BOUNCER CIRCUIT FOR A 120 MW/370 KV SOLID STATE MODULATOR

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1 BOUNCER CIRCUIT FOR A 120 MW/370 KV SOLID STATE MODULATOR D. Gerber, J. Biela Laboraory for High Power Elecronic Sysems ETH Zurich, Physiksrasse 3, CH-8092 Zurich, Swizerland This maerial is posed here wih permission of he IEEE. Such permission of he IEEE does no in any way imply IEEE endorsemen of any of ETH Zürich s producs or services. Inernal or personal use of his maerial is permied. However, permission o reprin/republish his maerial for adverising or promoional purposes or for creaing new collecive works for resale or redisribuion mus be obained from he IEEE by wriing o By choosing o view his documen you agree o all provisions of he copyrigh laws proecing i.

2 BOUNCER CIRCUIT FOR A 120 MW/370 KV SOLID STATE MODULATOR D. Gerber, J. Biela Laboraory for High Power Elecronic Sysems ETH Zurich, Physiksrasse 3, CH-8092 Zurich, Swizerland Absrac In his paper, a bouncer circui for a 120 MW/370 kv modulaor is described. The bouncer circui is a wowinding inducor bouncer which reduces he oupu volage droop. The bouncer circui is described and invesigaed in deail. Also, he influence of componen olerances is invesigaed. Finally, he benefi of using a bouncer circui is shown by presening he same modulaor wihou and wih bouncer circui. The amoun of sored energy was reduced by a facor of 3.3 which reduces he overall sysem volume significanly. Load I. INTRODUCTION In applicaion areas as e.g. radar sysems, cancer reamen or paricle acceleraors, more and more pulse modulaors are based on modern solid sae modulaor sysems. These offer he advanages of a variable pulse lengh/ampliude and a higher life-ime of he semiconducor swiches, which decreases he sysem operaion coss. In addiion he solid sae modulaors offer he benefi ha hey can be urned off during he pulse in case of a failure as e.g. shor circui in order o proec he sysem and/or he load (e.g. a klysron). A he PSI in Swizerland a compac and cos effecive X-ray free elecron laser faciliy for a wavelengh range of 0.1 o 10 nm is designed [1] (SwissFEL). This laser requires a solid sae modulaor o drive he klysron. The parameers of his modulaor are shown in ab. I. TABLE I SPECIFICATIONS OF THE SOLID STATE MODULATOR FOR SWISSFEL DC link volage 3 kv Oupu Volage 370 kv Oupu Power 120 MW Repeiion Rae 100 Hz Maximum Droop <0.5 % Rise/Fall Time <1 µs Pulse Lengh 3 µs Repeiion Accuracy < 10 5 To achieve a volage droop of he pulse fla op of 0.5 %, he sored energy E Cin has o be 100 imes higher han he pulse energy E p if only a capacior is discharged. This huge amoun of sored energy is a disadvanage as more sored energy always implies a bigger sysem volume and more difficul error handling. The amoun of sored energy and herefore also he sysem volume can be subsanially reduced by bouncer circuis. However, wih he classical RL bouncer in series wih he pulse ransformer high addiional losses are generaed in he considered case up o a few kilowas. A more efficien and compac soluion is obained wih an LC bouncer, which uses an LC resonance for droop compensaion. C in C r S m S r Pulse Generaor Pulse Transformer Acive Rese Circui Bouncer Fig. 1. Schemaic of he modulaor based on a spli core ransformer wih 6 cores, an acive pre-magneizaion circui as well as a wo-winding inducor bouncer. There, an addiional swich is required for saring he oscillaion before he pulse. In [2] an improved wowinding inducor bouncer is presened, which enables o adap he bouncer operaing volage o he blocking volage of available semiconducors. In [2] also a design mehod and an opimizaion procedure for deermining he bouncer parameers is presened. However, in he opimizaion procedure only ideal componens wihou olerances are included and only a limiaion for he peak curren in he bouncer swich is considered. Limiaions of oher componens, as for example he volage raing of he bouncer capacior, are negleced. Therefore, in his paper an improved design and opimizaion procedure is presened and applied o he design of a bouncer circui for he 120 MW/370 kw solid sae modulaor. Firs, he basic schemaic of he modulaor wih bouncer is described in secion II. Aferwards, he bouncer circui is described in deail in secion III and he influence of he differen bouncer parameers on he oupu waveform is discussed in secion IV. Finally, a design mehod for he 120 MW/370 kw solid sae modulaor is presened. II. MODULATOR DESCRIPTION In he following, he hree basic modulaor componens generaor circui, pulse ransformer, bouncer circui as shown in fig. 1 are shorly discussed, because hey are

3 imporan for undersanding he derivaion of he bouncer model. V pri,1 N sek V pri,1 A. Pulse Generaor N pri, 1 N pri, 1 The pulse generaor circui consiss of an inpu capacior C in, which serves as energy sorage, a semiconducor swich S m and he pre-magneizaion circui (S r and C r ). The considered modulaor wih he specificaions in ab. I is based on 12 such generaor circuis, which are conneced o he primary windings of he pulse ransformer as discussed below. Since he volage V pri on he ransformer primary side is unipolar during he pulse, a pre-magneizaion circui is required o achieve a symmerical flux swing in he ransformer core and fully uilize he ransformer core. Furher deails on he operaion principle of he acive rese circui is given in [3]. B. Spli Core Pulse Transformer The pulse ransformer is a key elemen of he modulaor since i significanly influences he pulse shape and enables o adap he inpu volage o he blocking volage of semiconducor swiches. Addiionally, a single semiconducor swich is no capable o provide sufficien oupu power, so ha a series and/or a parallel connecion of swiches is necessary. In case of a series connecion, he balancing of he swich volage mus be guaraneed, and in case of a parallel connecion, he currens hrough he swiches mus be equally disribued. By uilizing a spli core/marix ransformer hese problems can be solved, since such a ransformer provides inheren curren balancing beween swiches conneced o windings on differen cores, e.g. N pri,1 and N pri,n (cf. fig. 3) as explained in [5]. The curren beween he pair of swiches conneced o he same core is no inherenly balanced. To achieve he curren balancing for hese pairs of swiches, an acive gae conrol can be used as described in [4]. C. Bouncer Circui The bouncer circui is basically an LC resonan circui, which could be eiher placed on he primary side or on he secondary side of he pulse ransformer. If he bouncer V Cr V Cc0 Fig. 2. V ou Oupu volage during one pulse cycle. S r S b S m V pri,n N pri, n N pri, n V sek V pri,n Fig. 3. Spli-core/marix-ransformer wih n cores, 2 primary windings per core and 2 parallel conneced secondary windings. is placed on he primary side, he curren hrough he swich of he bouncer mus be higher han he curren hrough he main swich during he pulse. On he oher hand, for a bouncer on he secondary side, he curren hrough he bouncer swich is lower han for a bouncer on he primary side, bu he swich volage is much higher. In boh cases, he design and he maximum volage droop, ha can be compensaed, could be significanly limied by he semiconducors which are available. For his reason in [2], a wo winding inducor bouncer is presened, where he bouncer inducance is replaced by a wo-winding inducor, which is basically a ransformer where he magneizing inducance is used as an inducor. A furher degree of freedom is available wih he urns raio in he bouncer design process, ha enables o use a single semiconducor swich for he bouncer because he bouncer operaing volage and curren can be adjused o available swiches. III. BOUNCER CIRCUIT OPERATION To explain he operaion of a bouncer circui, he marixransformer is firs simplified o a ransformer wih one core and one primary/secondary winding. Then, he componens of he generaor and he bouncer are ransformed o he secondary side as shown in fig. 4. The pre-magneizaion circui is no included in he model as i does no influence he basic operaion of he bouncer if he pre-magneizaion is properly designed. In he following, he resonan ransiion of he bouncer is spli ino hree ime inervals T 1 o T 3 refer also o he waveforms in fig. 5 and 6. a) T 1 : A he beginning of a pulse cycle, he wo capaciors C in and C c are charged o V Cin0 and V Cc0 and boh swiches are open. To iniialize he pulse cycle, he bouncer swich S b is closed, so ha capacior C c sars o discharge and he curren i Lc in he bouncer inducor L c rises. b) T 2 : A he beginning of T 2, swich S m is closed and he load curren sars o flow. The load curren has o flow hrough capacior C c because he curren in he bouncer inducance has o be coninuous. The volage across he bouncer capacior sill drops as long as he load curren is smaller han he curren hrough he bouncer inducance. Because he oupu pulse is cenered around T B 4, where T B is he period of one resonan ransiion of he bouncer circui, he volage of he bouncer capacior swings from a posiive volage o a negaive volage wih applying he same peak value. Since, v ou () = v Cin () + v Cc (), he volage across he load v ou () is reduced by he bouncer a he beginning of he pulse and raised a he end of he

4 i in V Cin0 C in i in S m S b v ou R l R l V Cin0 C in i Cc i Lc V Cc0 C c v Lc L c i Cc V Cc0 C c Modulaor wih Marix Transformer and Two-Winding Inducor Bouncer Circui wih simplified Marix Transformer Simplified Circui wihou Galvanic Insulaion, Values refered o Secondary Side Fig. 4. Simplificaion of he modulaor firs he marix ransformer is replaced a ransformer wih a single core and hen all componens are ransferred o he secondary side of he ransformer. pulse. This resuls in a more or less consan volage across he load during he pulse. c) T 3 : A he beginning of T 3, he main swich S m is opened, so ha he bouncer is a pure parallel LC resonan circui again. The bouncer capacior volage swings back o a volage close o is iniial volage a he beginning of he pulse. A his poin, swich S b is urned off o sop he oscillaion a he zero crossing of he bouncer curren. i Cc() = C c dv Cc () v Lc() = L di Lc () c v Lc() = v Cc() i Cc() = i Lc() (1a) wih he iniial condiions: v Cc(0) = V Cc0 i Lc(0) = 0 (1b) V Cc0 Tp/2 T B i Lc i Cc v Cc For he second ime inerval, boh swiches are closed. The iniial condiions are given by he soluion a = 1 of he differenial equaion sysem for he ime inerval T 1. T/4 T/2 0 T 1 1 T 2 2 T 3 Fig. 5. Volage and curren waveforms of bouncer circui shown in fig. 4. Bouncer Model: The bouncer circui can be described wih hree simple differenial equaion sysems, one for each of he hree ime inervals T 1 o T 3. During ime inerval T 1, swich S m is opened and swich S b is closed. Capacior C c is charged o V Cc0 and here is no curren flowing hrough he bouncer inducor L c. Therefore, he equaion sysem is: Droop wih Bouncer 3 Droop wihou Bouncer i Cc() = C c dv Cc () v Lc() = L c di Lc () i in() = v ou() R l i in() = C Cin dv Cin () i Cc() = i in i Lc() v Cin() = v ou () + v Lc() v Lc() = v Cc() (2a) wih he iniial condiions: v Cc( 1 ) = V Cc1 v Cin( 1 ) = V Cin1 = V Cin0 i Lc( 1 ) = I Lc1 (2b) The equaion sysem during T 3 is basically he same as for T 1, bu he iniial condiions are given by he soluion of he differenial equaions a he end of T 2 : Fig. 6. Oupu Volage wihou Bouncer Oupu Volage wih Bouncer Oupu waveform wih bouncer circui. i Cc() = C c dv Cc () v Lc() = L c di Lc () v Lc() = v Cc() i Cc() = i Lc() (3a)

5 wih he iniial condiions: v Cc( 2 ) = V Cc2 i Lc( 2 ) = I Lc2 (3b) The algorihm for calculaing he waveforms and he droop of he pulse is graphically described in fig. 7a. Iniial Condiions 1b Iniial Condiions 2b Iniial Condiions 3b 0 < 1 Equaions 1a 1 <2 Equaions 2a 2 <3 Equaions 3a Droop (a) Calculaion of he bouncer response. Fig. 7. Se C c Opimize L c for min =0.5% wih 2π L c C c 2T p Opimize L c for =0.5% and V Cc0 = V Cc0,max Opimize L c for =0.5% and I Cc,peak = I Cc,max L c,min L c,max,vcc L c,max,icc (b) Calculaion of circui value limiaions. Algorihms used for calculaions. IV. BOUNCER PARAMETERS The wo-winding inducor bouncer has four degrees of freedom: Bouncer capaciance C b, bouncer inducance L c, iniial bouncer volage V Cc0 and urns raio of he wowinding inducor (bouncer ransformer). The urns raio is only used o adjus he curren and volage of he bouncer o values suiable for semiconducor swiches a he end of he design process. Therefore, in a firs sep, all componens are ransferred o he secondary side of bouncer ransformer and he bouncer ransformer is replaced by an equivalen inducor in order o simplify he calculaions. The urns raio is only considered when he componen limiaions are aken ino accoun as discussed laer in deail. A. Iniial Bouncer Capacior Volage The pulse droop is compensaed wih he bouncer capacior volage. The iniial value V Cc0 deermines he ampliudes of v Cc and i Lc for a given se of componen values. If V Cc0 is se oo low, v Cc is oo small a = 1 and he oupu volage is no reduced enough by he bouncer. Therefore, he droop compensaion is oo small (undercompensaed). If he iniial capacior volage is se oo high, v Cc is oo high a = 1 and he bouncer compensaes more droop han necessary (overcompensaed). Consequenly, here is an opimal volage V Cc0 o achieve exacly he argeed droop as can be seen in fig. 8. The opimal V Cc0 resuls in a minimum amoun of sored energy if i is in he undercompensaed region. B. Bouncer Capacior For considering he influence of he bouncer capaciance value on he droop, i is ineresing o fix he inducance value and calculae he opimal iniial capacior volage for he considered bouncer capaciance. For such a case, he droop of he oupu pulse is shown in fig. 9. The volage droop is becoming smaller and smaller wih increasing capaciance values. The reason is ha he minimum droop is given by he ripple of he capacior volage v Cc during he pulse. By increasing C c he resonan period T B of he LCbouncer increases, so ha he volage drop across C c during he oupu pulse becomes more and more linear. However, he peak ampliude of he bouncer curren increases also wih C c and he bouncer componens/swiches mus be designed for his curren. In fig. 9 also he opimal V Cc0 is given, which has a clear minimum. For large values of C c, a high iniial volage V Cc0 is required, since he resonan curren in he bouncer mus increase in order o obain a sufficien change of v Cc during he pulse. For small C c values also V Cc0 mus increase o obain a high enough ampliude of i Lc, so ha he influence of he load curren, which flows also hrough C c, is compensaed. Droop (%) Cc' (F) (a) VCc0' (kv) Cc' (F) 10-6 (b) Fig. 9. Minimum droop (a) and iniial capacior volage (b) depending on bouncer capacior value C c for C in = 121 nf and L c = 10 µh. C. Bouncer Inducor The influence of he bouncer inducance value L c is similar o he influence of he bouncer capaciance value. Again, he iniial capacior volage has o be increased for an increasing L c o ge a high enough capacior curren. A bigger inducance also resuls in a longer period which reduces he minimum droop. D. Componen Tolerances Droop (%) Undercompensaed Overcompensaed V Cc0 (V) Fig. 8. Droop as a funcion of V Cc0 for C in = 121 nf, C c = 1 µf, L c = 1 µh. Besides he componen values hemselves, also he olerances of he values influence he achievable droop if he iniial condiions and/or he poin of ime, when S b is swiched, is adaped o he modified componen values. In wors case, he droop requiremens migh no be me because he real circui values are no he same as he calculaed ones. Therefore, he componen olerances mus be aken ino accoun during he design process, o make sure ha he maximum droop is always below he maximum allowed one.

6 V. BOUNCER DESIGN Based on he bouncer operaion and he influence of he bouncer parameers explained in he previous secion, he influence of circui limiaions is discussed and a design sraegy is presened in he following. A. Design Consrains Besides he droop requiremens, also some design consrains mus be considered. Firs, he resonance frequency of he bouncer circui mus mee he following crieria, because he oupu pulse is cenered around T B 4. T B 4 > T p 2 T B > 2 T p, (4) where T B = 1/f B is he period of he LC bouncer and T p is he lengh of he oupu pulse including rise and fall ime. Second, he maximum allowed volage V Cc0 is limied by he klysron load, because he klysron usually has a maximal allowed reverse volage, which mus no be exceeded. Since he bouncer volage swings from V Cc0 o V Cc0 and back o V Cc0, he iniial volage V Cc0 mus be smaller han he maximum allowed klysron inverse beam volage. In he considered case, he pre-magneizaion also resuls in a negaive oupu volage. I has o be operaed in such a way, ha he resuling volage on he secondary side is half of he maximum inverse beam volage o achieve he maximum possible bouncer oupu volage swing (cf. fig 2). Therefore, he maximum V Cc0 is half of he maximum inverse beam volage. Third, he bouncer semiconducor swich limis he maximum bouncer volage/curren. Wih he urns raio of he bouncer ransformer, he peak volage/curren can be adaped o o he swich, however, he produc volage curren mus be kep below he limis of he swich. In he considered sysem a press-pack IGBT is used, which has a maximum blocking volage of 3 kv and a maximum curren of 4 ka. B. Design Room Wih he discussed design consrains and he limi for he oupu pulse droop, a design room for he bouncer circui is deermined and only cerain ses L c, C c and V Cc0 will mee hese consrains. The limis of he design room can be calculaed wih opimizaion algorihms like he gradien descen mehod. An example for such an algorihm is shown fig. 7b for a given C in. The resuling curves are shown in fig. 10. For each poin on a specific limiing curve, he droop is exacly he maximum allowed droop and he respecive limiing parameer is also exacly a is limi. During deermining he limiing curves, i has o be assured, ha he bouncer is always in he undercompensaed region. Oherwise, i would be possible o reduce V Cc0 and herefore also he swich curren. This migh lead o a soluion wih he same droop wihou violaing he given limiaions. The design room iself depends on he inpu capaciance C in. For a decreasing C in, he design room is geing smaller. Below a cerain C in, i is no possible o design a bouncer wihou violaing a leas one of he given limiaions. L c (H) Limied by maximum V Cc0 Limied by maximum Swich Curren Limied by minimum Droop Design Room Limied by minimum Resonan Transiion Time C c (F) Fig. 10. Design room for an inpu capaciance C in of 181 nf Because here is no unique soluion, i is possible o opimize he bouncer for various crieria. In [2], i was opimized for minimum volume. Oher opimizaions are possible, like minimum sored energy, minimum bouncer inducor volume or repeiion accuracy. When performing an opimizaion, i has o be aken ino accoun, ha all componens of he bouncer and he pulse generaor have olerances. Such olerances are e.g. componen olerances or jier of he swiches. If he bouncer is opimized for a cerain droop, i migh no always mee he requiremens because of hese olerances. One possibiliy o solve his problem would be o se he maximum allowed droop lower han he required maximum droop. However, he soluion found wih his mehod migh lead o a bouncer which mees he requiremens even wih componen olerances, bu i is no guaraneed ha his is he opimal soluion. A beer way o ake various uncerainies ino accoun is o calculae he wors case droop insead of he ideal droop. There, for a given se of L c, C c and V Cc0 he wors case droop is calculaed by maximizing he droop for he given componen olerances. VI. PROTOTYPE SYSTEM To show he benefis of he bouncer circui and he effec of olerances, a bouncer circui for he 120 MW pulse modulaor wih he specificaions given in ab. I has been designed. In a firs sep, he iniial bouncer capacior volage is adjused o mee he wors case droop requiremens. Then, he iniial capacior volage is calculaed o mee he droop requiremens wih ideal circui elemens and finally, hese wo bouncers are simulaed and compared wih a modulaor wihou bouncer. For illusraing he influence of he olerances, he bouncer circui parameers in he wo righ columns of ab. II are considered. If ideal componens wihou olerances are assumed an iniial capacior volage of 4.27 kv is sufficien for achieving a droop of 0.5 %. However, wih real componens wih olerances of ±10 % he wors case droop becomes 0.77 % (C in = 163 nf, C c = 550 nf, L c = 11 µh). One possible soluion o reduce he wors case droop is seing he iniial capacior volage higher. A a cerain poin, his is no possible anymore because he minimum droop is already reached. In ha case, differen bouncer circui values have o be chosen (e.g a higher L c). In our example, his is forunaely no necessary. By seing he iniial capacior volage V Cc0 o 5.13 kv, he wors case droop is 0.5 % which mees he requiremens. The simulaed waveforms for his bouncer are shown in fig. 11.

7 To show he benefi of a bouncer circui, in ab. II also he componen values for a modulaor wihou bouncer and a droop of 0.5 % are given. There i can be seen, ha he amoun of sored energy (and he sysem volume) is much higher for he sysem wihou bouncer. The specificaions of he wo-winding bouncer inducance are given in ab. III. 367' ' ' ' ' '200 V ou (V) 366' ' ' '400 Wors Case Droop Exac Componen Values Δ = 0.21% 365' Time (μs) Δ = 0.5% Fig. 11. Simulaed oupu pulse volage for he parameers given in II. There curves for ideal componens and for wors case droop in case of componen olerances are given. Finally, he effec of he leakage inducance of he wowinding inducor (bouncer ransformer) is invesigaed. Wih his leakage inducance, he load curren mus be coninuous and could no include seps (cf. fig. 5). Based on he specificaions given in ab. II and he design of he bouncer ransformer in ab. III, a simulaion of he circui including an equivalen circui of he bouncer ransformer and he klysron has been performed, which is given in fig. 12. To allow a comparison of he differen waveforms, he ampliudes are normalized. There one can see, ha he leakage inducance only slighly influences he oupu pulse waveform, because i is small compared o he bouncer inducor. The leakage inducance also influences he bouncer resonance frequency. To compensae his effec, he bouncer inducance could be adjused o keep he resonance frequency consan. In his case, his is no necessary. Addiionally, he leakage inducance acs like a volage divider, which is compensaed by adjusing he iniial capacior volage V Cc0. Fig. 12 shows ha he influence of he pulse ransformer is TABLE II COMPARISON OF THREE DIFFERENT BOUNCER CIRCUITS FOR THE SPECIFICATIONS GIVEN IN TABLE I. No Bouncer Wihou Tolerances Wih Tolerances C in 9.6 mf 2.88 mf 2.88 mf C c nf 500nF L c - 10 µh 10 µh R l 1075 Ω 1075 Ω 1075 Ω V Cin0 3 kv 3 kv 3 kv V Cc0-4.2 kv 5.13 kv I Cc,max - 1 ka 1.2 ka E Cin 43 kj kj kj E Cc J 6.58 J E oal 43 kj kj kj TABLE III PARAMETERS OF THE TWO-WINDING INDUCTOR FOR THE BOUNCER WITH TOLERANCES Core METGLAS AMCC 630 Core Size 90x130x70 mm Number of Primary Turns 4 Number of Secondary Turns 7 Air gap 8.8 mm Leakage Inducance (secondary side referred) 144 nh very srong. The finie rise ime influences he bouncer operaion remarkably. The bouncer operaes wih a relaively low curren compared o he load curren which produces a significanly differen oupu waveform. In he simulaed circui, he droop is even lower in he real sysem. The simulaion also shows, ha he pulse ransformer canno be considered as an ideal ransformer and has o be included in he bouncer design process which will be done in a fuure paper V ou (p.u.) Wih Pulse Transformer Model and Klysron Load Wih Bouncer Inducor Leakage Inducance Ideal Bouncer Inducor Time (μs) Fig. 12. Oupu volages wih leakage inducance. VII. CONCLUSION In his paper, a design and opimizaion procedure for wo-winding inducor bouncer circuis is presened. Firs, he basic operaion principle is described and hen he influence of he differen bouncer parameers on he oupu waveform is invesigaed and a new design mehod including circui limiaions and componen olerances is proposed. For validaing he design procedure, resuls for 120 MW/370 kv pulse modulaor wih and wihou bouncer circui are presened and he amoun of required sored energy is calculaed. Furhermore, he influence of he leakage inducance of he bouncer ransformer on he oupu pulse is invesigaed. I was shown ha he pulse ransformer has a large influence on he bouncer operaion and herefore has o be included in he bouncer design process. ACKNOWLEDGMENT The auhors would like o acknowledge he suppor of PPT in relaion o he pracical realizaion of he projec. References [1] A. Oppel e al., Towards a low Emiance X-ray FEL a PSI, Proc. of he Free-Elecron Laser Conference (FEL), 2007, pp [2] D. Boris, J. Biela and J. W. Kolar, Opimal Design of a Two-Winding Inducor Bouncer Circui, Proc. of he IEEE Inernaional Pulsed Power Conference, 2009, pp [3] D. Boris, J. Biela and J. W. Kolar, Design and Conrol of an Acive Rese Circui for Pulse Transformers, IEEE Transacions on Dielecrics and Elecrical Insulaion, vol. 16, (no. 4), pp , [4] D. Boris, J. Biela and J.W. Kolar, Acive Gae Conrol for Curren Balancing in parallel conneced IGBT Modules in Solid Sae Modulaors, 16 h IEEE Inernaional Pulsed Power Conference (PPC), 2007, pp [5] E. Herber, High Frequency Marix Transformer, Paen US 4,845,606 [Online], July 1989, Available: hp://

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