Magnetics Design For High Current Low Voltage Dc/dc Converter

Transcription

1 Unversty of Central Florda Eletron Theses and Dssertatons Dotoral Dssertaton (Open Aess) Magnets Desgn For Hgh Current ow Voltage D/d Converter 7 Hua Zhou Unversty of Central Florda Fnd smlar works at: Unversty of Central Florda brares Part of the Eletral and Eletrons Commons STAS Ctaton Zhou, Hua, "Magnets Desgn For Hgh Current ow Voltage D/d Converter" (7). Eletron Theses and Dssertatons. Paper 343. Ths Dotoral Dssertaton (Open Aess) s brought to you for free and open aess by STAS. It has been aepted for nluson n Eletron Theses and Dssertatons by an authorzed admnstrator of STAS. For more nformaton, please ontat lee.dotson@uf.edu.

2 MAGETICS DESIG FO HIGH CUET OW VOTAGE DC/DC COVETE by HUA ZHOU B.S. X an Jaotong Unversty, 994 M.S. X an Jaotong Unversty, 997 A dssertaton submtted n partal fulfllment of the requrements for the degree of Dotor of Phlosophy n the Shool of Eletral Engneerng and Computer Sene n the College of Engneerng and Computer Sene at the Unversty of Central Florda Orlando, Florda Summer Term 7 Major Professors: Thomas X. Wu Issa Batarseh Kha D. T. go

3 7 Hua Zhou

4 ABSTACT Wth the nreasng demand for small and ost effent DC/DC onverters, the power onverters are expeted to operate wth hgh effeny. Magnets omponents desgn s one of the bggest hallenges n ahevng the hgher power densty and hgher effeny due to the sgnfant porton of magnets omponents volume n the whole power system. At the same tme, most of the expermental phenomena are related to the magnets omponents. So, good magnets omponents desgn s one of the key ssues to mplement low voltage hgh urrent DC/DC onverter. Planar tehnology has many advantages. It has low profle onstruton, low leakage ndutane and nter-wndng apatane, exellent repeatablty of parast propertes, ost effeny, great relablty, and exellent thermal haratersts. On the other sde, however, planar tehnology also has some dsadvantages. Although t mproves thermal performane, the planar format nreases footprnt area. The fat that wndngs an be plaed loser n planar tehnology to redue leakage ndutane also often has an unwanted effet of nreasng parast apatanes. In ths dssertaton, the planar magnets desgns for hgh urrent low voltage applatons are thoroughly nvestgated and one CAD desgn methodology based on FEA numeral analyss s proposed. Beause the frequeny dependant parast parameters of magnets omponents are nluded n the rut model, the whole rut analyss s more aurate. When t s mplemented orretly, ntegrated magnets tehnque an produe a sgnfant reduton n the magnet ore ontent number and t an also result n ost effent desgns wth

5 less weght and smaller volume. These wll nrease the whole onverter s power densty and power effeny. For hgh output urrent and low output voltage applatons, half brdge n prmary and urrent doublers n seondary are proved to be a very good soluton. Based on ths topology, four dfferent ntegrated magnets strutures are analyzed and ompared wth eah other. One unfed model s ntrodued and mplemented n the rut analyss. A new ntegrated magnets omponent ore shape s proposed. All smulaton and expermental results verfy the ntegrated magnets desgn. There are several new magnets omponents applatons shown n the dssertaton. Atve transent voltage ompensator s a good soluton to the hallengng hgh slew rate load urrent transent requrement of VM. The transformer works as an extra voltage soure. Durng the transent perods, the transformer njets or absorbs the extra transent to or from the rut. A peak urrent mode ontrolled ntegrated magnets struture s proposed n the dssertaton. Two transformers and two ndutors are ntegrated n one ore. It an fore the two nput apators of half brdge topology to have the same voltage potental and solve the voltage unbalane ssue. The proposed ntegrated magnets struture s smple ompared wth other methods mplementng the urrent mode ontrol to half brdge topology. Crut analyss, smulaton and expermental results verfy the feasblty of these applatons. v

6 To my famly v

7 ACKOWEDGMETS Wth the snerest and warmest appreatons from my heart, I would lke to say thanks to my advsor Dr. Thomas X. Wu, and o-advsors Dr. Issa Batarseh and Dr. Kha go for ther gudane and enouragement through my studes at the Unversty of Central Florda. Ther extensve vson and reatve thnkng have been the soure of nspraton for all my work. Durng the past several years, I have learned from them not only knowledge but also ther strt approahes to sentf researh. These are gong to beneft me for the rest of my lfe. I would also lke to thank other ommttee members: Dr. Z. John Shen, Dr. Yanfe u and Dr. Jun Wang for ther support and enouragement. It has been a great pleasure to study n the Florda Power Eletrons Center at Unversty of Central Florda. I hersh the frendshps that I have made over there. I would lke to thank the followng vstng sholars or my fellow students: Dr. Hong Mao, Dr. Jaber A. Abu Qahouq, Dr. Xanfheng Wang, Dr. Jun u, Dr. Songquan Deng, Mr. Shangyang Xao, Mr. angbn Yao, Ms. Yangyang Wen, Mr. Osama Abdel ahama, Ms. Majd Batarseh, Mr. Feng Tan, for the useful dsussons. Fnally, my deepest and heartfelt appreaton goes to my famles for ther unondtonal love. v

8 TABE OF COTETS IST OF FIGUES... x IST OF TABES... xv CHAPTE : ITODUCTIO.... Magnets Components for Power Eletrons..... Power Transformer Power Indutor Planar Magnets ow Profle Hgh-Frequeny osses eakage Indutane Planar Wndng Tehnologes Integrated Magnets....4 Outlne of esearh... CHAPTE : CHAACTEISTICS OF MAGETICS COMPOETS FO HIGH CUET APPICATIOS Magnets Components Modelng and Smulaton Integrated Indutors for Hgh Current Applaton Integrated Transformer and Indutors Core oss for on-snusodal Waveforms... CHAPTE 3: PAA MAGETICS DESIG... 4 v

9 3. Dsrete Magnets Desgn for ow Voltage and Hgh Current Converter Desgn of Planar Transformer Spefatons Seletons of Core Shape and Materal Wndng Arrangements wth oss Smulatons Desgn of Planar Flter Indutor Spefatons Seleton of Core Shape and Materal Wndng ayout wth oss Smulatons Smulaton and Expermental esults Crut Model Smulaton esults Expermental esults Volume Optmzaton Atve Transent Voltage Compensator Magnets Desgn for VM Hgh Current and Hgh Slew ate VM Transformer Workng Modes Transformer Model Smulaton esult Experment Verfaton CHAPTE 4: ITEGATED MAGETICS Coupled Indutors... 7 v

10 4.. Model Dervaton Crut Analyss Analyss and Comparson Smualton esults and Experment Verfaton Integrated Transformer and Indutors Comparson of Dfferent Magnets Struture Dfferent Integrated Magnets Strutures Equvalent elutane Model Comparson CAD Methodology and Unfed Crut Model Experment Verfaton Half Brdge Integrated Magnets Desgn Desgn Proedures Proposed Core Shape and oss Comparson Smulaton esults Experment Verfaton Integrated Magnets for Peak Current Mode Control Half Brdge Converter Current Mode Control Issue Voltage Balane Tehnque Proposed Integrated Magnets Struture CHAPTE 5: COCUSIOS IST OF EFEECES x

11 IST OF FIGUES Fg.. Half brdge and urrent doubler rut topology... 9 Fg.. Four dfferent ntegrated magnet strutures... Fg. 3. Transformer desgn proedure... 4 Fg. 3. DC/DC onverter topology... 5 Fg. 3.3 Core shapes (E4.5)... 7 Fg. 3.4 Trak wdth wt, spang s and wndng wdth b w... 9 Fg. 3.5 Interleaved wndng strategy... 3 Fg D model and smulaton result of an nterleaved planar transformer n Maxwell 3D.. 3 Fg. 3.7 Planar Transformer wndng strategy Fg F35 Spefatons ( 35 Fg. 3.9 Indutor 3D Model and Smulaton esults Fg. 3. Tradtonal two-wndng transformer model Fg. 3. Transformer prmary mpedane urve Fg. 3. Physal strutures of dsrete magnets... 4 Fg. 3.3 Pspse model of the dsrete magnets struture... 4 Fg. 3.4 Seondary urrent waveform of the whole rut w/o lamp... 4 Fg. 3.5 Seondary urrent waveforms w lamp... 4 Fg. 3.6 Prmary urrent waveform w lamp... 4 Fg. 3.7 Experment board Fg. 3.8 Prmary voltage and urrent waveform x

12 Fg. 3.9 Prmary voltage and urrent waveform after retfy Fg. 3. Smulaton prmary voltage and urrent waveform after retfy Fg. 3. MMF of non nterleavng transformer Fg. 3. MMF of nterleavng transformer Fg. 3.3 Flow hart of the optmzaton program Fg. 3.4 Mnmal ore volume vs. frequeny Fg. 3.5 Mnmal ore volume vs. effeny... 5 Fg. 3.6 Power delvery struture: (a) ntal CPUs power delvery struture and (b) the urrent... 5 Fg. 3.7 ATVC mplementaton rut Fg. 3.8 Transformer model Fg. 3.9 Tradtonal transformer model Fg. 3.3 Inverse transformer model Fg. 3.3 Indutane values vs. ar gap length... 6 Fg. 3.3 Flux densty dstrbutons for dfferent turns-rato... 6 Fg Indutane values vs. frequeny Fg Indutane values vs. turns-rato Fg esstor vs. turns-rato Fg Maxwell 3D transent smulaton results Fg Experment prototype Fg VM expermental results wthout ATVC Fg VM expermental results wth ATVC x

13 Fg. 3.4 Step down detal waveform, VM and ATVC work together Fg. 3.4 Step up detal waveform, VM and ATVC work together Fg. 4. Proposed Y-shape ntegrated oupled ndutor struture... 7 Fg. 4. elutane model... 7 Fg. 4.3 Crut Model Fg. 4.4 Mode Crut Fg. 4.5 Mode Crut Fg. 4.6 Mode 3 Crut Fg. 4.7 Crut waveforms... 8 Fg. 4.8 Current rpples vs. ouplng oeffent... 8 Fg. 4.9 Indutor urrent waveform smulaton results Fg. 4. Experment rut Fg. 4. Indutor urrent expermental result Fg. 4. Prmary urrent waveform of dsrete struture Fg. 4.3 Prmary urrent waveform of oupled ndutors struture Fg. 4.4 Four phase rut Fg. 4.5 Dfferent ntegrated magnets strutures... 9 Fg. 4.6 Dfferent relutane model strutures Fg. 4.7 Current doubler workng modes Fg. 4.8 IM struture model dervatons Fg. 4.9 IM struture model dervatons... Fg. 4. IM struture 3 model dervatons... x

14 Fg. 4. IM struture 4 model dervatons... 4 Fg. 4. Double-D methodology... 7 Fg. 4.3 Unfed 3 ports eletral rut... 8 Fg. 4.4 Experment prototypes... 3 Fg. 4.5 Output urrent waveforms for dfferent magnets struture... 4 Fg. 4.6 Dfferent strutures effeny omparson... 6 Fg. 4.7 Proposed new ore shape... Fg. 4.8 Maxwell 3D smulaton result... Fg. 4.9 Interleaved wndng arrangement... Fg. 4.3 Interleaved wndng struture... Fg. 4.3 Integrated magnets Pspe model... 4 Fg. 4.3 Seondary sde urrent waveforms... 4 Fg Prmary sde urrent waveform... 4 Fg Parameter Matrx... 6 Fg Seondary sde urrent waveforms... 7 Fg Prmary sde urrent waveforms... 7 Fg Integrated magnets PCB board... 8 Fg Expermental waveforms vs. smulaton waveform... 9 Fg Power loss vs. load... 9 Fg. 4.4 Current mode ontrol onept rut... 3 Fg. 4.4 Half-brdge voltage unbalane ssue... 3 Fg. 4.4 Half-brdge voltage balane rut x

15 Fg Improved half-brdge voltage balane rut Fg Proposed half-brdge voltage balane IM rut Fg elutane mode Fg Proposed rut workng mode Fg elutane mode Fg Proposed rut workng mode Fg elutane mode Fg. 4.5 Proposed rut workng mode Fg. 4.5 Unbalaned waveforms for onventonal half brdge urrent mode ontrol... 4 Fg. 4.5 Balaned waveforms for proposed half brdge urrent mode ontrol... 4 xv

16 IST OF TABES Table 3. Dsrete Struture Parameter Matrx... 4 Table 3. Transformer Optmze esult Table 4. Comparson of Dfferent Strutures Table 4. Four IM strutures parameters omparson Table 4.3 IM Struture Impedane Matrx... 9 Table 4.4 IM struture mpedane matrx... Table 4.5 IM Struture 3 Impedane Matrx... Table 4.6 IM Struture 4 Impedane Matrx... Table 4.7 Power oss of Dfferent Components... 3 Table 4.8 Parameter Matrx... 3 Table 4.9 Dsrete struture vs. ntegrated struture... 5 Table 4. Power loss of dsrete struture vs. ntegrated struture... 8 Table 4. Maxwell 3D Couplng Matrx... 4 xv

17 CHAPTE : ITODUCTIO. Magnets Components for Power Eletrons The orgn of modern power eletrons was stmulated by the development of power semondutor deves for hgh frequeny swthng purposes. At the same tme, magnet ores for transformers and ndutors are another mportant and neessary aompanyng omponent. There are varous magnet funtons that are used n a swthng power supply. They are:. Power transformer;. Power ndutor or hoke; 3. In-lne or dfferental-mode hoke; 4. Common-mode hoke; 5. EMI suppresson; 6. Pulse transformer for transstor frng; 7. Magnet amplfer; 8. Power fator orreton. The hoe of the best magnet omponent s determned by:. The type of onverter topology used;. Frequeny of the rut; 3. Power requrements; 4. The regulaton needed (perentage varaton of output voltage permtted); 5. Cost of the omponent;

18 6. Effeny requred; 7. Input and output voltages and urrents possble onsstent wth other fators. Wth the nreasng demand for small and ost-effent DC/DC onverters, the power onverters are expeted to operate wth hgh effeny. However, even wth modern mproved and advaned topologes, magnets desgn s stll one of the bggest hallenges n ahevng the hgher power densty and hgher effeny due to the sgnfant porton of magnets volume n the whole power system []. At the same tme, most of the expermental phenomena are related to the magnets omponents. In many power applaton stuatons, the magnets omponents an not be omtted due to the safety reasons. So, good magnets omponents desgn s one of the key ssues to mplement low voltage hgh urrent DC/DC onverter. In reent years, there are two dstnt trends n power eletrons magnets desgn. One onsders the use of planar strutures []. Planar has loser board spang, apples smpler ondutor assembly methods, and therefore aheves lower profle and better manufature ablty. The planar eletral features are also repeatable. These advantages makes planar preval n the power onverter ndustry. The other trend s to push the frequenes. Beause magnet ores are tradtonally the largest omponent n a sold-state rut, operaton at hgh frequenes s seen as a possble soluton to derease the volume. Several hundreds of klohertz systems are beng extended; and there s also a push of swthng frequenes n the several-megahertz range [3]. However, the desgn of transformers and ndutors s usually a lmtng tehnology for hgher frequeny systems. The ntegrated magnets as an approah to aomplsh low profle and hgh power densty n power applatons has been nvestgated ntensvely [4][5]. Wth ntegrated magnet

19 tehnques, several magnet omponents an be onstruted n one magnet ore by sharng a ommon magnet path. Thus, the number of magnet ores an be redued. The flux rpple and the urrent rpple an also be suppressed. Hene, wth magnet ntegraton tehnologes, low ost and hgh power densty power onverter an be aheved. The magnet omponents often oupy a large porton of sze n a power onverter. How to get an optmal magnets desgn s rtal to mnmze the system profle and further nrease ts power densty. Integrated magnets tehnology, planar magnets tehnology and passve ntegraton tehnology are developed to redue the profle and the omponent ounts and to elmnate some of the nteronnetons between dfferent omponents. In the onventonal approahes, magnet omponents are often desgned based on magnet-rut relutane models. Core loss and onduton loss n magnet deves are roughly estmated. Wth the nrease of swthng frequeny drven by the ontnuously lower profle and hgher power densty, t beomes dffult to evaluate the loss due to skn effet and proxmty effet through the tradtonal analyss methods. Subsequently, FEA (Fnte Element Analyss) method based on numeral analyss of eletromagnet felds has been adopted. From the omputed eletromagnet felds results, FEA an aurately evaluate onduton loss, ore loss and magnet feld dstrbuton for eah of the wndng strutures wth dfferent ore geometry. Then, an optmzed magnets desgn an be aheved... Power Transformer For power transformer, beause hgh permeablty ores are always used to maxmze the ouplng between dfferent wndngs, the magnetzng urrent s small ompared to load urrent 3

20 (% to %). But, the stablty of magnetzng and leakage ndutanes may be poor, sne t vares wth mehanal handlng, eletral or thermal shoks. esonant frequeny of prmary may be well below maxmum operatng frequeny for wdeband transformers. Most of the tme, the voltage rato dffers slghtly from atual turn rato. The performane s affeted by wndng resstane whh s ndependent of sgnal level, but nreases wth frequeny due to the skn effet. The performane s also affeted by leakage ndutane whh appears n seres wth the wndng resstane due to mperfet magnet ouplng between wndngs. Power transformers have one ommon requrement: the materal saturaton value should be as hgh as possble, onsstent wth other fators suh as small ore loss. At very low frequenes, the materals are saturaton-drven and the eddy urrent losses are moderately low. At hgh frequenes, the materals are ore-loss-drven so that the materals suh as ferrtes are generally used. For medum hgh frequenes, materals suh as thn gage slon ron, amorphous materals and the new ano-rystallne materals are avalable. In power transformer funtons, a hgh saturaton materal wth low losses under the operatng ondtons s desrable. The desrable materals for transformer ores are those that have a hgh flux densty and keep the temperature rse wthn desrable lmts. The major magnets omponents materal for the power eletrons s the ferrte. Planar transformers desgned for power applatons must satsfy the same requrements as onventonal power transformers. These requrements nlude the mehansms mnmzng the loss and the provson of an aeptable oolng strategy. The task of mnmzng the ore losses s smlar to that of a onventonal wound magnet. It requres sutable hoes of the swthng frequeny, ore shape and sze, and ore materal. For dfferent desgn, the man dfferene les 4

21 n the hoe of ore shape and sze. For magnets omponents, there s no best ore shape and the tradeoff must be made. It depends on the applaton, spae onstrants, temperature, wndng apabltes, assembly, and a number of other fators. Mnmzng opper losses at hgh frequeny requres a good understandng of the prnples of skn effet and proxmty loss. Interleavng s a well-known tehnque used to mnmze hgh frequeny effets ontrbutng to wndng losses wthn planar turns. However, the level of nterleavng s lmted by onsderatons of apatve effets between dfferent wndngs and the onerns of provdng adequate levels of solaton between the wndngs. So, t s usually not the best soluton to fll the ore wndow wth opper. In fat, n many applatons hgh levels of nterleavng of relatvely thn layers results n a hgh nsulator to opper. Ths makes the use of prnted rut boards partularly sutable for transformer wndng strutures despte the upper lmt of approxmately 45% to 5% on opper utlzaton of the wndow. In some very low profle applatons, the opper utlzaton fator an be nreased through the use of thnner nsulaton systems. In the ase of sngle-turn, sngle-layer wndng desgned to arry hgh urrent, thk external opper stampngs an augment or replae PCB layers. In some applatons where further nterleavng s undesrable or not pratal, thker opper may be used for mproved thermal transfer wthout a loss or effeny penalty... Power Indutor Power ndutor applatons are manly foused on ther apablty to store large amounts of power n ther magnet feld. They are dfferent from the ndutors used n C ruts for frequeny ontrol. As suh, they an lmt the amount of AC voltage and urrent. Sne there are 5

22 large DC urrent and smaller supermposed AC urrent, ar gaps are needed to prevent the ore from saturaton. The amount of gap depends on the maxmum DC urrent, the shape and sze of the ore and the ndutane needed for energy storage. Beause of a large DC omponent n power ndutors, the gapped ferrte ores are used for many hgh urrent power applatons. The gap s added when there s a threat of saturaton that would allow the urrent n the ol to buld up and overheat the ore atastrophally. Gapped ore an also be used to ontrol the ndutane and to rase the Q value of the ore. Sne the AC omponent s small, ore loss s not as mportant as n the ase of the power transformers. The shape of the omponent nfluenes the performane of the deve. The reduton n temperature rse wll depend on some fators suh as the operatng frequeny, the gap length and the wre dameter.. Planar Magnets Phlps (998) lams the advantages of the planar tehnology nludng low profle onstruton, low leakage ndutane and nter-wndng apatane, exellent repeatablty of parast propertes, low ost, great relablty and exellent thermal haratersts. The haratersts of planar magnets are not all advantageous. Although t mproves thermal performane, the planar format nreases footprnt area. Even the wndngs an be plaed loser to redue leakage ndutane; t usually has an unwanted effet of nreasng parast apatanes. The repeatablty of haratersts obtaned from PCB wndngs struture also omes at the pre of havng a greater porton of the wndng wndow flled wth deletr materal, thus redung opper fll fator and lmtng the number of turns. Further more, typal 6

23 problems of planar strutures are the thermal management and the hgh value of the apatve effets. In many applatons, t stll has some advantages to use mult-layer PCBs n planar magnets. Sne the mult-layer PCBs allow the nteronneton of arbtrary layers, the nterleaved prmary and seondary wndngs an be mplemented muh more easly than wth onventonal magnets. Ths provdes the means to further redue leakage ndutane value and derease hgh frequeny wndng losses. Ths s a good feature for hgh frequeny square wave swthng applatons. Another advantage of the planar magnet s that t enhanes thermal performane beause of the greater surfae area to volume rato provdng more area to ontat the heat snk. Ths s llustrated n the smaller value of thermal resstane quoted for planar ores over onventonal ores... ow Profle An mportant feature of planar transformers s ther low profle. Ths feature makes possble the use of planar transformers n on-board onverters. Ths s one reason that planar magnets has large footprnt area. The term low profle s often used to desrbe planar magnets. However, not all low profle magnets are planar. In partular low profle ores, suh as the EFD type, use onventonal wre wound tehnology, lakng many of the haratersts of planar magnets. The effet of ore heght on power densty has been studed n several referenes. Some of these studes have ompared planar magnets to more onventonal low profle magnets and found that the low profle magnets an have better volumetr effeny and hgher power densty for ertan applatons. 7

24 .. Hgh-Frequeny osses Some earler studes assess wndng onfguratons, nvestgate the optmal plaement of wndngs, ompare dfferent wndng tehnologes and optmze layouts of turns to mnmze overall wndng resstane. Among dfferent wndng onfguratons nvolvng the use of sold wre, tz wre, PCB and fol wndngs at 5 khz, PCB wndngs have lower AC resstane (approxmately 85% 9%) than smlar sold wre wndngs but hgher than tz wre wndngs (approxmately 5%). eakage ndutanes of the PCB mplementatons are lower than both the wre and tz wre mplementatons. It also beame evdent that rularly wound planar wndngs an have sgnfant D feld effets n the wndng wndow, whh gves rse to losses not aounted for by the tradtonal approah to the wndng loss omputaton. These effets are also nvestgated for fol wndngs and onlusons are drawn as to how these D or edge effets mght be mnmzed. The onlusons are that wndng losses are mnmzed for prmary and seondary layers wth equal wdth, and wth mnmum spang between wndng end and ore enter leg...3 eakage Indutane The easy nterleavng n planar strutures allows the mnmzaton and ontrol of leakage ndutane wthn the wndngs. However, partular attenton should be pad to the termnaton of the wndngs. For example, dependng on the seondary termnaton method used, the leakage ndutane presented to the rut an be up to three tmes that omputed by the lassal short rut seondary approah. 8

25 It s obvous that the benefts of areful transformer desgn an easly be nullfed by a lak of are n the onneton of the transformer to the rest of the rut. Inapproprate termnaton desgn an aount for as muh as 75% of the short rut AC resstane of a planar deve...4 Planar Wndng Tehnologes Varous tehnologes an be used to mplement the planar wndngs. The most popular ones are Prnted Crut Board (PCB), flex rut and stamped opper. Wndngs fabrated n thk flm and TCC have also been used prmarly n lower power applatons. The use of PCBs gves a hghly repeatable means of mplementng planar wndngs. In prnple, the wndngs an be an ntegral part of the system nteronneton substrate thus totally elmnatng all termnatons. In prate, however, the nteronneton substrate rarely has suffent layers to fully aommodate the magnet omponent wndngs. But, t s stll better than other wndng tehnology. The dsadvantage of PCBs s that the wndow utlzaton fator an be qute low (typally ompared to.4 for onventonal magnets) due to a typal nter-turn spang and mnmum deletr thkness. Flex rut (opper on a thn, flexble polymer substrate) gves an mproved utlzaton fator as the deletr thkness s as low as 5µm. Many layers of flex rut an be lamnated together resultng n a rgd struture smlar to a PCB but wth nreased utlzaton fator. On the other sde, t an faltate the use of tehnques suh as the z-foldng method. Ths foldng method an be used to mplement a large number of layers wthout the need for va or solderng for layer nteronnets. Smlar to PCBs, flex ondutor thkness may be lmted to standard thkness, typally 7, 35, 7, and 5µm, wth mnmum ondutor spang nreasng wth 9

26 thkness. Unlke PCBs, the flex tehnologes are more suted to muh heaver opper weghts, e.g. µm or larger. Stamped opper wndngs provde an nexpensve means to mplement thk sngle turn wndngs. The man dsadvantages are that nsulaton layers must be separately appled and layer nteronneton s provded by some external means..3 Integrated Magnets One of the more nterestng magnets desgn tehnques n prate today s onstruton of the transformer and ndutor on a sngle magnet ore struture. Ths tehnque has ome to be known as Integrated Magnets (IM) desgn. IM methods have beome nreasngly popular sne 977, when oupled-ndutor assembly onepts and assoated onverter desgns [5] [6] [7] are more fully dslosed. Implemented orretly, IM tehnques an sgnfantly redue the magnet ore ontent of related power ruts and result n ost-effent desgns. Ths knd pakagng has been extended to nlude mplementatons n planar forms, usng prnted-rut approahes for wndngs together wth low profle ferrte ore onstrutons. It was subsequently demonstrated n 984 [8] [9] for rut arrangements and n 987 [] on a system level that all power onverson rut desgns of the swth mode have one or more IM forms. Pror to these ponts n tme, t s ommonly beleved that only those power ruts where transformer and ndutor have dynamally proportonal wndng potentals ould have IM forms. Suh speal onverter ruts nlude transformer-solated versons of the C uk [6], SEPIC and ZETA topologes. However, by usng ore strutures that possess more than one major materal flux path [8], IM tehnques an be appled to all swth mode power systems,

27 and an be extended to nlude other magnet elements often exluded. One example of suh elements s the seondary stage nput and output flter ndutanes used for redung onduted AC urrent rpples. IM desgns typally use soft-ferrte E-I or E-E ore strutures. The man dfferene among dfferent strutures s dfferent wndng arrangements on the three legs of the ore. For the ore leg where ndutor wndngs are stuated, an ar gap s needed to obtan the desred ndutane values and keep the ore from saturaton. Effetve ore leg areas must be hosen n aord wth the maxmum flux levels that wll our as a result of onverter operaton so as to prevent saturaton of the ore under maxmum loadng ondtons of the system. The use of prnted wrng methods for the IM wndngs an lower the heght profle of the overall pakage of the magnet omponent. Conventonal IM onstrutons, whether they use PCB style or wre wndngs, do have some undesrable lmtatons. Beause wndngs are putted on the outer legs of the ore, t s not possble to ompletely surround all wndngs wth ore materal to restrt magnet leakage levels. Also, beause onventonal onstrutons usng E-I or E-E ores restrtng wndow loatons for wndngs to two loales and materal flux paths to a maxmum of three, other power magnet omponents n a onverter rut (lke nput and output flter ndutanes) annot be easly aommodated n an IM arrangement wthout sgnfant topology hanges. Ths, n turn, often leads to undesrable ompromses n power onverter performane.

28 .4 Outlne of esearh In ths dssertaton, magnets omponents desgns for low voltage hgh urrent applatons are nvestgated thoroughly. Some spef desgns are desrbed n detal. The researh work s manly foused on these followng tops:. magnets omponent strutures; Four dfferent ntegrated magnets strutures are analyzed and ompared thoroughly n ths dssertaton. The haratersts and power loss mehansm of IM strutures are nvestgated. To nrease the effeny of magnets omponent, one optmzed IM struture s proposed. Ths desgn optmzes the ore shape to derease the opper loss.. unfed magnets omponent model; When dfferent ntegrated magnets strutures are ompared, the unfed rut model s needed. Otherwse, for dfferent wndng number and dfferent wndng loatons, t s hard to get the reasonable omparson results. One unfed rut model s ntrodued n ths dssertaton. Only the termnal parameters are onsder n ths model and t s onstruted from the smplfed and unfed mpedane matrx. Then, any omponent model an be unfed by several oupled ndutors. Ths smplfes the rut analyss.. desgn methodology; Conventonally, magnets omponent desgns are based on the relutane model analyss results. Before the omponent s real onstruted, the performane an only be roughly estmated. In ths dssertaton, FEA smulaton s nluded n the desgn proedure and one CAD desgn methodology s ntrodued. Beause the parast effets and termnal effets are all nluded n the smulaton results, the model based on ths smulaton result s aurate. Ths

29 helps to evaluate magnets desgn before t s really made. Ths s also helpful to derease the desgn perod and desgn ost. 3. dfferent applatons of magnets omponents. Generally, transformer s a passve deve whh transforms eletr energy from one rut nto another through eletromagnet nduton. In ths dssertaton, a new applaton for transformer n VM applaton s ntrodued. The transformer works as a voltage soure n atve voltage desgn. When transformer works durng the VM transent tme, t njets or absorbs the extra transent urrent to or from the load rut. It s smlar to an extra voltage soure added to the orgnal topology. Durng the transent tme, the workng frequeny s meager-hertz. So the transent response s fast. Another new applaton s ntrodued n seton 4.3. Beause of half brdge topology nherent voltage unbalane ssue, the urrent mode ontrol an not be used dretly. Beause the urrent mode ontrol has some advantages ompared wth voltage mode ontrol, suh as yle by yle over load lmtaton and fast transent response, a new magnets omponent struture s proposed to make up the topology shortage. The rut struture s smple and the ontrol method s easy to be mplemented. 3

30 CHAPTE : CHAACTEISTICS OF MAGETICS COMPOETS FO HIGH CUET APPICATIOS. Magnets Components Modelng and Smulaton The ntegrated magnets s a promsng tehnque to redue the sze of the magnet omponents and mprove the behavor of the rut. The use of magnets omponents ontanng wndngs n dfferent ore leg s a ommon prate to ntegrate transformer and ndutor n the same magnet ore. The use of a model for ntegrated magnets s a helpful tool to selet adequate wndng strategy. Beause the seleton of the ore, ar gaps and wndng setup are not easy, the aurate model s needed to selet the approprate onstrutve parameters. The voltage dfferenes between turns, between wndng layers and between wndngs to ore reate parast elements for magnets omponents. It s hard to model the rtal parast parameters just through the tradtonal relutane model. The relutane that models the leakage path s dependent on the geometry of the wndngs. Dfferent wndng arrangements produe dfferent leakage ndutanes. The leakage ndutane s extended to nlude flux n the radal feld. It s desrable to predt these leakages and develop an eletral model to ensure that the eletral propertes of the magnets omponents are sutable for the onverter topology. Aurate modelng and smulaton an redue the ostly delays. In the onventonal model, the relutane that models the leakage path annot always be related to the physal struture of the magnet omponents. The topology of the onventonal model has been prevously dsussed [6][7][8][9]. 4

31 The relatonshp between dual eletral ruts s based on the nterhange junton-ponts and meshes. An dental relatonshp exsts between the magnet rut of the magnet omponent and ts equvalent eletral rut. The physally-based model of the mult-wndng magnet omponent s ntrodued n []. The eletr-magnet dualty theorem s appled to extrat the eletral model form the magnet model. Therefore, the fnal eletral model s derved dretly from the atual physal magnet struture under nvestgaton. All the parameters n the model have one-to-one relatonshp wth orrespondng physal quanttes n the orgnal magnet struture. The eletral models of mult-wndng transformers an be expressed n several dfferent ways. The ladder model s one of the most popular and wdely used magnets models n power eletrons. It onssts of a magnetzng ndutane and a seres of eakage ndutanes onneted between the adjaent wndngs. In relatvely smple magnets strutures, the parameters of the ladder model an be easly related to the geometry of the ore and the wndngs. The ndutanes an be omputed by relatng the flux pattern to the physal arrangements of the ore and the wndngs. But, t should be noted that the wdely-used ladder model s an approxmaton based on wndng geometry: the ouplngs between non-adjaent wndngs are negleted. The author [8] has shown that geometry alone s nsuffent to justfy ths approxmaton. For an n-wndng transformer, the ladder model has n- ndependent parameters. On the other sde, the ndutane matrx n the general magnets model has n(n)/ ndependent parameters. FEA tools have been used to model dfferent ntegrated strutures. The goal s to obtan the ouplng parameters among dfferent wndngs, and then generate a smple model based on 5

32 lnearly oupled ndutors. Sne the 3D FEA solvers are not effent n terms of omputaton tme, a D approah has been developed by applyng the Double D tehnque [5]. Double D approah s based on the dvson of the wndngs of the magnet omponent n two parts. Eah part produes feld dstrbuton n dfferent planes of the spae. Usng ths tehnque t s assumed the lnearty n the ondutors. The preondtons of the double D method are: parts of the ondutors that are onsdered n eah smulaton are perpendular, the dotted produt of the felds reated by them s zero, and therefore the nteraton of both smulatons s null. The effet of the orners of the ondutors s negleted, whh s not a wrong assumpton for most pratal ases. The error s stll under the aeptable range. The man advantages of the FEA double D method are:. It s aurate and D effets (lke the frngng flux around the ar gap area) are onsdered, sne t s based on FEA alulatons;. Sne t s frequeny dependent, t s vald for non-snusodal waveforms. Ths s very useful for SMPS applaton; 3. The ouplngs between eah par of wndngs are aurately alulated; 4. Sne D FEA solvers are used nstead of 3D ones, the soluton tme s not very hgh. The man drawbak of the FEA solvers s that a FEA tool s needed and t s neessary to learn how to use t. Meanwhle, although the soluton tme s not an ssue usng the latest generaton omputers, the problem defnton n the FEA tool (geometry, materals and boundary ondtons) s tedous. However, ths s the only way to proeed wth FEA tools. 6

33 . Integrated Indutors for Hgh Current Applaton Powerng dgtal system needs hgh-urrent low-voltage power onverter wth fast transent response. The ombnaton of hgh urrent and fast response requres a voltage regulator module (VM) loated adjaent the load. At present, the standard desgn s a buk onverter wth multple staggered n phase parallel setons [7],[8],[9],[],[],[]. In a buk onverter, when the load urrent hanges, the ndutor urrent ramps up or down to math the new load urrent. At the same tme, the output apator supples the dfferene urrent. The small ndutor allows the rampng urrent to qukly mnmze the output apator requrement. On the other hand, the small ndutor leads to large urrent rpple. Beause the full urrent rpple flows through the MOSFET swth and the ndutor tself, hgher urrent rpple results n hgher losses and hgher peak urrent requrements. For a sngle phase onverter, large urrent rpple wll nrease the requrement of the output apator. Inreasng the operatng frequeny an redue the urrent rpple. But t also an nrease the swthng and gate-drve losses and magnets ore loss. Interleaved onverter s a sutable soluton for many applatons due to the better dynam response, better thermal management, smaller flters, less EMI ontent and better pakage. Ths allows the smaller ndutane wthout a large output apator. When a large number of phases are used, pakage ssues are very mportant, and magnet omponents volume s a rtal pont. In ths stuaton, oupled ndutor struture an derease the number of magnet ores and smplfy the rut omponents. At the same tme, t stll an derease the urrent rpple and have good transent response. In [3],[4], t s shown that oupled ndutors n nterleaved onverter an redue the urrent rpple. Ths reduton an extend to the ndutor wndng and swth tself. There are three knds of ntegrated ndutors: 7

34 . Dsrete ndutors pakagng: the ndutors are dsrete omponents and they are paked remanng ndependent one from others. Both dynam and stat performanes reman unhanged. The man drawbaks of ths knd ntegraton are hgh losses and bg sze.. Deoupled ntegrated ndutors: the ndutors are ntegrated on the same ore. The nterleavng onept s extended to magnet fluxes: fluxes wth the same waveform and tme shfted are added or subtrated. The omponent ats manly as an ndutor, storng energy n the ore. The man benefts obtaned wth ntegraton are the sze, losses and ost reduton. 3. Tghtly oupled ndutors: the wndngs are ntegrated on the same magnet ore. The omponent ats as a transformer beause, deally, no energy s stored n the ore, but t s transferred from one phase to the others. In ths stuaton, flterng needs are dramatally redued..3 Integrated Transformer and Indutors The urrent doubler retfer (CD), depted n Fg.., s wdely used and appears n several papers and textbooks []. 8

35 Fg.. Half brdge and urrent doubler rut topology The rut s redsovered reently for hgh frequeny DC/DC onverter applatons. The low urrent stresses n the transformer seondary sde, the ndutors and the retfers make ths rut espeally attratve for DC/DC onverters wth hgh output urrents. The rut an be used wth dfferent double-ended prmary topologes, suh as push-pull, half brdge, and full brdge [], [3]. Half brdge onverter s preferred for lower reversal voltage whh s equal to half of the nput voltage n theory. Moreover, beause the prmary leakage ndutane spkes an be lamped to the DC supply bus, the leakage ndutane energy s returned to the nput power supply nstead of to be dsspated n some resstve elements. At the same tme, beause the halfbrdge onverter has fewer omponents, t an smplfy the mplementaton of onverters. Many referenes have shown that half brdge topology s very promsng for low voltage hgh urrent applaton. A dsadvantage of the CD s the need for three magnet omponents, namely, one transformer and two ndutors. Besdes the sze and ost onerns, the nteronneton losses of these omponents also have negatve mpats on effeny, espeally n hgh-urrent 9

36 applatons. To solve ths problem, the two flter ndutors an be magnetally oupled, as suggested n [4]. At the same tme, ntegrated magnet strutures that mplement the transformer and the two ndutors on a sngle magnet ore have been proposed. Fg.. shows four suh strutures that have been publshed n the lteratures [5], [6], and [7]: Struture Struture Struture 3 Struture 4 Fg.. Four dfferent ntegrated magnet strutures In struture, the transformer and ndutor wndngs an be seleted ndependently. Ths provdes freedom n the desgn and allows hgher ndutane to be aheved. But, the separated

37 transformer and ndutor wndngs mply the use of more opper as well as hgher onduton loss and nteronneton losses. In struture [5], the transformer prmary and seond wndngs are loated n the dfferent legs. Then, the leakage ndutane between the prmary and seondary wndngs s hgh. Ths struture has lmted flter ndutane value. In struture 3 [6], t has lower leakage ndutane ompared wth struture. It also has lmted flter ndutane. In struture 4 [7], there s an extra wndng added n the enter leg. Ths an nrease the flter ndutane value. In [7], the flter ndutane value an be trpled when there s one turn extra wndng n the enter leg. When the frequeny s low, the opper loss of struture 4 s lower than the struture 3 beause of the lower urrent rpple. When the frequeny s hgh, the advantage s not so obvously beause the extra wndng wll brng n the extra opper loss. Based on the urrent-doubler retfer s workng modes, some paper derve the equatons from the relutane model for eah workng mode. The performane of the IM struture s evaluated based on these equatons. The queston s, f there s no spef workng rut, how the IM struture an be analyzed..4 Core oss for on-snusodal Waveforms Tradtonally, the Stenmetz s equaton s used to alulate the power densty of the ore. It expresses loss densty wth fxed exponent of frequeny and flux densty. P = kf α B β ( ) Ths equaton may work n a lmted frequeny or lmted flux densty range. It s not sutable for non-snusodal waveforms. These exponents are known to hange sgnfantly wth

38 frequeny, flux densty and waveforms. Ths knd of varaton represents the fat that relatve ontrbutons of the three fundamental loss mehansms (hysteret, lassal eddy urrent and exess eddy urrent) hange wth frequeny, flux densty and waveforms [6]. Swthng power onverters an have very dfferent waveforms and these non-snusodal waveforms wll result n dfferent losses [3], [3]. By the way, DC bas value an also sgnfantly affet loss [3], [33], [34]. In [9], the author defnes effetve ampltude as ampltude that may be substtuted nto a smple formula, orgnally ntended for smple waveforms, to enable alulaton of loss arsng from arbtrary waveforms. The use of rms ampltude for ths ase s dependent on the loss mehansm n the resstor. Effetve frequenes are less ommonly used than effetve ampltudes, but an be useful for frequeny-dependent wndng losses [5], [6], [7]. Agan, the alulaton of effetve frequeny s spef to the loss mehansm. A farly general hypothess for nstantaneous ore loss s [36]: db Pv ( t) = Pd, B dt ( ) Where P d s an unknown power dsspaton funton, a formula that an be used to alulate loss for any waveform for s [9]: P v P v = T T α db k B( t) dt β α dt ( 3 ) = k k ( 4 ) π α β osθ snθ α dθ α ( π )

39 To use Stenmetz equaton, what are needed are an effetve frequeny ampltude. B e f e and effetve α β α T db α β Pv = k B( t) dt = k f e Be ( 5 ) T dt The effetve frequeny should be related to the hange rate of the waveform, and the effetve ampltude should relate to the ampltude of the waveform features. B e = T T B () t b dt b ( 6 ) Where b = for average absolute value and b = for rms. f e = k T db dt T α B B () t () t β β α dt dt ( 7 ) Ths s a reasonable, defensble hoe for effetve frequeny. Equaton 5 s the generalzed Stenmetz equaton (GSE). It an be onsdered a generalzaton of the Stenmetz equaton for any waveform. It has an mprovement n that dfferent nomnal perods of the waveforms do not affet the result, and, for snusodal waveforms, t s expeted to provde the same auray as the Stenmetz equaton does. An mportant lmtaton of ths equaton s that t s typally neessary to use dfferent values of the parameters n the Stenmetz equaton for dfferent frequeny ranges. Ths shows that the GSE has lmted auray for a waveform ontanng harmons at a wde range of frequenes. 3

40 CHAPTE 3: PAA MAGETICS DESIG 3. Dsrete Magnets Desgn for ow Voltage and Hgh Current Converter 3.. Desgn of Planar Transformer The general desgn proedure s shown n Fg. 3.. Fg. 3. Transformer desgn proedure 4

41 3... Spefatons As t has been dsussed before, half brdge wth urrent doubler topology s hosen for ths hgh urrent and low voltage applaton. The objetve of ths work s to desgn a planar transformer usng mult-layer PCB wth low profle (. n), output power of 3 W, and hgh frequeny for the proposed DC/DC onverter. Fg. 3. shows proposed onverter topology wth the followng spefatons. Fg. 3. DC/DC onverter topology Sze:.9 n x.3 n x. n Input: 36~75V Output: oad Slew ate: Devaton: Effeny: Swthhng frequeny: I/O:.V@3A 5 amps/us, ST us max 3% wth zero external apatane full load 4kHz Surfae-Mount, onfguraton not spefed 5

42 Math Isolaton: Bas The desgn spefatons for the transformer are gven as: Prmary voltage V = 8~37.5V Turns rato n = 6 Duty yle D =.4 Swthng frequeny f = 5kHz Ambent temperature T a = 4 C Allowed temperature rse T = 5 C In ths prelmnary desgn, sne the profle of the magnets s strtly requred to be no more than. n, the ommerally avalable planar ferrte ores wth suh low profle requrement are evaluated frst Seletons of Core Shape and Materal To satsfy the spae and heght lmts, the E4.5 s hosen for the transformer. The shape and dmensons of the ore are shown n Fg

43 Fg. 3.3 Core shapes (E4.5) The next step s to determne the numbers of turns for prmary and seondary wndngs, and then evaluate the ore loss. Fnally the ore materal wll be seleted based on rough alulatons of ore losses. From the rut pont of vew, the turn s rato of the transformer s ntally assumed to be 6 ( n = 6 ), and the numbers of turns for prmary and seondary wndngs are hosen as n = 6 for the prmary wndng, and n = for the seondary wndng. Gven these parameters, the maxmum flux densty an easly be alulated usng followng equaton: B max = λ n A C = DT v ( t) dt n A C ( 8 ) Based on the estmated ore losses and workng frequeny, ferrte 3F35 s seleted as the magnet materal for the transformer. Meanwhle, the opper thkness of a 4-oz opper (around 4µm) s hosen. If the thkness of the nsulaton layer of the PCB s µm, the total thkness of the PCB wll reah: 7

44 8 4 7 = 8 µm =.8mm. By now we have determned the ore materal of ferrte 3F35 and ore shape as E4.5 for the transformer. In the followng sub-setons the opper loss, ether DC or AC loss, wll be evaluated by Ansoft FEM smulaton tools. By omparng the opper loss of varous nterleavng strutures, the optmal wndng layout s fnalzed Wndng Arrangements wth oss Smulatons Although the AC loss s usually domnant n the transformer wndngs loss, t s stll neessary to estmate the orrespondng DC loss. In the desgn, the skn depth of opper at 5kHz s 93.5µm for 5 C or 7.9µm for C and the thkness of 4-oz PCB s about 4µm whh s less than twe of the skn depth. Wth these parameters, the DC loss value should basally reflet the AC opper loss f the proxmty effet s negleted. Sne there s only one turn for the seondary wndng, t s very easy to alulate the DC loss n the seondary wndng. The DC loss estmaton of the prmary wndng s more omplex than that of the seondary wndng. For the prmary wndng, there are several possble wndng onnetons to obtan the desred 6 turns: (a) 6 turns for one PCB layer; (b) 3 turns for one PCB layer and layers n seres; () turns for one PCB layer and 3 layers n seres; and (d) turn for one PCB layer and 6 layers n seres. The number of turns per layer and the spang between the turns are denoted by the symbols and S respetvely. For an avalable wndng wdth bw, the trak wdth wt an be alulated wth followng equaton (see Fg. 3.4): 8

45 w t = b w ( ) S ( 9 ) w t w t w t S S S turns b w Fg. 3.4 Trak wdth wt, spang s and wndng wdth bw After the number of turns for eah layer and dmensons of the PCB trak are determned, t s possble to estmate the DC opper losses for both prmary and seondary wndngs. The DC onduton losses for the 4 possble wndng onnetons above are then estmated. By omparng the results, t s obvous that the DC opper loss s least when the prmary wndng s omposed of layers n seres and eah layer wth only 3 turn. So far we have seleted the ore materal (3F35), ore shape (E4.5), and wndng layers for the transformer ( layers n seres and 3 turn eah layer for prmary wndng, 4 layers n parallel for seondary wndng). However, suh desgn s usually far away from beng optmal to estmate the opper loss only based on the DC analyss. Therefore, t s rtal to quanttatvely determne the total AC opper loss for varous nterleavng wndng strutures. By properly nterleavng the prmary and seondary wndngs, the extra AC loss resultng from proxmty effet an be redued to the largest degree. 9

46 In order to aurately determne the hgh-frequeny onduton loss n transformer planar wndngs, an effetve eletromagnet smulaton tool based on fnte element analyss (FEA) s usually desred. Ansoft Maxwell Feld Smulator (D or 3D), as one of the most popular software tools n the ndustry, provdes us wth numeral solutons to the omplated D and 3D strutures. AC onduton losses performane n the transformer wll be smulated usng Ansoft Maxwell software. The urrent dstrbutons on the ross-setonal area of the wndngs are nvestgated for varous nterleavng wndng strutures. By analyzng the urrent dstrbuton and onduton loss, the desred nterleavng wndng struture an be found from smulaton results. The aurate AC opper loss an be extrated usng Maxwell 3D feld smulator. Consderng the strutural feature of E ore, an axs-symmetral model s adopted n Maxwell D smulaton. Fg. 3.5 shows the possble wndng arrangements for the transformer. The red ondutors represent the prmary wndngs whle the green are the seondary wndngs. 3

47 Fg. 3.5 Interleaved wndng strategy Usng Maxwell D smulaton software, urrent dstrbutons for above four strutures are llustrated respetvely. It an be seen that the urrent dstrbutes more unformly n the nterleaved arrangements than that n non-nterleavng struture. Maxwell D smulaton results also present the hgh-frequeny opper resstane value n dfferent wndng strategy. The smulated results show that nterleavng prmary and seondary wndngs an dramatally mprove the urrent dstrbuton and therefore redue the AC opper loss. The wndng resstor value ndates that the loss for nterleavng strategy s the best one among the three nterleavng strutures. It should be noted that the effet of wndng termnatons and onnetons n the transformer s negleted n Maxwell D smulatons. To aurately alulate the AC loss n transformer 3

48 wndngs, t s desrable to smulate the onduton losses from 3-dmensonal pont of vew. Maxwell 3D smulaton an aurately ompute the AC wndng losses and further optmze the nterleavng wndng arrangements. Fg. 3.6 shows the 3D model of the mult-layer PCB planar transformer. It s always tme-and-memory-onsumng to do 3D smulatons, but the result s more aurate. Fg D model and smulaton result of an nterleaved planar transformer n Maxwell 3D The Maxwell 3D smulaton result learly shows that the flux densty dstrbuton and magntude meet the desgn requrements. The prelmnary desgn results of mult-layer PCB transformer are summarzed n as follows: Core: Materal: E4.5 3F35 3

49 Wndng Strategy: Fg. 3.7 Planar Transformer wndng strategy 3.. Desgn of Planar Flter Indutor There are obvous nentves for onverters to operate at hgher frequenes. Converters operatng at hgh frequenes requre sgnfantly smaller ndutane values and therefore smaller magnet omponents. However, as the frequenes nrease, ore loss and wndng losse may also dramatally nrease and hgher swthng frequenes do not always result n the expeted sze reduton Spefatons The ndutor desgn spefatons are as below: Crut Input voltage: 36~75V Output voltage:.v Output power: Swthng frequeny: 3W 5 KHz 33

50 Indutor heght:. n Appled urrent: 5 A AC pple 3... Seleton of Core Shape and Materal Magnet omponent desgn generally nvolves a tradeoff between the reduton of ore loss and the nreasng of wndng loss or ve versa. The loss haraterst of the magnet materal tself presents a fundamental lmtaton on ore loss reduton so that the ntrns reduton of ore loss densty depends on magnet materal mprovements. Desrable haratersts of magnet ores for power ndutors and transformers an be summarzed as follows: frst, hgh saturaton flux n order to obtan hgh saturaton urrent; seond, hgh permeablty to obtan hgh ndutane; thrd, hgh resstvty to redue eddy urrent loss. For power ndutor, the ar gap s needed n the ore. The tradtonal ar gap alulaton equaton for ndutor s shown: A l µ E = ( ) g Here, l s the gap length and A s the effetve ross setonal area of the ore. If the g frngng effets at the gap and the permeablty of the ore are onsdered, the more aurate ar gap length and ndutane equatons are: ( ) E D D VnTs le I M Bmax A µ µ r l g = ( ) Bmax D( D) VnTs µ r Bmax µ η µ µ r Al e η 34

51 A = µ l r η l g e ( ) Here, µ : Permeablty of free spae µ r : elatve permeablty of the materal l e : Effetve magnet path length of the ore η : Core s ross seton area orreton parameter for frngng effet (between.5 and.) A : Indutane fator wthout the ar gap (provded by manufaturer) B max : Maxmum operatng flux densty seleted for the desgn By nvestgatng some ommeral ores, ore E9.5 s hosen and 3F35 s ore materal. The spefaton of 3F35 s shown n Fg Fg F35 Spefatons ( 35

52 3...3 Wndng ayout wth oss Smulatons PCB strutures are utlzed to fabrate planar wndngs. In ths desgn, there are also several layers paralleled together for one turn beause of the hgh urrent. To nrease the ndutane value and derease the urrent rpple, there are two turns for ths ndutor. Fg. 3.9 Indutor 3D Model and Smulaton esults The Maxwell 3D smulaton result learly shows that the flux densty dstrbuton and magntude meet the desgn requrements. The desgn result of ndutor s as follows: Core: Materal: Wndng Strategy: E9.5 3F35 every four layers paralled and then onneted n seral 36

53 3..3 Smulaton and Expermental esults Crut Model The tradtonal two-wndng transformer model s shown n Fg. 3.. The prmary wndng resstane s represented by, the leakage ndutane by, magnetzng ndutane by, p ore loss by, and self-apatane by C. The seondary wndng resstane s, the p seondary self-apatane s C, and ross apatane between prmary and seondary s C. s The parameters n ths model an be used for haraterzng omponents and dentfyng rut smulaton. However, ths smple model s omplated beause all of the resstors and ndutors of the model are nonlnear funtons of ether frequeny, or extaton level, or both. The apators also exhbt mnor nonlneartes, but they are further omplated by a very rude approxmaton to the multple nter-wndng apatane effets that really exst n the omponent. lk s m m p lk C m s C p m C s Fg. 3. Tradtonal two-wndng transformer model Fg. 3. s the seondary open and short-ruted measurement results, two mpedane urves are drawn. The open-rut measurement gves the prmary resstane, magnetzng 37

54 ndutane, and apatane (va the resonant frequeny). ormally, the magnetzng ndutane s treated as a onstant value over workng frequeny range. In fat, t vares sgnfantly due to materal varatons, temperature and frequeny. The short-rut measurement gves the seondary resstane and leakage ndutane whh wll sgnfantly nfluene the rut performane. At very low frequenes or DC stuaton, we an dretly measure the prmary d resstane. Beyond that low frequeny, the value of the prmary and refleted seondary resstane an be measured from the prmary termnals. When frequeny s above ertan value, the short rut mpedane rses due to an nrease n AC resstane. From the mpedane urve, real and magnary parts of the mpedane are separated out and the value of eah of these parameters an be extrated. Transforme r _ prmary _ mpedane Ohms open _ rut m lk p p s short _ rut Frequeny(Hz) Fg. 3. Transformer prmary mpedane urve Beause the leakage ndutane wll ause rngng n the rut at hgh frequenes, so t s mportant to know the value at the rngng frequeny n order to be able to desgn a proper snubber. There s an ndustry rule that t s often quoted: The leakage ndutane should be % of magnetzng ndutane for a transformer. In real desgn example, wth the tghtly oupled 38

55 wndngs, the leakage an be less than.% of magnetzng ndutane at klo Hz, and.% at mega Hz. All these nformaton are derved from the extended frequeny response measurements on transformers. How to get these parameter values before we have the real omponents beomes an ssue. In addton, when there are several magnet omponents or there are mult wndngs n one ore, the aurate and smple rut model s needed for rut analyss and evaluaton before we have the real magnet omponents. For onventonal rut smulaton, the magnets model s onstruted usng the smple transformer and ndutor model. Ths method omts the frequeny dependent feature of the magnets omponent. The method also omts parast effet of the omponent. In ths desgn, a CAD desgn methodology s proposed and Maxwell 3D FEA smulaton s adopted. From the 3D smulaton, the parameter matrx s extrated. Ths matrx nludes the frequeny nfluene and parast effet. The desgn proedure s as follows: CHAPTE : Usng FEM to do the EM feld analyss for magnets omponents; CHAPTE 3: Extratng mpedane matrx from the FEM smulaton result; CHAPTE 4: Generatng onverter spefed model parameters; CHAPTE 5: Construtng rut model and applyng the model to the onverter desgn. The physal struture model of the dsrete magnets struture s shown n Fg

56 Fg. 3. Physal strutures of dsrete magnets From the FEA smulaton results, the mpedane matrx s derved: Table 3. Dsrete Struture Parameter Matrx P S esstor (ohm) Indutor (H) esstor (ohm) Indutor (H) esstor (ohm) Indutor (H) esstor (ohm) Indutor (H) P E E-5 S E E E E-7 The whole magnets struture an be treated as 3 port rut network when t referred to other part of the onverter rut. So, the 4x4 matrx s hanged to 3x3 matrx. The Pspse model s onstruted from the 3x3 matrx. In ths model, the H blok s used to model the mutual resstane and the k parameter s used to model the ouplng among the dfferent wndngs. 4

57 7 K K K_near COUPIG = uH H6 H - - H7 5nH.568 K K3 K_near COUPIG =.8 H H4 H - -H5 H H8 - H - H H K K 5nH K_near COUPIG = Fg. 3.3 Pspse model of the dsrete magnets struture Smulaton esults Puttng the magnets omponent model nto the Pspse whole rut model, the smulaton results are shown n Fg Fg. 3.4 Seondary urrent waveform of the whole rut w/o lamp To derease the urrent rngng and nrease the effeny, the atve lamp s added n the prmary sde. The urrent waveform s followng: 4

58 Fg. 3.5 Seondary urrent waveforms w lamp Fg. 3.6 Prmary urrent waveform w lamp Beause the model parameters are frequeny-dependant and nlude the parast effet, the smulaton results are more aurate. Ths pont s shown learly n the next seton Expermental esults Experment rut board s shown n Fg It s shown very learly that the footprnt of the magnets omponents oupes almost 5% of the whole area. 4

59 Fg. 3.7 Experment board Fg. 3.8 and Fg. 3.9 are the expermental results of the prmary voltage and urrent waveform. Fg. 3. s the smulaton result of the prmary voltage and urrent waveform. The two results are almost same. Ths means the magnets omponent model s aurate. Fg. 3.8 Prmary voltage and urrent waveform 43

60 Fg. 3.9 Prmary voltage and urrent waveform after retfy 4V V V -V -4V 5.V V(7:,S5:4).5V V SE>> -.V 4.us 4.us 43.us 44.us 45.us 46.us 47.us 48.us 49.us V(D8:,) Tme Fg. 3. Smulaton prmary voltage and urrent waveform after retfy 3..4 Volume Optmzaton In urrent dstrbuted power system (DPS) applatons, there are nreasng demands on hgh-power-densty, low-profle, and hgh-effeny front-end d/d onverters. In most ases, the overall sze and volume of front-end DC/DC onverters are prmarly determned by the sze and volume of the passve omponents and the nteronnetons between them. ots of efforts 44

61 have been made n the past few years to redue the footprnt and profle of the passve omponents. The total loss an be approxmately dvded nto two parts: the ore loss and the wndng loss, assumng that the loss fator of the nsulaton materals, as well as volume of leakage layer magnet materals s small, so that the losses n those materals an be negleted. The AC wndng loss modelng for transformers and ndutors has been a researh top for many years. The fnte-element model (FEM) s beleved to be more aurate than the -D analytal models provded n [38]-[43]. However, n order to redue the alulaton error to an aeptable level by usng the FEM method, a long omputaton tme s always needed, makng the teratve optmal desgn proedure tme onsumng and almost mpratal. On the other hand, the -D model s very tme effetve and an gve an aeptable result as long as the ondtons for the -D approxmaton an be well satsfed. For the passve omponents, the wndng ondutor thkness s always less than or equal to the skn depth of the ondutor at the fundamental frequeny, whle t s also muh smaller than the ondutor wdth. The wndngs are also always plaed far away from the ar gap. Ths mples that the frngng effets and edge effets an be negleted n ths struture. After these ondtons are satsfed, the -D wndng loss model s used n the volume optmzaton. ( t) = I ϕ = P j P = I j u = I I j os( jωt) j= jϕ j d d jϕ m P j Q m ( 3 ) 45

62 For PWM onverters, the extaton urrent s normally a square wave. The effets of harmons have to be taken nto aount. The Fourer seres s shown n equaton 3. Beause of the nterleavng arrangement of the wndngs, the MMF of eah layer wll be hanged. At last, the power loss wll be dfferent for dfferent layer. Fg. 3. MMF of non nterleavng transformer Fg. 3. MMF of nterleavng transformer The Fg.3. and Fg.3. show how the wndng arrangement wll nfluene the MMF. After two parameters have been defned: l nsulaton l w η = ( 4 ) w 46

63 δ δ ' = ( 5 ) η h h ϕ = = η δ ' δ ( 6 ) The power loss n eah layer an be alulated: P = I ϕq' ( ϕ, m) d Q' ( ϕ, m) = (m m ) G ( ϕ) 4m( m ) G snh(ϕ ) sn(ϕ ) G( ϕ) = osh(ϕ ) os(ϕ ) snh( ϕ)os( ϕ) osh( ϕ)sn( ϕ) G( ϕ) = osh(ϕ ) os(ϕ ) ( ϕ) ( 7 ) The ore loss alulaton has been dsussed before. After the AC loss model has been obtaned, the optmal desgn program an be developed. The desgn proedure s an teratve proess. The detaled desgn steps are lsted as follows. ) Spefyng all the omponents parameters from rut analyss. These parameters are transformer turns rato, magnetzng ndutane, extaton voltage, urrent waveforms, profle, effeny, swthng frequeny, nsulaton thkness, and learane dstane, et.. ) Choosng ore materal based on t the frst step result. The desgn varables nlude the dmenson range of the ore, wndng urrent densty range, and of wndng turns number. 3) Settng up the alulaton equatons. The target an be power densty, profle, footprnt, et., as a funton of the onstrants and the desgn varables. In ths desgn, gven the effeny value, the mnmal ore volume s the desgn target. 47

64 4) Startng the teraton proess by hangng the ore dmensons and alulatng the power densty of eah desgn. A set of desgn urves s obtaned from the alulaton. For one ertan wndng urrent densty value, an optmal desgn pont ould be obtaned. 5) Wrtng down the results after the smallest ore volume desgn s dentfed. Input data dsplay the transformer parameters for maxmum power densty W=Ww W<Wmax? Y =l <max? Y n=p/(ppt) H=Hh H<Hmax? n>n and Bm<Bm? Y Y Hw=Hwhw Ve=Ae*e Hw<Hwmax? Ve<Vmn? Y Y Pt=PPw Vmn=Ve Fg. 3.3 Flow hart of the optmzaton program A transformer optmzaton results are shown n Table 3., Fg. 3.4 and Fg

65 Table 3. Transformer Optmze esult k K 3K 4K 5K 6K 7K 8K 9K M wdth length hght wdow hght Ve 7.66E E-7.55E-7.8E-7 8.7E-8 7.5E-8 7.5E-8 6.9E-8 6.9E-8 6.9E-8 Ae.73E E-6 5.3E-6 4.E-6 3.8E-6 3.E-6 3.E-6 3.E-6 3.E-6 3.E-6 e enter Bm Ptotal Cu_loss ore_loss effeny Mnmal ore volume vs. frequeny Mnmal ore volume vs. frequeny Core Volume 8.E-7 6.E-7 4.E-7.E-7.E-8 k K 3K 4K 5K 6K 7K 8K 9K M Frequrny Fg. 3.4 Mnmal ore volume vs. frequeny When the frequeny s nreased, under the gven effeny requrement, the ore volume an be dereased. Beause the opper loss s nreased as well, there s an optmzed mnmal ore volume for the gven power effeny. 49

66 For the same output power, a hgher effeny normally requres a larger ore volume. But when effeny beomes hgh, a small nrease n effeny results n bg nrease n the ore volume. So, there s trade off between the effeny and mnmal volume. Mnmal ore volume vs. effeny Mnmal ore volume vs. effeny Core Volume 6.E-6 4.E-6.E-6.E Transformer Effeny Fg. 3.5 Mnmal ore volume vs. effeny 3. Atve Transent Voltage Compensator Magnets Desgn for VM 3.. Hgh Current and Hgh Slew ate VM The advane of mroproessor tehnology sets hgh requrements for the power delvery system. When the number of transstors n the mroproessor nreases, the urrent demand also nreases. The supply voltage s expeted to derease to redue the power onsumpton. Moreover, the mroproessor s load transent speed s also nreased wth the nreased operatng frequeny. The low voltage, hgh urrent and fast load transton speeds are the 5

67 hallenges mposed on mroproessor power supples. When the mroproessor swthes between sleep mode and atve mode, the urrent demand of the mroproessor swthes between no load and full load. Beause of the very hgh lok speed, the transton proess mposes very hgh urrent slew rates to the rut. Atve transent voltage ompensator (ATVC) [47] s a good soluton to the hallengng hgh slew rate load urrent transent requrement of VM. ATVC only works n transent perods. At the same tme, beause the man V only operates n low frequeny n steady perod, the effeny of the V s hgh. In general, transformer s a deve whh transforms alternatng (AC) eletr energy from one rut nto another rut through eletromagnet ndutor. Here, the atve transent voltage ompensator (ATVC) mproves transent response through the same bas onept. It s shown n Fg. 3.6: Vnj s the njeted voltage soure and s s the equvalent mpedane of ATVC. It only engages nto the rut n transent perods wth several MHz operaton frequenes, whle the man V operates at low frequeny (several hundred KHz) for good effeny. In ths applaton, a transformer has been adopted to work as the Vnj voltage soure. The rut njets or absorbs the hgh slew rate urrent through the transformer. The transent urrent value s manly determned by the transformer leakage ndutane value. At the steady state, the voltage soure s removed from the rut. In the steady state workng mode, the transformer just works as a bg flter ndutor [47]. 5

68 p p Vo Multphase Vs s V nj CPU C Cp Fg. 3.6 Power delvery struture: (a) ntal CPUs power delvery struture and (b) the urrent For the ATVC, the transformer s an mportant omponent. Beause of the DC bas urrent (ndutor), hgh frequeny (MHz) and the hgh slew rate load urrent, the desgn of the transformer s a key ssue n the ATVC desgn. The turns- rato and the leakage ndutane value of the transformer wll nfluene the urrent slew rate. When the transformer works as an ndutor, an ar gap s needed to keep the ore from the saturaton. The ar gap length wll nfluene the transformer leakage ndutane values. On the other hand, every parameter s frequeny dependant. The small hange of the parameters wll ntrodue bg dfferene to the transent response. Instead of the normally smple magnet rut analyss, the FEM (fnte element method) analyss s adopted. The frequeny dependent transformer parameters are extrated from the frequeny dependent mpedane matrx dretly. Ths model s useful for the desgn of whole VM rut. 3.. Transformer Workng Modes The transformer workng modes are analyzed frst to make thngs lear. How the parameter values nfluene the rut performane s also analyzed. The whole AVTC mplement rut s 5

69 shown n Fg There are fve parameters n ths two wndng transformer model. The dea transformer turns rato s :. The seondary sde of the transformer s paralleled to the man V rut and the prmary sde s onneted to the MOSFET. In ths fgure, M s the transformer equvalent resstane value; M s the transformer magnetzng ndutane value; lk lk and are the leakage ndutane of eah transformer wndng; s the transformer magnetzng urrent value; s the transformer total njeted urrent; and are the value of eah transformer wndng s urrent. ATVC K K M Fg. 3.7 ATVC mplementaton rut There are three workng modes for ths transformer: Buk rut state: Qa s on, Qa s off and transformer works at hgh frequeny (MHz). The mroproessor swthes from sleep mode to the atve mode. Ths s the step up load. Beause of theω >> M prmary voltage an be smplfed as, we an omt the resstor n the theory analyss. The transformer 53

70 V V = dk dt K M dm dt ( 8 ) The transformer seondary voltage s gven as V V = K d dt K M d dt M ( 9 ) The voltage drop between the V and V s near zero. So that M d dt M = K d dt K ( ) K Beause of the dea transformer, we an assume M and P = K. Then t an be yelded dk V V = K K dt dk dt ( ) From the equaton (), when the voltage value s settled, the leakage ndutane value of eah wndng wll dede the urrent slew rate value. The transformer total njets urrent an be expressed as d ATVC dt dk = ( ) dt d dt M ( ) Steady state: Qa s off, Qa s off and transformer works as an ndutor. The transformer works as a flter ndutor. The flter ndutane value s equal to transformer seondary wndng s self ndutane value. 54

71 I ATVC P P M I ( 3 ) I ATVC s the output DC urrent. From ths value, the ar gap length an be deded. In ths workng mode, the transformer total output urrent equals the transformer seondary urrent. The man VM rut works n the low frequeny (KHz) nstead of transent hgh frequeny (MHz). At the same tme, the large flter ndutor means the small urrent rpple. The hgh effeny of the whole onverter an be aheved. Boost rut state: Qa s off, Qa s on and transformer works at hgh frequeny. Ths s step down load. The transformer prmary voltage s gven by V = dk dt K K d K dt ( 4 ) The transformer total absorbs urrent s d dt dk ( ) dt ATVC = d dt M ( 5 ) The equatons also show that the transformer leakage ndutane values wll determnate the transent slew urrent value. Desgnng the transformer wth sutable parameters value s the man task of the whole desgn. 55

72 3..3 Transformer Model For the onventonal approahes, magnet omponents are often desgned based on magnet equvalent rut models. The ore loss and onduton loss n magnet deves are roughly estmated. However, wth the nrease n the swthng frequeny, t beomes dffult to apply the tradtonal analyss to evaluate the power losses aused by skn effet and proxmty effet [48]. Furthermore, the leakage ndutane value has a bg mpat on the whole rut performane [49]. From the workng modes whh s explaned before, t s very mportant to know the leakage ndutane value of eah transformer wndng. Ths annot be alulated just from the normal transformer open rut and short rut model. In the steady state, the transformer works as an ndutor. The ar gap s needed to keep the magnet ore from saturaton. When the turns-rato s small, the value rato between the magnetzng ndutane and leakage ndutane s small. The open rut s not sutable to dede the magnet ndutane value. The new model s needed to derve eah wndng s leakage ndutane and the transformer magnetzng ndutane value. Ansoft Maxwell 3D software s adopted to desgn the transformer. The Maxwell 3D s the FEM numeral method. It begns from eletral magnet feld FEM analyss and smulaton. The skn effet, proxmty effet and parast parameters are all nluded n the smulaton. The smulaton result s aurate and frequeny dependent. The mpedane matrx of the omponent an be extrated from the eletral magnet feld smulaton results dretly. In ths desgn, the magnet ore E from Phlps s used for the transformer to redue the whole volume of the onverter. 56

73 Fg. 3.8 Transformer model The transformer model s shown n Fg The model nludes an dea transformer, the leakage ndutane of eah wndng and one effetve resstor. Here, t should be noted that the magnet omponent s alled transformer just beause the urrent waveforms are same as a real transformer. From the energy pont, t works lke two strong oupled ndutors. kp ks m V p s V B A Fg. 3.9 Tradtonal transformer model Fg. 3.9 s the tradtonal transformer mode. On the prmary sde, the referene dretons of the voltage and urrent are same and they are as same as the real dreton. So, the prmary sde of the transformer absorbs the energy from the soure. On the seondary sde, the dretons of the voltage and urrent are dfferent. The transformer sends the energy out to the load. From the 57

74 energy pont, the transformer an only transfer the energy. Beause of the leakage ndutane, there s small energy stored n the ore. V p kp m ks Vs B A Fg. 3.3 Inverse transformer model Fg. 3.3 s what we alled the nverse transformer n ths desgn. The referene voltage dreton for the seondary sde s dfferent from the tradtonal one. The seondary sde absorbs the energy too. So, from the energy pont, t s strongly oupled ndutors and stores the energy. But, beause the urrent waveforms are same as the real transformer, we all t nversed transformer. In ths model, the transformer s analyzed as a two ports network. From the Maxwell 3D smulaton, the aurate and frequeny-dependable mpedane matrx of ths model an be alulated. In the matrx, the real part s the resstor value and the magery part s the ndutane value. They have been automatally separated. To alulate the ndutane value, we only need to onsder the magery part of the mpedane matrx. The equaton of the network an be wrtten expltly as V V z = z z z ( 6 ) From the two ports rut, the seondary voltage s presented as 58

75 ( ) V M K M M K p M K M M K K = = = = ω ω ω ω ω ω ω ω ω ( 7 ) and the prmary voltage s gven by ( ) ( ) V M M K M K p M K M M K K = = = = ω ω ω ω ω ω ω ω ω ( 8 ) When ompared wth the Maxwell 3D mpedane matrx result, the matrx equaton an be smplfed to = M K M M M K z z z z Im ( 9 ) From the equaton (9), the transformer magnetzng and leakage ndutane value an be alulated. Same as the Maxwell 3D FEM numeral result, the ndutane value s aurate and frequeny dependent. The most mportant thng for the ATVC s that the leakage ndutane value for eah wndng an be shown learly n the model. Ths s useful for the whole V 59

76 rut analyss and smulaton. Through the same method, from the real part of mpedane matrx, the effetve resstor value M an be alulated Smulaton esult The ATVC rut requrements are: settng less resstor value to derease the power loss and nrease the effeny; settng less leakage ndutane to mprove the transent response and makng tradeoff between the swth loss and transent response. The Maxwell 3D software s used to perform the detal smulaton. Aordng to the transformer rut model, we an dede the turns-rato, ar gap length and operatng frequeny of the transformer for ATVC. From the equatons () and (5), an effetve leakage ndutane s defned as: 6

77 leakge = K K ( 3 ) m vs. Ar Gap ength m(:) m(:) m(4:) 5 nh 5.mm.4mm.6mm Ar Gap ength leakage vs. Ar Gap ength leakage(:) leakage(:) leakage(4:) 5 nh 5.mm.4mm.6mm Ar gap length Fg. 3.3 Indutane values vs. ar gap length When the ar gap s nreased, the magnetzng ndutane value dereases a lot and the effetve leakage ndutane just hanges a lttle. To keep the magnetzng ndutane value far larger than leakage ndutane value and keep leakage ndutane value small, the ar gap length.mm s enough. Beause the transformer works as the ndutor n the steady state, the flux densty dstrbuton wth the ertan ar gap length s heked to keep transformer from saturaton when t works as a flter ndutor. 6

78 Turns rato : Turns rato : Turns rato 4: Fg. 3.3 Flux densty dstrbutons for dfferent turns-rato From the smulaton results of flux densty dstrbuton whh are shown n Fg. 3.3, E ore wth dfferent turns- rato meets the flux densty requrements. When the frequeny s nreased, for dfferent turns-rato, the magnetzng ndutane almost stays onstant and the leakage ndutane nreases a lttle. For better effeny durng the transent perod, the frequeny.5mhz s dentfed. 6

79 m vs. Frequeny m(:) m(:) m(4:) 5 nh 5.5M M.5M Frequeny leakage vs. Frequeny leakage(:) leakage(:) leakage(4:) nh 5 5.5M M.5M Frequeny Fg Indutane values vs. frequeny When the transformer turns-rato s nreased, the magnetzng ndutane and the leakage ndutane are both nreased. For the better effeny and better transent response, the turnsrato : s adopted. 63

80 m vs. Turn ato m(.mm) m(.4mm) m(.6mm) I Core 5 nh 5 over over 4over Turn rato leakage vs. Turn ato leakage(.mm) leakage(.6mm) leakage(.4mm) I ore nh 5 5 over over 4over Turn rato Fg Indutane values vs. turns-rato esstor vs. turn raton esstor vs. turn raton Ohm over over 4 over Fg esstor vs. turns-rato When the turns-rato s nreased, the effetve resstor value s also nreased f the ore sze s settled. 64

81 Aordng to the smulaton results, the transformer wth the swthng frequeny.5 MHz, : turns-rato and.mm ar gap length s hosen. In ths desgn, the effetve leakage ndutane value s 6.5 nh and the magnetzng ndutane s 38 nh. The ore sze s E and the ore materal s 3F35. () Input voltage for the transformer () Flux lnkage waveform (3) Transformer urrent waveform Fg Maxwell 3D transent smulaton results 65

82 Beause of the hgh frequeny (MHz), the eddy urrent effets n the wndng and ore have to be n onsderaton. At the same tme, beause the ore s permeablty hanges wth frequeny and flux densty, all of these wll affet the performane of ATVC [5]. The Maxwell 3D transformer transent smulaton s a good way to understand the transformer transent workng performane. In the transent smulaton, the atual voltage s added to the Maxwell 3D model of the magnet omponent. In Fg. 3.36, the transent flux lnkage waveform dstrbuted n the ore and transformer transent wndng urrent waveform are gven. From the smulaton results, t s lear that the transformer transent urrent slew rate an reah.a/ns Experment Verfaton Usng the proedure ntrodued above, a transformer has been desgned. A two hannel VM [53] and ATVC prototype was bult to verfy the desgn. It s shown n Fg The man VM swthng frequeny s 3 KHz and the ATVC operatng frequeny s.5 MHz. Qa Qa ATVC ontroller Transformer Fg Experment prototype 66

83 VM expermental results wthout and wth ATVC are shown n Fg and Fg separately. The load urrent s swthed between A and 5A. We an see that the VM wth ATVC has better transent response. The transent urrent an ath the load urrent qukly. Fg VM expermental results wthout ATVC Fg VM expermental results wth ATVC. 67

84 When the load s nreased suddenly, the transformer njets urrent to the rut. When the load s dereased suddenly, the transformer absorbs urrent from the rut. From the expermental waveform, t s lear that the transformer desgn an satsfy the ATVC rut requrement. The ATVC transent urrent slew rate an reah.a/ns. Fg. 3.4 Step down detal waveform, VM and ATVC work together Fg. 3.4 Step up detal waveform, VM and ATVC work together 68

85 Fg. 3.4 and Fg. 3.4 are detaled waveforms and MOSFET gate sgnal n ATVC. The two MOSFETs are turned on at dfferent tme perods aordng to dfferent workng ondtons. The expermental results verfy the ntutve magnets omponents desgn for hgh urrent and hgh slew rate applaton n VM. 69

86 CHAPTE 4: ITEGATED MAGETICS 4. Coupled Indutors Current-doubler topology s presented n the lterature as a possble soluton to derease the power losses n the transformer seondary sde wndngs of the full-wave buk-derved onverters, suh as push-pull, half-brdge [68], [69] and full-brdge [7], [7]. In omparson to onventonal enter-tapped topology, urrent-doubler topology an redue the losses by approxmately 5%. The penalty for the mprovement s an addtonal ndutor. Ths nonvenene an be partally allevated by ntegratng both ndutors on a ommon ore. Integraton wthout magnet ouplng of the wndngs was dsussed n [68] and [7]. Compared wth the dsrete struture, ntegrated struture has smaller effetve flter ndutane value. For the dsrete ouple ndutor struture, there s only one ndutane value whh has lmted workng range. In the [7], three oupled ndutor strutures are ompared and analyzed. The objetve s to searh the zero rpple ondton when the ndutors have dental voltage waveform. In [75] and [76], the ntegrated oupled ndutors struture between the hannels s proposed to mprove both the steady state and dynam performanes wth easer manufaturng. But, they all have lmted ndutane adjustable range. The eletral shemat and ndutor wndng arrangement for a Y-shape oupled ndutor are shown n Fg. 4.. The wndngs loated at the out legs are nversely oupled and the turn numbers are same. It has large ndutane adjustable range to optmze the ndutane value for good rut performane. 7

87 (a) Proposed rut (b) Physal struture Fg. 4. Proposed Y-shape ntegrated oupled ndutor struture 4.. Model Dervaton In Fg. 4., the represents the relutane of eah outer ore leg and represents the equvalent relutane of the enter leg. value s normally domnated by the length of the ar 7

88 gap. In prate, however, the stray feld omponent an strongly nfluene the value and the alulaton of the ar gap s dffult. s the out leg wndng turn number and s the enter leg wngng turn number. C Fg. 4. elutane model The flux n eah ore leg s gven by followng equaton: = φ φ φ ( 3 ) Beause of, the equaton s hanged to: = ( ) ( ) = φ φ φ ( 3 ) 7 From the magnet bas equaton dt d v φ =,

89 = dt d dt d dt d A v v v (33 ) = A (34 ) = = C C C C C dt d dt d dt d M M M M M M dt d dt d dt d M M M M M M v v v (35 ) Beause of the symmetry struture: = =,, M M M = = C C C C C M M M M M = = = = 73

90 = (36 ) = (37 ) M = (38 ) M = (39 ) The ouplng oeffents are: = = = α M k (4 ) ( ) α / = = = M k (4 ) In these equatons, = α and < < α. We an see from here: s between.5 and and s between and.5. k k = dt d dt d M M M M M M M M v v v (4 ) 74

91 = dt d dt d M M M M M M v v e e (43 ) = = n out e n out e V V v V V v (44 ) To keep the magnet ore from the saturaton, from the vew of mehanal stablty, there s an ar gap loated n the enter leg and. When enter leg turns number s small, the. So, the nversed dea transformer model s used to deouple the ndutors. The equvalent rut model an be onstruted n Fg In ths model, the leakages ndutors are used to mode the effetve flter ndutors. The leakage ndutane value equals to the effetve flter ndutane value. >> < M M Fg. 4.3 Crut Model 75

92 dt d dt d dt d v dt d dt d dt d v m e m e = = (45 ) In these equatons, ( ) k k M M 4 4 = = (46 ) m k k M M = = (47 ) = e e m m m m v v dt d dt d (48 ) We an see from these equatons that the effetve flter ndutane value s ontrollable for the Y-shape onneton. Beause the effetve ndutane value s adjusted by the ar gap length and the enter leg wndng smultanety, the adjustable range s large. For the two wndng oupled ndutor struture shown n [76], the ndutane value s hanged through adjustng the ar gap length only. So, the adjustable range and the effetve value are small. 4.. Crut Analyss There are four workng modes for ths Y-shape oupled ndutor struture when the duty yle for eah ndutor wndng s less than.5. 76

93 Mode : [ t,t ] In ths mode, the swth S s off and S s on. Transformer S S Fg. 4.4 Mode Crut In ths mode: v and e = Vn V v e V =. d dt m = V V n (49) m d dt = m m V n V (5 ) d dt ( V V ) = n (5 ) For eah wndng, the urrent slope s less than that n the dsrete urrent doubler struture. From ths pont, the oupled ndutor struture s helpful to derease the urrent rpple n eah wndng. At the same tme, the output urrent rpple s also dereased. Mode : [ t,t ] 77

94 Transformer S S Fg. 4.5 Mode Crut In ths mode, the swth S s on and S s on, the rut s workng on free wheelng status. In ths tme perod: and v e = V v e V =. d dt = V (5 ) d dt = V (53 ) d dt = V (54 ) Mode 3: [ t,t 3 ] 78

95 Fg. 4.6 Mode 3 Crut In ths tme perod: v e V = and ve = Vn V. d dt = m m V n V (55 ) d dt = m V m n V (56 ) d dt ( V V ) = n (57 ) Mode 4: [ t 3,t 4 ] Ths mode s same as the mode, the swth S s on and S s on. The whole rut s workng on free wheelng status. The urrent waveform s shown Fg

96 I o I o I o Fg. 4.7 Crut waveforms For the unoupled ase, the urrent rpple for eah ndutor s: V I unoupled _ = ( D) T ( 58 ) The urrent rpple for total output s: V I unoupled _ out = ( D) T ( 59 ) For the oupled ase, from the equatons derved before, the urrent rpple for eah wndng s: 8

97 T D V D T D V V I m m n m m oupled = = _ ( 6 ) The urrent rpple for total output s: ( ) ( ) T D V T D V I out oupled = =.5 _ ( 6 ) So, the total output urrent rpple s determned by the effetve ndutane value The larger effetve ndutane value, the smaller urrent rpple.. If K s defned as the ouplng oeffent parameter and: K m m = ( 6 ) In ths way the nfluene of the ouplng oeffent on the urrent-doubler parameters an be onvenently analyzed wthout affetng the value of ndutane. If the urrent rpple rato s defned as: K K D D D D I I P m m unoupled oupled = = = ( 63) 8

98 Then the eah ndutor urrent rpple vs. ouplng oeffent s shown n Fg Gven dfferent duty yle, when the ouplng oeffent s nreased, the urrent rpple s dereased. Espeally when duty yle equals.5, the urrent rpple wll be near zero. The strong ouplng means small urrent rpple. Fg. 4.8 Current rpples vs. ouplng oeffent 4..3 Analyss and Comparson In ths seton, the performane of the rut wth the dsrete urrent doubler struture s ompared wth onventonal two oupled ndutors and Y-shape oupled ndutors rut. To 8

99 make the omparson far, the foot prnt area and the effetve flter ndutor value same for dfferent struture. are kept When the ore sze s equal, adjustng the oupled ndutors ouplng oeffent values an get the bggest effetve flter ndutane value. In ths workng ondton, the oupled ndutor strutures have lest output urrent rpple. The Y-shape oupled struture has larger adjustable range for the effetve flter ndutane value. The strutures not only derease the power loss, but also derease the output flter apator value. In other words, the Y-shape struture an nrease the output ndutane value and derease the output apatane value further. When the effetve ndutane value of ouplng-ndutor struture s equal, then the total output urrent rpple are same. But the urrent rpple for eah ndutor wndng s deded by the ouplng oeffent K. Strong ouplng means small urrent rpple. When K value s near, eah oupled ndutor urrent rpple s just half of the dsrete struture. Furthermore, ths deduton s extended to the MOSFET rut and dereases the swthng losses. For Y-shape oupled ndutor, beause the effetve ndutane value s larger than other ases, the urrent rpple wll be dereased further. 83

100 Table 4. Comparson of Dfferent Strutures Topology Current Doubler Coupled Indutor Y-Shape Struture umber 3 Core umber -Effetve Indutane m Average Current Current pple ( k ) ( k ) 4k I v v ( D) T α I m m D V D T v.5α α I m m D V D T Total pple ( D) T ( D ) T ( D ) T v I v ( D) T 4..4 Smualton esults and Experment Verfaton The Y-shape struture s appled to a half brdge DC/DC onverter. One par of EE ore s used n the rut. The ore sze s E8 and the ore materal s 3F3. The ore was mlled n the enter leg to keep from saturaton and get the sutable ndutane value. Through adjustng the ar gap length and enter leg wndng turn number, the effetve flter ndutane value an be hanged. Steady state asks for hgh ndutane value and less urrent rpple and the transent response asks for small ndutane value. There must have some trade off between the steady 84

101 state and transent state. To keep reasonable transent performane, the enter leg wndng turn number s. The rut operaton ondton s Fs = KHz, Vn = 36 V, Vout = 3.3 V and the effetve ndutane value = 5 nh. Due to the nverse oupled out leg wndng, the DC flux n the outer leg s partally anelled by the two orrespondng wndngs. If the effetve ndutane values are same, the overall DC flux n the oupled ndutor struture s almost same as those n the nonoupled ore struture. So, when we mlled the ore enter leg, the nonoupled ndutor measurement method s adopted. The eletral rut smulaton result s shown n the Fg The output urrent rpple s almost the double of the eah oupled ndutor urrent rpple. The pture of the hardware s shown n Fg. 4.. Wth the nverse oupled ndutors, the urrent rpple n eah ndutor wndng s almost half of the total output urrent rpple. The expermental results verfed the analyss and the smulaton results. Fg. 4.9 Indutor urrent waveform smulaton results 85

102 In ths stuaton, the ouplng oeffent s about.9. Fg. 4. Experment rut The expermental result s showng n Fg. 4.. Fg. 4. Indutor urrent expermental result 86

103 The smulaton and expermental results learly show that strong ouplng an substantally redue the rpple n the steady-state waveform. Fg. 4. Prmary urrent waveform of dsrete struture Fg. 4.3 Prmary urrent waveform of oupled ndutors struture The ndutor wndng urrent waveforms of the oupled ndutor struture and dsrete struture are showng n Fg. 4. and Fg Under the same rut spefaton and keepng same effetve ndutor value and same footprnt area for magnet omponent, the oupled ndutor struture an derease prmary urrent rpple. 87

104 Ths rut an be used as unt and parallel several together for multphase hgh urrent applaton. The fgure was shown n Fg Beause of the large flter ndutane value, the Y-shape an derease the phase number and omponents number. So, for the whole rut, the ost wll be dereased. Transformer S S 4 S4 3 S3 Fg. 4.4 Four phase rut 4. Integrated Transformer and Indutors As an alternatve retfaton rut, the urrent doubler retfer has been proven to be sutable for hgh urrent DC/DC onverters. The applatons for ths knd of onverter nlude hgh-nput Voltage egulator Modules (VMs), both load-end onverters and front-end modules 88

105 of Dstrbuted Power Systems (DPS), and so on. Compared wth the onventonal enter-tap retfer, the urrent doubler retfer smplfes the struture of the solaton transformer, and uts the seondary wndng onduton loss n half. The nherent dsadvantage of ths topology s the three magnet omponents thus nreasng the ost and sze of the system as well as ausng termnaton power loss. By ntegratng all the magnet omponents nto one sngle ore, several ntegrated magnet solutons have been proposed to solve the problems above. Unlke onventonal magnet ntegraton whh only fouses on ore ntegraton, both ore and wndng ntegraton are realzed n these desgns. For hgh urrent applatons, ths wndng ntegraton s beomng more mportant beause of lower termnaton loss and lower onduton loss. In ths seton, four ntegrated magnets strutures for urrent-doubler retfer are nvestgated and ompared thoroughly. Hgh order relutane model of eah ntegrated magnets struture s onstruted and the qualty mpedane matrx s derved. Wth the same ore shape, same wndng arrangement, same rut onnetons and same foot prnt area, numeral FEA smulaton results are ompared and mpled to the eletral rut analyss. After unfed eletral rut modes are proposed, the omparson of dfferent strutures s more reasonable. The expermental results verfy the new ore shape desgn. Due to the less rut onnetons and urrent rpple anellaton, the effeny of the ntegrated struture s hgh. 89

106 4.. Comparson of Dfferent Magnets Struture 4... Dfferent Integrated Magnets Strutures As explaned before, power ndutors and transformers are the key omponents to dede the sze, weght and power densty n low voltage, hgh urrent DC-DC onverter. Espeally for hgh urrent applatons, the wndng ntegraton s beomng more mportant beause of lower termnaton loss and lower onduton loss. IM desgns typally use soft-ferrte E-I or E-E ore strutures. The man dfferene s only n wndng arrangements on the three legs of the ore struture. For the ore leg where ndutor wndngs are stuated, an ar gap s added to obtan the desred ndutane values. Effetve ore leg areas must be hosen n aord wth the maxmum flux levels, whh wll our as a result of onverter operaton, to prevent saturaton of any leg under maxmum loadng ondtons of the system. The use of prnted wrng methods for the wndngs of an IM an lower the heght profle of the overall pakage of the magnet omponent. Ths planar magnets omponent an derease the ost and s easy assembly. In addton, the magnet features and eletr parameters are repeatable. Several ntegrated magnes ruts have been nvestgated to derease the volume and nrease the power effeny [79] [8]. Four dfferent ntegrated magnets strutures are shown n Fg In struture, the transformer and ndutor wndngs an be seleted ndependently. The transformer and the ndutors are deoupled from eah other. Ths provdes freedom n the desgn and allows hgher ndutane to be aheved. But, the separated transformer and ndutor wndngs mply the use of 9

107 more opper as well as hgher onduton and nteronneton losses. In struture [8], the prmary and seond wndngs of transformer are loated on the dfferent legs. So, the leakage ndutane of the transformer s hgh. Ths struture has lmted flter ndutane value. Struture 3 [8] has lower leakage ndutane than struture. The transformer prmary wndng s onstruted by two wndngs onneted n seres. Ths struture an be onsdered as the two transformers onneted n seres. Beause the leakage ndutor works as the flter ndutor, ths struture also has lmted flter ndutane. Compared wth other strutures, the orthogonal wndng struture 4 s proposed [79] to nrease the flter ndutane value. There s an extra orthogonal wndng loated on the enter leg. The sum of the leakage ndutor and the extra wndng ndutor works as the output flter ndutor for the onverter. For ths struture, the orthogonal wndng struture s not normal. So the fabraton omplexty s nreased. Beause the extra wndng nreases the extra opper, the onduton loss s also nreased when the urrent rpples are same. 9

108 Struture Struture Struture 3 Struture 4 Fg. 4.5 Dfferent ntegrated magnets strutures 4... Equvalent elutane Model Comparson o matter whh knd ntegrated magnets omponent, the equvalent eletral rut of magnet omponent s needed to enable mproved analyss of rut performane. There are two man methods that an derve the equvalent eletral rut from the magnet deve physal propertes: Gyrator-Capator method and elutane-dualty method. 9

109 Gyrator-Capator s one wdely used method to defne magnet omponent equvalent eletral rut. It s easer to relate eletral performane bak to the magnet elements. A major advantage of Gyrator-Capator s that t does not requre the magnet rut be "planar", as the relutane dualty method does. However, the equvalent eletral rut derved from ths method looks nothng lke a lassal ndutor or transformer. Indutve energy storage elements are replaed by apators and transformer wndngs are replaed by gyrators. An equvalent rut wth apators and gyrators replang ndutve elements whose layout losely resembles the struture of the magnet deve. Ths faltates nsght nto the physal eletral relatonshp, but severely dmnshes nsght nto rut analyss [8]. The onventonal relutane-dualty method defnes an eletral rut whose magnet elements nlude leakage, magnetzng ndutanes and transformer wndngs, et. Ths faltates ntutve and nsghtful rut analyss, but t does not resemble the magnet deve physal struture, dmnshng nsght nto the physal-eletral relatonshp. Magnet ruts and eletral ruts are n a dfferent realm, and the duals are truly equvalent. In the ntegrated magnets omparson and analyss, the magnetzng ndutane, leakage ndutane and effetve wndngs are very mportant for the rut performane. So, the onventonal elutane-dualty method s adopted here. For these four dfferent IM strutures, the smple relutane model s shown n Fg

110 Struture Struture Struture3 Struture 4 Fg. 4.6 Dfferent relutane model strutures There are four workng modes for urrent doubler retfer and t was shown n Fg In these relutane models, s the out leg relutane and s the enter leg relutane; s the p prmary wndng turns number and s the seondary wndng turns number; φ and φ are s flux n out legs and φ s the flux n the enter leg. 94

111 Mode Mode Mode3 Mode 4 Fg. 4.7 Current doubler workng modes For struture : The flux n eah ore leg s shown: ( ) = s s p p φ (64) ( ) = s s p p φ (65 ) 95

112 ( ) ( ) ( ) s s p p = φ (66 ) The prmary and seondary wndng voltage equatons are n the followng: dt d dt d dt d dt d V s p p s p p p p p n = = φ (67 ) dt d dt d dt d dt d dt d V s s s p P s P s = = φ φ (68 ) dt d dt d dt d dt d dt d V s s s p P s P s = = φ φ (69 ) Aordng to the workng modes and voltage-seond balane, the voltage rato MD s: p s D MD = (7 ) The effetve flter ndutane value s derved as: ( ) 3 s s = (7 ) The magnetzng ndutane value as: p m =.5 (7 ) 96

113 The mutual ndutane value between the two flter ndutors s: s p p M = (73 ) Usng the same analyss method, the qualty parameters for dfferent IM strutures are shown n Table 4.. Table 4. Four IM strutures parameters omparson Turn rato m s p ( ) 3 s s p.5 s p s p.5 3 s p s p 4 s p s s 4 4 p From the table, we an see that the struture and struture are smlar to eah other. Struture has less turn rato and less effetve ndutane value. Struture 3 and 4 are smlar to eah other, exept that struture 4 has larger effetve ndutane value. It s easy to understand that the less the ar gap length, the larger the magnetzng ndutane value. To obtan a better understandng of the magnet operatons of the IM strutures, equvalent rut models are developed, usng the hgh order relutane-to-ndutane modelng method desrbed n followng. These models an be used to study the dynams and magnet 97

114 nteratons between the transformer and ndutve setons of an ntegrated magnets omponent. The methodology to onstrut the dual rut from the orgnal physal struture onssts of the followng proedure:. Construt the magnet rut from the orgnal physal struture.. Put a referene dot nsde eah loop of the magnet rut and a referene dot outsde. These ponts beome the nodes of the eletr ruts. 3. Draw a lne between any two nodes of the magnet rut to pass through one and only one rut element. epeat the same proedure for eah element of the magnet ruts. 4. Sale the dual magnet rut model by the number of turns on the prmary. 5. eplae relutanes wth ndutanes and use deal transformer symbols where approprate. The physal struture of ntegrated magnets struture s shown n Fg. 4.8 (a). Then, the hgh order relutane mode s onstruted n Fg. 4.8 (b). Usng the methodology that we have ntrodued before, the equvalent rut model s presented n Fg. 4.8 (). The means the leakage relutane to the ar around the ore out leg; ps s the leakage relutane between the prmary wndngs and the seondary wndngs; s the seondary wndng leakage relutane; m s the ore relutane for the top and bottom; s the enter leg relutane. 98

115 S S P P (a) Physal Model (b) Hgh Order elutane Model () Equvalent Crut Model Fg. 4.8 IM struture model dervatons Through the relutane-dualty method, we sale the dual magnet rut model by the number of turns on the prmary. Eah physal wndng s modeled as a voltage soure. In the equvalent hgh order rut model, all the parameters are refleted to the prmary and they are dretly related to ther physal struture. From the rut, the mpedane matrx an be extrated. 99

116 ( ) ( ) ( ) ( ) ps ps ps ps ps ps v v v v p p ps p = (74) Through the same method, the physal struture of ntegrated magnets struture s obtaned and shown n Fg. 4.9 (a). The hgh order relutane mode s onstruted n Fg. 4.9 (b). Usng the methodology that we have ntrodued before, the equvalent rut model s presented n Fg. 4.9 (). From the rut, the mpedane matrx an be extrated.

117 P P (a) Physal model (b) Hgh order relutane model Vp V*p/ V*p/ () Equvalent Crut Model Fg. 4.9 IM struture model dervatons v v v p p p ( ) = (75)

118 The physal struture of ntegrated magnets struture 3 s shown n Fg. 4. (a). The hgh order relutane mode s onstruted n Fg. 4. (b). The equvalent rut model s llustrated n Fg. 4. (). From the rut, the mpedane matrx s derved. P P P P (a) Physal model (b) Hgh order relutane model () Equvalent rut model Fg. 4. IM struture 3 model dervatons

119 Z = ps ps ps ps ( ) m m m m m ps ps m ps ps mm m ps ( ) m m m ps (76) The physal struture of ntegrated magnets struture 4 s shown n Fg. 4. (a). The hgh order relutane mode s onstruted n Fg. 4. (b). The equvalent rut model s gven n Fg. 4. (). From the rut, the mpedane matrx s shown. 3

120 C C P P P P (a) Physal model (b) Hgh order relutane model / VC*p/C / ps / C / ps Vp Vp V*p/ m m V*p/ () Equvalent rut model Fg. 4. IM struture 4 model dervatons 4

121 ps ps ps ps ps ( ) m m m m ps m m m m ps ps m ps m ( m ) m m m m m ps m m m m m m (77) The order of the matrx s deded by the wndng number. Eah wndng s molded as a voltage soure. Even though the prmary wndng s onstruted by two sub wndngs, t s stll onsdered as one soure beause the two sub-wndngs are onneted n seres and the urrents flowng through them are always same. Compared wth the smple relutane model, the hgh order relutane model has an aurate alulaton method for the leakage ndutane, properly predts a small leakage between adjaent wndngs and eah leakage ndutane s dretly related to the spae between the wndngs. The models predt there s more devaton from deal transformer turn rato as the wndngs move further from the prmary wndng beause the urrent has to flow through more leakage ndutane. 5

122 4...3 CAD Methodology and Unfed Crut Model The smple relutane model an only gve some qualty omparsons. When there s ar gap, the aurate parast value s dffult to obtan. Even though the hgh order relutane model s adopted, t s sutable for qualty analyss nstead of quantty analyss. At the same tme, the nterleaved wndng strategy and non-nterleaved strategy have the same relutane model. The magnetzng and leakage ndutanes (the ouplng oeffents) of both ases are dfferent. Sne these values are very senstve to the wndng strategy, ther alulatons are very dffult usng analytal expressons. To mprove or enhane the rut performane, the magntude of relevant parast magnet elements s needed and the quantty omparson s needed. The FEA numeral analyss s adopted to do the smulaton. Double -D s a methodology used to alulate the energy and losses n 3-D strutures (EE and torods), takng nto aount the 3-D effets and usng -D FEA solvers. Ths s shown n Fg

123 Fg. 4. Double-D methodology The double D smulaton omts the orner effets and t s sutable for the E ore. When the frequeny s nreased and the raton of the skn depth and ooper thkness s dereased, the auray of the D smulaton dereases. The smulaton result s only aurate durng reasonable range. Otherwse, the 3D smulaton s needed. From the smulaton results, the mpedane matrxes are extrated. The order of the mpedane matrx s deded by the wndng number. If the total wndng of the IM struture s n, the matrx wll be the n X n matrx. In ths stuaton, t s hard to ompare the parameters of the dfferent struture. To make a reasonable omparson, all the models have to been hanged to one 3 port eletral net. The unfed format s onstruted n Fg. 4.3 (a). 7

124 (a) Physal struture (b) Pspe unfed rut model Fg. 4.3 Unfed 3 ports eletral rut All the mpedane matrx and ouplng oeffent matrx an be hanged to 3 by 3 matrx. The Pspe smulaton model s onstruted based on the 3 by 3 matrx. The H blok s used to onstrut 8

125 the mutual resstors. K lnear s used to onstrut the ouplng oeffent. When the unfed model s putted nto the model, t s easy to analyze and to mprove the performane of the rut. It has been explaned before that the magnets omponent parameters are deded by the physal dmenson of the ore, wndng struture and termnal onnetons. It does not make sense to ompare the strutures f the omparson ondtons are not fxed. The dfferent ntegrated strutures may have same performane due to the dfferent ondtons. So, to make the results more reasonable, we set followng ondtons: same ore shape (E8), same ore materal (3F3), same foot prnt (nludng ooper area), and same termnal onnetons. For these spefed desgns, we ondut the smulatons and ompare them wth eah other. The FEA results for ntegrated strutures are as follows: Table 4.3 IM Struture Impedane Matrx esstor (ohm) P Indutor esstor Indutor esstor (H) (ohm) (H) (ohm) Indutor (H) P P P

126 Table 4.4 IM struture mpedane matrx esstor (ohm) P Indutor esstor Indutor esstor (H) (ohm) (H) (ohm) Indutor (H) P P P Table 4.5 IM Struture 3 Impedane Matrx esstor (ohm) P Indutor esstor Indutor esstor (H) (ohm) (H) (ohm) Indutor (H) P P P

127 Table 4.6 IM Struture 4 Impedane Matrx esstor (ohm) P Indutor esstor Indutor esstor (H) (ohm) (H) (ohm) Indutor (H) P P P In eah table above, the frst matrx s the resstane and ndutane value and the seond matrx s the ouplng oeffent. From the matrx, we an see that strutures and are almost the same. Struture 3 and 4 are smlar. In the frst two strutures, the output two ndutors are almost deoupled. For the urrent doubler applaton, the strong ouplng between these two ndutors an derease the urrent rpple. The mpedane matrx learly shows that struture 3 has the least power loss (least resstor value). The preondton for omparson s to keep the total footprnt area equal for eah struture. At the same tme, the effetve flter ndutane values are also equal. For strutures and, the two ndutors are almost deoupled from eah other and the self ndutane value equals the flter ndutane value. The ouplng oeffent value s near zero. But for strutures 3 and 4, there are strong ouplng between the two ndutors. The oupled ndutors an be molded as an

128 deal nverse transformer and the effetve flter ndutor value an be modeled as the leakage ndutane value of ths transformer. For strutures and, the prmary and the seondary wndngs have less ouplng ompared wth strutures 3 and 4. So the leakage ndutane values for them are large. But, even the other two strutures are strongly oupled; the ouplng oeffent values are stll less than the dsrete magnets struture. The one feature of ntegrated magnets s the hgher leakage ndutane value ompared wth the dsrete struture. It should be mentoned that the ndutor resstane value for the struture 4 s larger than other three. Ths omes from extra wndng loated on the enter leg Experment Verfaton Through the proedure desrbed above, dsrete magnets urrent doubler struture and four dfferent ntegrated magnets strutures are analyzed and ompared wth eah other. To verfy the analyss, a half brdge onverter s onstruted. Eah dfferent magnets struture s added to the same power rut. Through the experments, the nput voltage and the load urrent are kept equal for eah dfferent struture. At the same tme, the effetve ndutane values for eah IM strutures are equal to the dsrete ndutane value. The footprnt areas of these strutures are the same. These entre requrements are gong to derease the nfluene omng from the semondutor omponents and rut onnetons. The experment s tryng to make the man effeny dfferene between the rut effeny to represent the dfferent power loss between dfferent magnets omponents. The expermental prototype s shown n Fg. 4.4.

129 (a) Experment power rut (b) Dfferent magnets struture Fg. 4.4 Experment prototypes The expermental waveforms are shown n Fg

130 (a) Dsrete struture output urrent (b) Integrated magnets struture output urrent () Integrated magnets struture output urrent (d) Integrated magnets struture 3 output urrent (e) Integrated magnets struture 4 output urrent Fg. 4.5 Output urrent waveforms for dfferent magnets struture 4

131 For the dsrete struture, beause the ar gap length for the two dsrete ndutors s adjusted separately, t s easy to get unequal ndutane value. Ths phenomenon happens to strutures and. Beause for these two strutures, the ar gaps are loated on the two out legs and the ore parts onneton s loated on the enter leg. These strutures are mehanal unstable n prate. Even when the ar gap lengths are same, the shake durng the experment wll make the ndutane value unbalane. For other strutures, beause the ar gap s loated on the enter leg, the results of strutures 3 and 4 are symmetry. Compared wth other strutures, struture 4 really has hgh ndutane value resultng from the extra flter wndng. But, the extra wndng also brngs the extra opper loss. The effeny omparson urves are shown n Fg From the effeny urve of dfferent strutures, obvously, the dsrete struture has the least effeny for lght load. The effenes for other four ntegrated magnet strutures are almost same. The small dfferene s manly beause the magnets omponents resstor value s small ompared wth the whole rut swthng loss, semondutor onduton loss and the rut onduton loss. Compared wth the dsrete struture, the ntegrated magnets strutures have larger leakage ndutane than the dsrete magnets struture, beause there are ar gaps n the ore. When the load urrent s small, the advantage of IM struture s more obvous. If the load urrent s onstantly nreased, the leakage ndutane effet wll be nreased and the dfferene between the IM strutures and dsrete struture wll be dereased. 5

132 Effeny Comparson Dsrete Struture IM Struture IM Struture IM Struture 3 IM Struture 4 Effeny Output Current (A) (a) Dsrete struture and IM strutures effeny omparson 8 IM Comparson Struture Struture Struture 3 Struture 4 Effeny oad Current (b) IM strutures effeny omparson Fg. 4.6 Dfferent strutures effeny omparson 4.. Half Brdge Integrated Magnets Desgn desgn: The spefaton of the ntegrated magnets desgn s same as that of the dsrete magnets 6

133 Sze:.9 n x.3 n x. n Input: 36~75V Output: oad Slew ate: Devaton: Effeny: Swthhng frequeny: I/O: Math Isolaton:.V@3A 5 amps/us, ST us max 3% wth zero external apatane full load 4kHz Surfae-Mount, onfguraton not spefed Bas Based on the omparson results of the prevous seton, the IM struture 3 s appled to the rut desgn Desgn Proedures The IM struture and relutane model are shown n Fg. 4.5 and Fg. 4.6 separately. The desgn proedure s as follows:. Calulatng the effetve flter ndutane value; The effetve flter ndutane value s expressed as: (.5 D) V = ( 78 ) I. Dedng the ore seton area; In ths desgn, the ore struture s symmetry and the out leg areas are same. So the mnmal out leg seton area an be wrtten as: 7

134 A V D T I D T s s s s s = A ( 79 ) Bmax V The mnmal enter leg seton area s: A V s ( ) (.5 D) s ( ) B max T s I ( 8 ) When the ore materal s hosen, the maxmum flux densty value wll be determnated. Then, the ore seton area wll be deded. 3. Seletng heght; In ths desgn, the heght s deded by the low profle rut requrements. 4. Seletng wndow area; The ore wndow area should be bg enough to aommodate all the wndngs and avod the thermal ssue. In the followng dsusson, two parameters are defned: K r : wndng fllng fator, pratally,.-.4; J : maxmum allowable urrent densty, A / m, pratally, 5- MegA / m, dependng max on the type of wndngs. Then, for eah wndow, the mnmal requred wndow area s estmated to be: I p s A max D D W K J D D D r ( 8 ) mn max max s 5. Calulatng the ar gap length; 8

135 When the ore dmensons are deded, the ar gap length an be alulated from the equatons: = s ( 8 ) H g = µ A r µ µ g A ( 83 ) 6. CAD methodology s adopted whh s ntrodued n seton 4... The ore dmenson parameters are verfed n the system smulaton and the value an be adjusted to optmze the desgn Proposed Core Shape and oss Comparson The proposed magnet ore optmzaton nludes two parts: ore shape optmzaton and ore volume optmzaton. ormally, the E ore s sutable for the ntegrated magnets desgn. To derease the opper loss further, the new ore shape s proposed. The onept omes from the bas dea: for the same area, the rle shape has least permeter. So, hangng shape of out legs an derease the opper loss espeally for the hgh urrent applatons. The proposed new ore shape s shown n Fg

136 (a) E Core and the proposed ustomer ore (b) Dmensons of proposed ustomer ore Fg. 4.7 Proposed new ore shape Beause more opper areas are not overed by the magnets ore, the leakage ndutane value of new shape s nreased a lttle. ormally, the leakage ndutane value s not as hgh as our transtonal thought (5%). Most of the tme, t s less than % or 3% of magnetzng ndutane value. So, the lttle nreasng of leakage ndutane value s not an ssue at all. On the other hand, we are more about the absolute value of the leakage ndutane value. If the

137 absolute value s under ontrol, the power stage wll stll work well. The 3D FEA model s onstruted and smulated. The results are shown n Fg From the smulaton results, the average flux densty dstrbutons satsfy the desgn requrements. But at the edge of the ore, the flux densty s hgh. So, some angles should be added to the vertal shape. Fg. 4.8 Maxwell 3D smulaton result For the passve omponents, the -D model s very tme effent and an gve an aeptable result as long as the ondtons for the -D approxmaton an be well satsfed. In planar magnets, the wndng ondutor thkness s always less than or equal to the skn depth of the ondutor at the swthng fundamental frequeny, whle t s also muh smaller than the ondutor wdth. The wndngs are also always plaed far away from the ar gap. Ths mples that the frngng effets and edge effets an be negleted n ths struture. The -D wndng loss

138 model s used n the volume optmzaton. The proedure s same as the one ntrodued n seton The wndng arrangement of the ntegrated magnets s as follows: Fg. 4.9 Interleaved wndng arrangement The nterleavng wndng arrangement s seleted and the struture s shown n Fg Fg. 4.3 Interleaved wndng struture In ths desgn, the DC resstor value omes from the smple alulaton. The AC resstor value omes from the Maxwell 3D smulaton. The result nludes all the parast effet, ross talkng effet and so on. So, the result s more aurate. Table 4.7 s the power loss of dfferent struture. From the alulated results, we an see that, f the ustomer ore shape s adopted, the power loss an be dereased a lot.

139 Table 4.7 Power oss of Dfferent Components Separate ndutors Separate transformer Integrated ndutor Integrated ndutor and transformer ore EQ3 EQ3 E4.5 E8 Custom Core Core loss (w) Cope loss (w) Total loss (w) ength (mm) x Wdth (mm) x Heght (mm) Smulaton esults In the whole PCB board, the footprnt area of ntegrated magnets s less than that of the dsrete magnets struture. The footprnt area of the ntegrated magnets s 7% of the dsrete magnets struture. From the Maxwell 3D smulaton, the 3x3 matrx s extrated: Table 4.8 Parameter Matrx P esstor (ohm) Indutor (H) esstor (ohm) Indutor (H) esstor (ohm) Indutor (H) P.794.9E E E-4 9.5E E E-3 9.E-7 5.7E-4-7.6E E-4 9.5E-6 5.7E-4-7.6E-7 3.5E-3 9.3E-7 Through the same method as the dsrete magnets, the Pspe model s onstruted: 3

140 - 7 K K9 K_near COUPIG = uH H6 H - - H7.9uH.4 K K7 K_near COUPIG = -.84 H H4 H -H5 H H8 - H H9-9 5 H K K8.9uH.4 K_near COUPIG = -.9 Fg. 4.3 Integrated magnets Pspe model Puttng the ntegrated magnets model nto the whole rut, the smulaton result s shown the Fg. 4.3 and Fg Fg. 4.3 Seondary sde urrent waveforms Fg Prmary sde urrent waveform 4

141 The omparson between the dsrete struture and IM struture s shown n Table 4.9. Table 4.9 Dsrete struture vs. ntegrated struture Dsrete Struture Integrated Struture Footprnt Area mm*6mm.8mm*9.7mm Effetve Indutane Value 7nH 4nH Prmary esstor AC:.374 ohm DC:.6 ohm AC:.79 ohm DC: 7.5m ohm Indutor esstor AC: 5.68m ohm DC:.375m ohm AC: 4.54m ohm DC:.4m ohm Total wndng number 4 3 Turn rato 6 over over Wndng Strategy Smple Complex The omparson ondtons are same footprnt area and same output urrent rpple. Beause the ntegrated struture has less effetve ndutane value, the transent response wll be better. If the effetve ndutane values are same, the ntegrated struture wll have smaller urrent rpple. The effeny wll also be hgher. The man reason for the dfferent performane omes from the dfferent ouplng oeffent. Ths pont s shown very learly from the followng parameter matrx. 5

142 Fg Parameter Matrx The resstor value of the dsrete struture s bgger than that of ntegrated magnets struture. Ths means hgh prmary sde power loss. The ntegrated magnets struture has strong ouplng n the seondary sde. The seondary sde an be treated as two oupled ndutor struture. From the analyss n seton 4..3, ths an derease the seondary urrent rpple. 6

143 Fg Seondary sde urrent waveforms Fg Prmary sde urrent waveforms 7

144 The man omponents power loss s shown n Table 4.. The total power loss s almost same. If the ndutor value of ntegrated magnets an be nreased further, the effeny of the ntegrated magnets struture wll be nreased. Table 4. Power loss of dsrete struture vs. ntegrated struture Experment Verfaton Fg Integrated magnets PCB board The prmary urrent waveform and drver sgnal are shown n the Fg

145 Fg Expermental waveforms vs. smulaton waveform Power oss of 48V Input Smulaton esult Experment esult Effeny oad Current Fg Power loss vs. load In Fg. 4.39, the power loss s shown when the rut works under 48V nput. 9

146 4.3 Integrated Magnets for Peak Current Mode Control As far as the ontrol method s onerned, the use of standard peak urrent-mode ontrol s preluded for half brdge retfer by low-frequeny stablty problems, whh show themselves through a drft of the nput apators mdpont voltage. Thus, voltage mode ontrol s generally used to ope wth the two pole transfer funton of the onverter. In ths ase, for ontnuous onduton mode (CCM) of operaton, a standard PID ontroller s adopted to aheve reasonable ontrol loop bandwdth, wth the drawbak of an nrease of hgh frequeny nose oupled wth the ontrol rutry and, above all, wth the strong dependeny of the rossover frequeny on output apator ES. Compared wth the voltage mode ontrol, peak urrent-mode ontrol s more attratve due to the followng advantages: nherent over load lmtaton, hgher loop bandwdth ahevable wth respet to voltage mode ontrol and lower audo suseptblty. Due to the above mentoned nstablty problem, some provsons must be taken to mplement the peak urrent ontrol for half brdge topology Half Brdge Converter Current Mode Control Issue Current mode ontrol uses the error between the desred and atual output voltage to ontrol the ndutor urrent. As t s shown n Fg. 4.4, output urrent sgnal s sensed and transformed to orrespondng voltage sgnal I mp. Ths sgnal s ompared wth the assoated referene Iref, whh reflets the error between output voltage and ts referene, to gve the duty ontrol sgnals for the power deves. When I mp 3 nreases and s equal to ts referene, the

147 orrespondng power deves are turned off. The output voltage s ontrolled ndretly by the aton of ontrollng ndutor urrent. Ths feature provdes very fast dynam response as ompared wth onventonal voltage mode ontrol. At the same tme, urrent ontrol offers the yle by yle urrent lmtng. Vref Voutd PI Iref Imp PWM PowerStage H I Vout H v Fg. 4.4 Current mode ontrol onept rut Fg. 4.4 shows the nput stage of half-brdge onverter. When the voltages of the two nput apators are slghtly dfferent due to manufaturng and load varaton, the duty yle wll be dfferent for Fg. 4.4 (b) rut and Fg. 4.4 () rut. For example, when the Vn Vn, the duty for Q s greater than that of Q f Vn s smaller than Vn. As the result, the apator wth smaller voltage value dsharges more than the apator wth greater voltage value. The same dsharge ases our n the followng perods untl the duty reahes ts maxmum value. 3

148 Cn Q A C s V n B Cn Q (a) (b) () Fg. 4.4 Half-brdge voltage unbalane ssue 4.3. Voltage Balane Tehnque Changng the ontrol loop s a soluton to solve the voltage unbalane ssue. Unfortunately, t needs more omponents for ontrol desgn and ontrol loop s more omplated ompared wth other methods. 3

149 One voltage balane tehnque ss presented n [46]. The topology s shown n Fg But t an't work well sne the urrent sense rut ontans both load urrent and the magnetzng urrent for the auxlary wndng. Fg. 4.4 Half-brdge voltage balane rut Another mproved tehnque s ntrodued n [45] and t s shown n Fg The prnple s smlar to that shown n [46]. However, the magnetzng urrent of auxlary transformer wll not go through the prmary wndng of the man transformer of onverter. Therefore the urrent sense rut an presely reflet the load workng ondtons for urrent mode ontrol. Moreover, the presented tehnque provdes a degree of freedom for auxlary transformer desgn and mplementaton. Sne the seondary sde of auxlary transformer needs to overome the voltage drop aused by the seres dode, the voltage should be slghtly greater than that of the prmary voltage of man transformer. Wth the presented tehnque, ths requrement an be easly aheved by proper desgn of the turn rato for auxlary transformer. 33

150 Q D Cn A V n B Cn Q D Fg Improved half-brdge voltage balane rut Proposed Integrated Magnets Struture Here, one new ntegrated magnets struture based on the same onept s proposed. The rut struture s shown n the followng fgure: D Cn Q A : p s Q3 C Vn D C Cn Q B Q4 p s Fg Proposed half-brdge voltage balane IM rut 34

151 Fg elutane mode modes. The steady state operaton of the proposed half brdge rut nludes three bas workng Mode [, DT], Q s on and Q s off. Q3 s on and Q4 s off. D Cn Q A : p s Q3 C Vn D C Cn Q B Q4 p s Fg Proposed rut workng mode 35

152 Durng ths tme perod, the dode D s on and the node C voltage s settled near. The urrent dreton n the blue wndng s shown wth the red lne n the Fg Beause the turn rato of the two blue wndngs s :, the voltage between node A and node B s same as the voltage between the node B and node C. The voltage V (A, B) s the apator voltage Vn. The voltage V (B, C) s the apator voltage Vn. In ths stuaton, the two blue wndngs are workng as extra voltage soures to fore the two apator voltages to be equal. The voltage unbalane ssue s solved and the urrent mode ontrol an be appled to the half brdge rut. The relutane mode s gven n followng fgure: p*ip *Ip *Ip s*i p*ip Fg elutane mode The flux equatons are: ( ) ( ) ( ) ( ) ( ).5 p p s p p s p p p p s p p = = = φ φ φ (84) 36

153 From the Maxwell equatons, the frst seondary wndng voltage: V = V. (85) s The seond seondary wndng voltage: V = Vn V. (86) The output voltage s V.So the effetve transformer turn rato s: :. (87) p p s Mode [DT,.5T], Q s off and Q s off. Fg Proposed rut workng mode Durng ths tme perod, the Q and Q are off. The voltage between the node A and node B V (A, B) s zero. D and D are off. There s no urrent flow n blue wndngs and wndng p. The two seondary wndngs s work as the flter ndutor for the onverter. The two wndngs are oupled wth eah other and share the total load urrent. Ths s sutable for hgh urrent applatons. The relutane mode s: 37

154 Fg elutane mode The flux equatons are: ( ) ( ) ( ) ( ) ( ) ( ) ( ).5 p p s s p p s s p p s s = = = φ φ φ (88) From the Maxwell equatons, the effetve ndutane value for the oupled ndutors s: s = (89) Mode 3 [.5T, (.5D) T], Q s off and Q s on. Q3 s off and Q4 s on. 38

155 D Cn Q A : p s Q3 C Vn D C Cn Q B Q4 p s Fg. 4.5 Proposed rut workng mode 3 Smlar to the mode, the dode D s on and the node C voltage s hold near Vn. The urrent dreton n the blue wndng s shown wth the red lne n the Fg Beause the turn rato of the two blue wndngs s :, the voltage between node A and node B s same as the voltage between the node B and node C. The voltage V (A, B) s the apator voltage Vn. The voltage V (B, C) s the apator voltage Vn. The two blue wndngs are workng as extra voltage soures to fore the two apator voltage to be equal. The unbalaned apator voltage of urrent mode ontrol s solved. Beause the rut s symmetry, the relutane mode s smlar to the mode. Mode 4 [(.5D) T, T], Q s off and Q s off. It s same as the mod. Smlar to the mode, the two seondary wndngs work as two oupled ndutors. The relutane mode s same as the mode. 39

156 The Maxwell 3D smulaton has been fnshed for the ntegrated magnet omponent. The ouplng oeffent matrx s shown n Table 4.. In ths matrx, the and are the two seondary wndngs. The prmary s the two part of prmary wndng that s onneted n seres. The P and P are the wndngs that are wound on the enter leg. Table 4. Maxwell 3D Couplng Matrx Prmary P P Prmary P P For eah wndng, the self ouplng oeffent s. The mutual ouplng oeffent s deded by the wndng arrangement. The matrx shows that the wndngs on the enter leg are almost deoupled from the other wndngs. These two wndngs work lke a separate transformer. Ths transformer feeds forward to the prmary sde to apply the urrent mode ontrol. Beause t s deoupled from the other wndngs, the performane of the seondary sde does not nfluene the ontrol rut. In ths ntegrated magnet struture, blue wndng works as the solated voltage soure. It wll fore the two apator voltage to follow eah other and make the urrent mode ontrol possble. Strongly oupled ndutors an derease the urrent rpple. Therefore, we an hoose smaller ndutane value to mprove the transent response of the rut. 4

157 Smulaton results are shown n Fg The green urve and the yellow urve are the drver sgnal of the prmary MOSFET. The purple urve s the prmary urrent waveform. Fg. 4.5 s the prmary waveform of onventonal half brdge rut wth urrent mode ontrol when the unbalane problem exsts. Fg. 4.5 s the prmary waveform of proposed rut. The unbalane problem s solved. Fg. 4.5 Unbalaned waveforms for onventonal half brdge urrent mode ontrol Fg. 4.5 Balaned waveforms for proposed half brdge urrent mode ontrol 4