapton and adhesive thickness are both 0.5 mils. The Kapton and

adhesive thickness of 1 mils could be used with less cost; however in order to fit two flexes

into the window height of the core (4 mm total for two cores), the Kapton and adhesive

thickness of 0.5 mils were chosen.











S- / //- / / / LEGEND

(a) 1i4 mRs Copper
[ 0.5 mis Kapton
F[30.5 mlls Adhesive

(b)
Figure 3-12. Vertical drawing. (a) First flex. (b) Second flex
After folding, the total height of both the flexes were calculated from Figure 3-12
-3
and was 3.536 mm [(1.4 x 2 +0.5 x 6) x 24 x 10- x25.4= 3.536mm].

3.2. Folding Sequence

The first and second flex of the transformer shown in Figure 1-1 should be folded

along the folding lines according to the sequences. Otherwise, the primary and secondary

winding flexes cannot be interleaved. The first and second flex of the transformer along

with folding lines are shown in Figure 3-3. In Figure 3-3, the dotted lines are the folding

lines, and they are numbered from 1 to 9 to maintain a folding order. For both the first and

second flex, they are first z-folded along folding lines 1 and 2, as shown in Figure 3-13 and

Figure 3-14, respectively.

Then they are z-folded along the folding lines 3, 4, 5, 6, 7, 8, and 9, respectively, as

shown in Figure 3-15 and Figure 3-16. The two flexes are folded along folding lines 1

fl=folding
line







fil 1 fl 2


Figure 3-13. First flex folded along Folding Lines 1 and 2












l=fkolding
line


fl I


Figure 3-14. Second flex folded along Folding Lines 1 and 2


... = follding
line






_fl_


.... ...... .. ...... ...iii::
.. ......... .. .. .. ....
::ii:::i: i:.:i::::,:.i i ::i ::i : :i :::.:iii -...::i:.: :: ::::i : ::. ============================ iii: ::::. : :::.: :::i.: ::a 'ii
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::: :::::::::::::::::::::::-::::::::: :::.:::::: :::::::::::::: :;:.: :::i il!: ;!..::::i: i:i
:.:::iiiiiiiiiiiiiiiiiiii'i:.ii::.!:i iii :.:.:i:iii i ::. i:::::::::::::::::::::::::::::::::::: : .i: i ::::::. i:i iii:::l: ii:: : i.::::::::::::::::::::::::: :: 2.::.` ::::i : ::::'i: :~i i: N
ii~ i"::i::::i "::.: .:...i :.i:: ...'::i::': :i ::ii.:i ..i':i ::i.i ..:.:iiii:'i':: ........... .. ............. ........... ""............
::.::, .-: .. -::.:.:. .:: ::::::: :::::::::: .:.. : .:: ...: ..: ... .: :: .:..: ......:.: ..: ... ..................:':: ::::::: :iiiiii i-.. :
::.:.. ......... ... : ......................: :::: :::. ::
.................................
..... ..... ... ................. ..... : ---
................ ........ .. .. ....... ... .... .. ... .....

...... .......; .... .. ..... .
........... .. .. .. ... ..... ............. ..
.. ..... .. .. ... ...... .. .................. ..............

.. .......... ...... ... .. .. .. .. . ..... .. ... ........ ......


Figure 3-15.


fl9 fl8 fl7 fl6 fl5 fl4 fl3
First flex folded along Folding Lines 1 and 2 first, and then Folding
Lines 3, 4, 5, 6, 7, 8, and 9


and 2 first because if they are folded along folding lines 3, 4, 5, 6, 7, 8, and 9 first, it

would be difficult to fold flex along the folding lines 1 and 2 because of the thick copper-

stack. After folding along the folding lines, the two flexes are unfolded, and the second

flex is placed on top of the first flex, to interleave the primary and secondary windings as

shown in Figure 3-17. They are then folded again along folding lines 1 and 2 first. Then

the folded first small rectangle is inserted in the E18/4/10 core, and then the two coupled

windings are z-folded along the folding lines 3, 4, 5, 6, 7, 8, and 9, and then inserted


into the core. This was done so that the apertures of the windings become aligned.


The complete transformer is shown in Figure 3-18.


fl 2 --


.... ... 0 4 .......... ..
.:. ...... .'i'.... .. ..
." .. .: . .... . ... .i.


: : :.:: :.... .. ... ....... :... :. .
.... :::::... ......:.... : ... ... ..... ....: .:.. ... .... ... : :
.......................................:.. ...
.
...... .
......... ...... ..... ......... ... ..
.. .. .. .. .... .. ..... ... ........ ... ..


I












fl=folding
line







flI



fl9 fl8 fl7 fl6 fl5 fl4 fl3

Figure 3-16. Second flex folded along Folding Lines 1 and 2 first and then Folding
Lines 3, 4, 5, 6, 7, 8, and 9



fl=foldin
line










Figure 3-17. First flex placed on top of the second flex, and Folded along folding
Lines 1 and 2 first, then Folding Lines 3, 4, 5, 6, 7, 8, and 9

























9-
9+
R+
6-
P+ 6+

P- > 5-
R- > 5+






Figure 3-18. Complete transformer















CHAPTER 4
MODELING OF THE TRANSFORMER

Modeling of multiwinding magnetic components is difficult in view of the

cross-coupling among the windings. Analytical expressions are invariably complex

and difficult to obtain for such cases. Additionally, such an approach is limited to

specific geometries and/or number of windings. Modeling a magnetic component

from terminal port measurements is necessary in many cases for verifying or

predicting converter dynamics. For applicability, the model has to be sufficiently

broad-band to deal with the high frequency nonsinusoidal waveforms present in

present-day converters.

The Extended Cantilever Model in [13], modified in [15], [21], and [22] is

used to model the transformer. However, the measurement setup itself tends to have

parasitic elements that can alter the observed frequency response of the Device Under

Test (DUT). The four-point measurement system is preferred for its ability to reduce

the effects of parasitic elements. Measurement of leakage impedances in the ECM

requires sensing short-circuit currents. This is an extremely stringent condition. In

fact, non-idealities in measurement of short-circuit currents can affect the very

topology of the impedance being measured. It is important to understand the

requirement of a "good short" with respect to the ECM.




















n5:1 I l:n3




w3
W5

1:n4
1____________________________ PPS



SW4

Figure 4-1. Extended cantilever model for a five-winding transformer


4.1. Modeling

An equivalent circuit model is developed that is useful for the simulation of the

converter into which the transformer is embedded. The procedure described in [21] is

employed to measure the model parameters for the frequency of interest which is 300

KHz.

The model topology, an extended cantilever model (ECM) [13], is shown in

Figure 4-1. In ECM, N(N+1)/2 independent parameters are required to model a trans-

former containing N winding. Each parameter of the ECM can be directly measured. The

self-impedance Z11 can be measured by open-circuiting W2, W3,..., and measuring the

impedance of winding W1. The self-impedance Z11 is given by,









v1
Zl= ,ik = 0,2k5 (4.1)
1

To measure the effective turns ratios n2,n3,..., a voltage is applied to winding W1

with other windings open-circuited. The effective turns ratio nk is given by,

vk
nk -, for k# 1, 2< k 5 (4.2)
k vI
1

A negative value of nk indicates that the winding polarity marks should be reversed.

To measure the effective leakage impedance Zjk, winding Wj is driven with voltage

source vj, while all other windings are short-circuited. It is important that good low-

impedance short-circuits be used. The current ik in winding Wk is measured. The effective

leakage impedance is Zjk is given by,

V.
Zjk n.n *i, k j; vn= 0, n j (4.3)
J k k

4.1.1. Basic Measurement Methodology

The measurement of the ratio of the applied voltage to the output current/

voltage is the first step in determining the desired transfer function. The actual

transfer function is measured as a ratio of the applied and measured waveforms using

an Impedance/Gain-Phase analyzer (Figure 4-2). A Hewlett-Packard 4194A

Impedance/Gain-Phase analyzer was used to characterize the device under test

(DUT). The quantities required for the model have dimensions of resistance (Ohms)

for the self and leakage impedances or are dimensionless for the turns ratios. In other

words, the applied stimulus is always a voltage, and the observed stimulus is a

current for measuring the impedances or a voltage for the turns ratios. Measurement

of the current is accomplished using current sense resistors in series with the winding































Swept Frequency
Source


Figure 4-2. Basic measurement setup


being measured. This transforms the measurement of current to a measurement of

voltage. For each leakage impedance, a current sense resistor is used to short the

winding in order to sense the current in the "short-circuited" winding, as shown in

Figure 4-3.

All other windings being excited have true shorts across their terminals. The

effects of using current sense resistors in place of a "true short" is discussed in

Section 4.2. The two voltages are then fed to the 4194A, and the ratio between the

two voltages is scaled by the value of the current sense impedance to obtain the

impedance being measured. For the self impedance, the current sense resistor is










12

+




13




n3
+ i

Vapp Vp i4




n4

i5




[5


Figure 4-3. Measuring leakage impedances

simply placed in series with the winding to obtain the current through it. These

relations can be formally written as follows:


Z = appj Z (4.4)
VSense,i ninj ense



where VSense' is the ratio measured by the 4194A.
Vapp,i
The turns ratios are directly measured as the values recorded by the 4194A

(Figure 4-4).













n2 2 VSensel


i3

SO
vp


v O--14



n4

15






Figure 4-4. Turn ratio measurement.

n VSensek (45)
njk v(45)
app,j

It should be noted that all these values are measured across a frequency range of 10 KHz to

1.01 MHz. Then these data were post-processed for 300 KHz.

The self-impedance of the primary winding, Z]], is measured using the

impedance analyzer, as this would avoid any parasitic effects by using the other

measuring systems. Because Z]] is large at high frequencies, parallel cable

capacitances can cause problems if it is measured in a similar fashion to the leakage

impedances.








4.1.2. Why Use the Four-point Measurement System?

In this section, the advantages of the four-point measurement system are

illustrated using the case of self-impedance measurement. The oscillator of the

4194A typically sources out a sine wave of preset magnitude into the terminals of the

DUT. During this measurement, the reference and the test inputs of the 4194A are set

to a high impedance level of 1Mg. The reference and test waveforms are fed back to

"- Zpar src---
'1III I,


+ v
L j + DUT







Figure 4-5. Reference waveform being sampled at the terminal where the source
waveform is applied

the 4194A from the DUT. For the case shown in Figure 4-5, the reference waveform is fed

back to the 4194A through a T-connector at the same point the source waveform is being

applied to the DUT. In this case, the terminating impedance is 1 MQ in parallel with a 28

pF Capacitance. Hence, the current in the cables connecting the reference and test

potentials to the 4194A will be small. Again, the parasitic drops across the cable will be

small. However, the drop across the exciting cable and its interconnects will be substantial

as the cable carries the sourcing current, which could be large. In fact, the Zpar(s)i src

voltage drop shown in Figure 4-5 is now being erroneously fed back as part of the reference

voltage ref, instead of the actual voltage Vp.











-Zparisrc---
'^^ II


Vapp -ar Vp


Vref


Figure 4-6. Four-point measurement system

The four-point measurement system avoids this problem by using separate

points for the sourcing and reference voltages (Figure 4-6). This ensures that the

reference voltage does not include the parasitics caused by the interconnects as the

current in this case is low. While series parasitic effects are avoided, parallel parasitic

effects, such as the cable capacitance, can still affect the measurement.

4.1.3. The Measurement Board: Layout and Interconnections

The measurement board was fabricated on a double layer FR4 copper board

using a T-Tech circuit board milling machine. Its dimensions are 4"x4". The board

layout is based on the four-point measurement system with an emphasis on keeping

the reference and test points close to the actual windings and/or current sense

resistors (Figure 4-7). The sourcing inputs are located farther from the test and

reference points. Figure 4-8 details the actual layout of the bottom of the test board.

All the BNC connections and transformer windings are soldered on the bottom of the

board. The current sense impedances or shorts for various test configurations are

soldered on the top of the board. The vias on the board connect the windings directly










n2 12
*+
BNCsen r rst BNC in rst


n3 i3


P+ 1 BNC sen 9t 9t BNC in 9t
BNCinri BCsepri

P n4 i4


5t \ BNC in 5t
BNC sen 5t


n5 i5


BNC sen 6t 6t BNC in 6t



Figure 4-7. Circuit diagram indicating the testing terminals for the transformer

to the shorts or current sense impedances. The connections on the top of the board

are shown in Figure 4-9.

The BNC terminations shown on the top of the board are connected to the

4194A through specially made short coaxial cables to reduce parasitics. Caddock 10

mQ current sense resistors (Part No. MP916, [23]) with 5% precision were used for the

measurement of leakage impedances. The inductance was estimated in the manufacturer's

data sheets at 7.5 nH. A 10 cm coaxial cable (17 pF capacitance) was used to sense the

applied voltage, and a 13 cm coaxial cable (21 pF capacitance) was used to sense the

voltage across the current sensor.









4.2. Effect of Nonzero Current Sense Impedances

There are three kinds of measurements to be performed. For the turns ratio

measurements, no current sensors are needed. The measurement of the self-

impedance Zpp(s) is performed on the impedance analyzer and does not need a

current sensor. However, current sensors are needed for the measurement of leakage

impedances, and Equation (4.3) requires short circuit conditions at the winding

where the current is sensed.

Figure 4-10 shows the actual measurement setup referred to the primary

node. If Zsc(s) is to be a good short, at all frequencies,

White= Cu
Black= Isolation



BNC In ot


BNC sen ot
BNC sen 5t


BNC in c't


BNC n 5t

BNC sen ct
BNC in rst





BNC inprl BNC_senirst
BNC_sen_pri


Figure 4-8. Layout diagram of the bottom of the test fixture showing interconnects
between the BNC connectors and the various ports of the transformer.









White= Cu
Black= Isolation



BNC in ot


BNC sen 6t


BNC i 9t (



BNC sen 9t


BN _in_p


BNC sen 5t


BNC in 51


BNC in rs


BNC sen pri


BN
BNCsenrst


Layout diagram of
terminations.


Zij(s)


Vapp(s)
ni(s)


the top of the test fixture showing the BNC


1:nj(s) isc,j


Z j(s)
~A2 i iC (S


Figure 4-10. Leakage impedance measurement referred to the primary node


Figure 4-9.









Zs (s)
Zs'(s))| < (Zlj(s) I Z2j(s) ...Z) II | ...|| IIZNj(s))| whereZsc'(s) = Z(4.6)
nj(s)|

At low frequencies, the right-hand side of the inequality will be extremely

small, and it is difficult to use extremely small current sensors. Also, this is

impractical at high frequencies because of the parasitic inductance of the current

sense resistor. For instance, a 0.1 Q surface mount precision resistor would realistically

have a series inductance of about 5 nH. At 10 MHz, the imaginary part current sense

impedance is approximately 30 mQ. This would severely distort the measured phase and

magnitude response. Hence, we have to change the measurement procedure suitably in

order to avoid this problem.

The quantity being measured in Figure 4-10 is the leakage impedance Zij(s).

The measured_leakage impedance Zi,,mea(s) is given by,

v' (s) v (s)
Zlm,mea(S) app() where v'app(s) app (4.7)
sc, jnj(s) ni(s)

A relation between the measured and actual impedances can be derived easily by using the

admittance equivalent of the measurement circuit in Figure 4-10. The Norton equivalent of

the circuit is shown in Figure 4-11.

The short circuit current isc(s) is related to the input current iapp(s) by the

following relation:

Y's(S
isc(s) = N iapp(s) (4.8)
Yij(s) + Y'(s) + Yn(s)
n= 1, n j


where iapp(s) = Ylm(s)v'app(s).












isc(s)


iapp(S) =

V'app(s)Yij (s)


(Yj(s)+ Y2j(s) + ... + YN(s))


Y'sc(s)


Figure 4-11. Norton equivalent of leakage impedance measurement circuit

The measured leakage impedance Ylm,m,,(s) is given by


Ylm,mea(s)


isc(s)
v'app(S)


(4.9)


Combining Equation (4.8) and Equation (4.9), we get


Ylm,mea(s)


(4.10)


Y'sc ()Yij(s)
N
Yij(s) + Y'sc(s)+ Ynj(s)
n= 1, n j


Simplifying the equation,

N

Y (s) Yn (s)
Yij,mea(S) 1 +Y'(s +n=l, n Y(s)
Y'sc(S) '(Y s)



Equation (4.11) can be rewritten as


Ylj(s) 1 ~ me- (Y_(s) (+Y2j(s) + ...+ YNj(S)) Ys'( ij, mea(s)
S SC )2 SC'


(4.11)


(4.12)









Equation (4.12) represents a set of linear equations with one equation formed

by each measurement of a leakage impedance. Hence, the number of unknowns

(leakage impedances) is equal to the number of equations. The system is, therefore,

uniquely determinable. By solving this set of linear equations, we can compensate

for the non-ideality of the current-sense resistor. For an ideal short (Ysc'(s) --- ),

Equation (4.12) reduces to the ideal case as defined in the ECM, i.e., Yij(s) = Yij, mea(S)

4.3. Experimental Results

The transformer constructed has five windings, including the reset one. The pri-

mary and reset windings are referred to as winding W1, W2, respectively, and the nine-,

five-, and six-turn secondary windings are referred to as W3, W4, and W5, respectively.

The transformer was designed for a 20W, 300 KHz forward converter. The length and

width of the windings vary in different segments of the layout. So, the length and width at

different segments are calculated from the layout, and then the dc resistances are calcu-

lated and summed up to get the total resistance. The dc resistances are calculated from the

design Equation (4.13),

Rdc = P (4.13)
wt

where Rdc is the dc resistance of the winding, p is the resistivity of copper, 1 is the length

of the winding, w is the width of the winding, and t is the thickness of the winding.

Table 4-1 Summary of the dc resistance measurement

Thickness, Average Total length Measured Calculated
Windings (cm) width, w () ( )
t (cm) (cm) (mQ) (mQ)
(cm)
W1 0.0036 0.278 55.488 91 97
W2 0.0036 0.020 55.488 1210 1230
W3 0.0036 0.182 41.616 125 111
W4 0.0036 0.244 23.120 49 46
W5 0.0036 0.135 27.744 108 100









After fabrication, the dc resistance was measured by a Keithley 2001 multimeter.

The dc resistances are summarized in Table 4-1, indicating good agreement between the

measured and calculated values.

To measure the ECM parameters, the transformer was implemented in a test

fixture, as shown in Figure 4-12, which is the top of the test fixture. The bottom view

of the test fixture is shown in Figure 4-13. The measurement board was fabricated on

a double layer FR4 copper board using a T-Tech circuit board milling machine. Its


Figure 4-12. Transformer implemented on a test fixture to measure ECM parameters
(top view of the test fixture)


dimensions are 4" x 4". The board layout is based on the four-point measurement

system with an emphasis on keeping the reference and test points close to the actual

windings and/or current-sense resistors. The sourcing inputs are located farther from









the test and reference points. Measurements of the extended cantilever model

parameters were made, as described in Section 4.1. Hewlett-Packard 4194A

Impedance/Gain-Phase analyzer [24] was used to measure all the parameters. The

turns ratios were measured using the Gain-Phase function of the HP 4194A. The

magnetizing impedance Z11 was measured using the Impedance function of the HP

4194A.

Table 4-2 Summary of the ECM parameters measurement at 300 KHz

Measured Extracted
Parameters Measured Real Extracted Real
Imaginary imginary
n2 1.010 0.0000 1.01 0.000
n3 0.760 0.0000 0.76 0.000
n4 0.420 0.0000 0.42 0.000
n5 0.510 0.0000 0.51 0.000
Z11(Q) 7.3570 651.35 7.36 651.3
Z12(Q) 3.383 -1.0500 3.36 -1.060
Z13(Q) 0.263 0.0970 0.27 0.100
Z14(Q) 0.425 0.3530 0.41 0.360
Z15(Q) 0.459 0.1710 0.44 0.175
Z23(Q) 2.206 0.5200 2.21 0.510
Z24(Q) 6.047 3.1710 6.05 3.170
Z25(Q) 9.287 2.4810 9.28 2.475
Z34(Q) 1.170 0.9940 1.17 0.992
Z35(Q) 1.930 0.6800 1.92 0.680
Z45(Q) 1.268 2.1800 1.27 2.170

To measure leakage impedance Zjk, the current-sense resistor was used to

short winding k in order to sense the current in the "short-circuited" winding k. The

other windings j, except the excited winding k, had true shorts across their terminals.

The ratio of the voltages across the windings k and j is then measured by the Gain-

Phase analyzer. This was scaled by the current-sense admittance and the turns ratios

nj and nk* to compute Zjk. All voltages were measured at the winding terminals to

avoid interconnect and cable parasitics. It is necessary to mention that the value of

the current sense resistor is 10 mQ with 5%-precision and a package inductance of




































Figure 4-13. The bottom view of the test fixture

7.5 nH (Caddock part number MP916 [23]. It is shown in [21] that the measured

parameters with current sensor of 50mQ+15nH, the extracted parameters do not vary

much starting at 100 KHz. Since the operating frequency of the designed transformer

is 300 KHz, 10mQ+7.5nH was considered a sufficiently good "short." The model

parameters are summarized in Table 4-2.

To verify the measured ECM parameters, the transformer model was

generated in PSPICE [25]. All the impedances were modeled as resistance in series

with inductance except Z12 because it has a negative imaginary component. Since

PSPICE cannot use negative inductance, L12 is implemented by using an inductance



























Figure 4-14. Ideal transformer

block. An inductance block is generated using a Voltage-Current G(s) block

(Glaplace, Figure 4-14).

The ideal transformer in Figure 4-14 was implemented by using a voltage

controlled voltage source (VCVS) and a current controlled current source (CCCS)

connected in an antiparallel sense. The voltage controlled voltage source transforms

the primary voltage to the secondary, and the current controlled current source

transforms the secondary current to the primary. Since the transformer terminals

cannot be shorted to reproduce measurement results, as this would lead to topological

and convergence errors, the transformer was shorted by using a 10nQ resistor when

needed. The gain multiplier was set to the turns ratio. To verify the implemented

ECM, 15 virtual experiments were performed on PSPICE. The schematic generated

on PSPICE, along with the ECM parameters, is shown in Figure 4-15. All virtual

experiments generate virtually the same data as the actual experiments, shown on

Table 4-2












GLA P LCE


-S .... :S I G3 le

L34
L4S
.11.1T






Figure 4-15. Extended cantiliver model schematic implemented in PSPICE


A transient simulation was performed in PSPICE using the schematic as

shown in Figure 4-15. A square wave of 300 KHz was applied at the input of the

primary winding. All other windings were open-circuited except the six-turn

secondary winding. A 0.50 load was connected across the six-turn winding. To make

the open circuit, a le9Q resistance was connected across the reset, nine-, and five-

turn windings. The simulation waveforms of the voltages across all windings are

shown in Figure 4-16 in which Vin, V3,V4, and V5 are the voltages across the

primary, nine-, five-, and six-turn windings, respectively. As seen from the

waveforms, the voltage rise time and overshoot at the primary winding are 7.35 ns

and 110%, respectively. The rise time of the voltage at the six-turn winding is 37.6

ns, and there is no ripple. Since all other windings are open-circuited, the voltages

basically follow the voltage at the primary winding. The overshoot is defined by the










5.OU-


ou-
0U-


-5.0U-

2.OU-


ou-
OU-


-2.OU-

2.0U-


ou-
OU-


-2.OU-

1.OU-

OU-
SEL>
-1.OU-


0 o U(U3)


o o U(U4) Ideal PSPICE model
7/ ~ *


382us
D o UUS)


38I
384us


Ius
386us


Figure 4-16. PSPICE transformer winding voltage waveforms. (a) ECM model
(dotted lines). (b) Ideal PSPICE model (solid lines)

following equation:where yl is the maximum value of a waveform and Y2 is the final

value of a waveform.


Overshoot:


(YI -Y2)
x 100
Y2


o o U(Upri)


388us


390us


(4.14)










Tek n 50.0MS/s 211 Acqs



C1 High
1.2 V

V3






1.V4
C2 High



| 560mV
3 .. .... .. .4 V4
C4 High
640mV

V5


Ch 5.00 V Ch2 2.00 V M 1.00s Ch1 700mV 21 Jan 2001
Ch3 2.00 V i 1.00V 18:45:55

Figure 4-17. Experimental voltage waveforms across the windings

The transformer was tested, as shown in Figure 4-12, to reproduce the simulated

voltage waveforms. It was exactly the same setup as the simulation shown in Figure 4-15.

The experimental waveforms are shown in Figure 4-17 in which chl, ch2, ch3, and ch4

are the voltages across the primary, nine-, five -, and six-turn windings. The rise time and

the ripple at voltage of the primary winding were 8 ns and 110%, respectively, which are

consistent with the simulated values. The rise time of the voltage at the six-turn winding is

38 ns and there is no ripple. This value is also consistent with the simulated values.















CHAPTER 5
CONCLUSION

5.1. Summary

The practical design issues of multiple flexible magnetic windings for magnetic

components and their fabrication techniques were studied. A flexible five-winding

transformer was fabricated, and the dc resistances and the ECM parameters were measured.

It is very important to use the correct values of the resistance and parasitic inductance

values to measure ECM parameters, otherwise one might get unreliable values of ECM

parameters. The key results are summarized as follows:

* The dc resistances of primary, reset, nine-, five-, and six-turn windings were 97
mQ, 1230 mO~ 111 mQ, 46 mQ and 100 mO~ respectively.

* The transformer was modeled by ECM parameters. Turn ratios of 1.01, 0.76, 0.42,
and 0.51 was obtained for the reset, nine-, five-, and six-turn windings.

* To verify the measured ECM parameters, the transformer model was generated in
PSPICE, and 15 virtual experiments were performed. All virtual experiments
generate virtually the same data as the actual experiment.

5.2. Future Work

The following topics require further investigation to understand completely

the proposed method of frequency domain modeling:

* A more efficient use of copper as compared to its utilization in the half-turn copper
pattern.

* Evolving a topological or procedural procedure in model generation to take care of
nonsymmetrical cases, that is, for the cases when the impedances are not bilateral
in nature.

* Incorporating large signal core loss and hysteresis dependencies in the model.






48


* Effect of non-ideal grounds due to the test fixture parasites at high frequencies on
the measured parameters.

* Obtaining a physical circuit representation or basis from the measured parameters.

* Validation of simulation results with actual hardware testing.















APPENDIX
MATLAB SCRIPT TO CALCULATE THE REAL AND IMAGINARY PARTS OF
THE IMPEDANCES

% Load the measurement data
clear all;
V2=loadasc('N2.txt');
V3=loadasc('N3.txt');
V4=loadasc('N4.txt');
V5=loadasc('N5.txt');
V1 =loadasc('Z11.txt');
V12=loadasc('Y12.txt');
V13=loadasc('Y13.txt');
V14=loadasc('Y14.txt');
V15=loadasc('Y15.txt');
V23=loadasc('Y23.txt');
V24=loadasc('Y24.txt');
V25=loadasc('Y25.txt');
V34=loadasc('Y34.txt');
V35=loadasc('Y35.txt');
V45=loadasc('Y45.txt');
% Defining frequency data
f=100e3:2.5e3: 1.01e6;
f=f';
% Creating Vectors for Magnitude and Phase of the measured data
N2g=V2(37:401);
N2p=V2(438:802);
%N2p=N2p-180;
N3g=V3(37:401);
N3p=V3(438:802);
N4g=V4(37:401);
N4p=V4(438:802);
N5g=V5(37:401);
N5p=V5(438:802);
Zllg=V11(37:401);
Zllp=V11(438:802);
Y12g=V12(37:401);
Y12p=V12(438:802);
Y13g=V13(37:401);
Y13p=V13(438:802);









Y14g=V14(37:401);
Y14p=V14(438:802);
Y15g=V15(37:401);
Y15p=V15(438:802);
Y23g=V23(37:401);
Y23p=V23(438:802);
Y24g=V24(37:401);
Y24p=V24(438:802);
Y25g=V25(37:401);
Y25p=V25(438:802);
Y34g=V34(37:401);
Y34p=V34(438:802);
Y35g=V35(37:401);
Y35p=V35(438:802);
Y45g=V45(37:401);
Y45p=V45(438:802);
I=sqrt(-1);
% Defining the current sense resistor
Zsk=.01+f.*2*pi*7.5e-9*I;
Ysk=l./Zsk;
% Obtain magnitude and phase of magnetizing impedance
Z lg=(abs(Zsk))./Y1 g;
Z lp=(180/pi)*angle(Zsk)-Y 1p;
% Obtain magnitude and phase of leakage impedance
Z12g=1./(Y12g.*N2g.*abs(Ysk));
Z12p=-(Y12p-N2p+180/pi*angle(Ysk));
Z13g=l./(Y13g.*N3g.*abs(Ysk));
Z 13p=-(Y13p-N3p+180/pi*angle(Ysk));
Z14g=1./(Y14g.*N4g.*abs(Ysk));
Z14p=-(Y14p-N4p+180/pi*angle(Ysk));
Z15g=l./(Y15g.*N5g.*abs(Ysk));
Z15p=-(Y15p-N5p+180/pi*angle(Ysk));
Z23g=1./(Y23g.*N2g.*N3g.*abs(Ysk));
Z23p=-(Y23p+N2p-N3p+180/pi*angle(Ysk));
Z24g=1./(Y24g. *N2g. *N4g. *abs(Ysk));
Z24p=-(Y24p+N2p-N4p+180/pi*angle(Ysk));
Z25g=1./(Y25g.*N2g.*N5g.*abs(Ysk));
Z25p=-(Y25p+N2p-N5p+180/pi*angle(Ysk));
Z34g=1./(Y34g.*N3g.*N4g.*abs(Ysk));
Z34p=-(Y34p+N3p-N4p+180/pi*angle(Ysk));
Z35g=1 ./(Y35g.*N3g.*N5g.*abs(Ysk));
Z35p=-(Y35p+N3p-N5p+180/pi*angle(Ysk));
Z45g=1./(Y45g.*N4g.*N5g.*abs(Ysk));
Z45p=-(Y45p+N4p-N5p+180/pi*angle(Ysk));









% Compute real and imaginary parts
N2=N2g.*exp(I*N2p*pi/180);
N3=N3g.*exp(I*N3p*pi/180);
N4=N4g.*exp(I*N4p*pi/180);
N5=N5g.*exp(I*N5p*pi/180);
Zl =Zllg.*exp(I*Zllp*pi/180);
Z12=Zl2g.*exp(I.*Zl2pl*pi/180);
Z13=Zl3g.*exp(I.*Zl3p*pi/180);
Z14=Zl4g.*exp(I.*Zl4p*pi/180);
Z15=Z15g.*exp(I.*Z15p*pi/180);
Z23=Z23g.*exp(I.*Z23p*pi/180);
Z24=Z24g.*exp(I.*Z24p*pi/180);
Z25=Z25g.*exp(I.*Z25pl*pi/180);
Z34=Z34g.*exp(I.*Z34p*pi/180);
Z35=Z35g.*exp(I.*Z35p*pi/180);
Z45=Z45g.*exp(I.*Z45p*pi/180);
R11=real(Z11);
L1 =imag(Z11);
R12=real(Z12);
L12=imag(Z12);
R13=real(Z13);
L13=imag(Z13);
R14=real(Z14);
L14=imag(Z14);
R15=real(Z15);
L15=imag(Z15);
R23=real(Z23);
L23=imag(Z23);
R24=real(Z24);
L24=imag(Z24);
R25=real(Z25);
L25=imag(Z25);
R34=real(Z34);
L34=imag(Z34);
R35=real(Z35);
L35=imag(Z35);
R45=real(Z45);
L45=imag(Z45);
% Compute transfer function coefficients for Z12
[B12,A12]=invfreqs(Z12,f*2*pi,3,2);
hcl2=freqs(B12,A12,f*2*pi);
% Print real and imaginary parts of impedances at 300 KHz
k=81;
f(k)






52


[R11(k) L11(k);R12(k) L12(k);R13(k) L13(k);R14(k)4(k)L(k);R15(k) L15(k);...
R23(k) L23(k);R24(k) L24(k);R25(k) L25(k);R34(k) L34(k);R35(k) L35(k);...
R45(k) L45(k)]















REFERENCES


[1] A. Estrov, "1-MHZ Resonant Converter Power Transformer is Small, Efficient,
Economical,"Power Conversion, and Intelligent Motion, pp. 14-24, Aug. 1986.

[2] A. F. Goldberg, J.G. Kassakian, and M.F. Schlecht "Issues Related To 1-10 MHz Trans-
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[3] P.M. Gradzkiand F.C. Lee, "Design of High-Frequency Hybrid Power Transformer,"
Proceedings ofApplied Power Electronics Conference, pp. 319-326, 1988.

[4] A. Estrov, "Integrating Planar Magnetics in High-density Power Converters," Power
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[5] D.V.D. Linde, C.A.M. Boon, and J.B Klaassens, "Design a High-Frequency Planar
Power Transformer in Multilayer Technology," IEEE Transactions on Industrial Elec-
tronics, Vol. 38, pp. 135-141, Apr. 1991.

[6] A.J. Yerman, "High-Frequency Transformer," U.S. Patent No. 4,959,630, September
25th, 1990.

[7] K.D.T. Ngo, R.P. Alley, and A.J. Yerman, "Fabrication Method for a Winding Assem-
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[8] K.D.T. Ngo, R.P. Alley, and A.J. Yerman, R.J. Charles, and M.H. Kuo, "Evaluation of
Trade-offs in Transformer Design for Very-Low-Voltage Power Supply with Very
High Efficiency, and Power Density," Proceedings ofApplied Power Electronics Con-
ference, pp. 344-353, 1990.

[9] K.K Sum and E. Herbert, "Novel Low-Profile Matrix Transformers for High Density
Power Conversion," Power Conversion, and Intelligent Motion, pp. 102-104, Sept.
1988.

[10] M.P. Perry, "Multiple Layers Series Connected Winding Design for Minimum Loss,"
IEEE Transactions on Power Apparatus, and Systems, PAS-98, No. 1, pp. 116-123,
Jan. 1979.

[11] YQ. Hu, D.K.W. Cheng, and YS. Lee, "New Fabrication Method for Planar Multi-
layer Windings Used in Low-Profile Magnetic Components," IEEE Transactions on
Magnetics, Vol. 35, No. 2, pp. 1056-1059, Mar. 1999.









[12] YQ. Hu, D.H. He, and T.Y Jin, "Design, and Application of High-Frequency Low-
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[13] R.W. Ericson and D. Maksimovic, "A Multiple-winding Magnetics Model Having
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[14] Flex-Circuit Design Guide, Applicaion Aid # 24, Minco Products Inc., Minneapolis,
MN.

[15] K.D.T. Ngo and S. Srinivas, "Broadband Extended Cantilever Model for Magnetic
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[16] W. Schillhammer and C. Forman, "Advances in Flex/Rigid Flex Prototyping Technol-
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[17] Soft Ferrites, Data Handbook MA01, Phillips Components, 1996, Rockville Center,
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[18] Mathcad 2000 Professional, Mathsoft Inc, Cambridge, MA.

[19] R.W. Ericson, "Fundamentals of Power Electronics," Edition 1997, Chapman & Hall,
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[20] AutoCAD 2000 Education Version, Autodesk Inc., San Rafael, CA.

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[24] HP 4194A Impedance/Gain-Phase Analyzer Operation Manual, Hewlett-Packard
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[25] PSPICE student version 9.1, Cadence Inc., San Jose, CA.















BIOGRAPHICAL SKETCH

Mohammed S. Alam was born on August 30, 1973, in Rangpur, Bangladesh.

He recieved a BS degree in Electrical and Electronics Engineering with an emphasis

in Circuit Design from the Bangladesh University of Engineering & Technology,

Dhaka (Bangladesh), in August 1997. Since January 1999, he has been pursuing an

MS in Electrical and Computer Engineering at the University of Florida in the areas

of Power Electronics and Circuit Design. He is also interested in RF IC Design. Other

interests include photography and listening to music.