ZVS Modulation Scheme for Reduced Complexity Clamp-Switch TCM DC-DC Boost Converter

Transcription

1 his is he auhor's version of an aricle ha has been published in his journal. hanges were made o his version by he publisher prior o publicaion. he final version of record is available a hp://dx.doi.org/.9/pe ZVS Modulaion Scheme for Reduced omplexiy lamp-swich M - Boos onverer Oliver Knech, Suden Member, IEEE, ominik Boris, Member, IEEE and Johann W. Kolar, Fellow, IEEE bsrac - boos converer Zero-Volage-Swiching (ZVS) modulaion schemes such as riangular urren Mode (M) offer a highly efficien operaion bu suffer from large swiching frequency variaions, which are complicaing he EMI filer design and he digial conrol. s a soluion, a ri-sae boos converer operaed in ZVS mode, referred o as lamp- Swich M (-M) operaion can be inroduced, which allows o limi he swiching frequency variaion significanly. his paper presens wo variaions of he -M boos converer wih reduced number of acive swiches in he circui, which are suiable for high inpu-o-oupu volage conversion raios. In addiion, he ZVS modulaion schemes, is limiaions, he converer design and he conroller implemenaion are presened and analyzed in deail for boh converer opologies. he iming calculaions for he swiching signals are provided for wo operaing modes, eiher offering a minimized swiching frequency variaion and minimized RMS inducor curren or a consan swiching frequency operaion, which in urn comes a he expense of an increased RMS inducor curren. he ZVS operaion and he operaing modes are experimenally verified using a hardware prooype. Index erms - boos converer, zero volage swiching (ZVS), ri-sae boos, clamp swich, riangular curren mode (M) I. INROUION Zero-Volage-Swiching (ZVS) - buck or boos converers are commonly realized using a riangular urren Mode (M) operaion wih variable swiching frequency [] [] or a Synchronous onducion Mode (SM) operaion wih a fixed swiching frequency [] [7]. he main disadvanage of he SM operaion is he significanly reduced parial load efficiency due o he large peak-o-peak inducor curren ripple which is remained consan even a ligh load condiions. he M operaion mode insead offers a much higher parial load efficiency, which in urn comes a he expense of a large swiching frequency variaion and hence, complicaes he filer design and he implemenaion of he digial conrol. In order o overcome hese drawbacks, an addiional clampswich can be inroduced in parallel o he boos inducor, which allows o limi he swiching frequency variaion significanly, while achieving a high parial load efficiency similar o he M operaion. Such a opology is implemened in [8] and in he Picor ool-power ZVS Buck Regulaor series provided by Vicor orp. and is described in [9]. ZVS of he swiches in he half-bridge configuraion is enabled as for he he auhors are wih he Power Elecronic Sysems aboraory, Swiss Federal Insiue of echnology Zurich, 89 Zurich, Swizerland ( knech@lem.ee.ehz.ch; boris@lem.ee.ehz.ch; kolar@lem.ee.ehz.ch). I,max I,avg I,min () i P min I,pp on off on u m () I,max I,avg s s on R off i on i R Figure : Proposed 3-swich lamp-swich M (-M) boos converer opology. - ypical -M converer inducor curren waveforms a minimum and maximum oupu power. SM and M operaion by reversing he flow direcion of he inducor curren in each swiching period, and as a resul, allowing for ZVS for each swich in he half-bridge. he clamp-swich boos converer opology considered in his paper is depiced in Fig. and was proposed in a similar form as a hard-swiched converer in [], which is referred o as ri-sae boos converer and which allows o improve he dynamic performance of he converer by eliminaing he righ-half-plane zero in he small signal conrol-o-oupu ransfer funcion. In anoher more recen applicaion presened in [], a hard-swiched ri-sae boos converer was used on he receiver side of a wireless power ransfer sysem, which allows o implemen an adapive resonan frequency uning and load maching. In [] and [3], a relaively complicaed ZVS modulaion scheme referred o as lamp-swich M (-M) operaion was inroduced, where he clamp-swich is realized wih an ani-series connecion of wo acive swiches. he modulaion scheme allows for ZVS for all swiches, independen of he oupu power level and wihou resricions on he inpu-ooupu volage conversion raio, given he naural boundaries for boos operaion. similar ZVS operaion was achieved wih a bidirecional buck-boos converer for he use in hybrid elecric vehicles, as described in []. In his paper, a simplified ZVS modulaion scheme [] is proposed for he -M converer which allows o reduce he hardware complexiy and which increases he reliabiliy of he converer by replacing he clamp-swich used in [8], [3] wih an ani-series connecion of an acive swich and a opyrigh 7 IEEE. Personal use is permied. For any oher purposes, permission mus be obained from he IEEE by ing pubs-permissions@ieee.org.

2 his is he auhor's version of an aricle ha has been published in his journal. hanges were made o his version by he publisher prior o publicaion. he final version of record is available a hp://dx.doi.org/.9/pe [, ] i [,, ] [, 3, ] i i [, ] [, 7 ] i i [, ] [ 7, 8 ] i i I,max I, I, I,min () u SW () s i () s s u F, 8 = Figure : Operaing saes of he proposed 3-swich -M modulaion scheme for a full swiching cycle [, 8]. ypical waveform of he inducor curren and he swich-node volage, belonging o he swich conrol signals s i. single diode, as shown in Fig.. In his paper, his ype of converer is referred o a-swich -M boos converer and allows for zero-volage swiching and unidirecional power flow. Furhermore, in his paper, a unidirecional -swich - M converer operaion is proposed and explained in deail, which allows for ZVS of all swiches as well, bu reduces he complexiy of he converer hardware and he modulaion scheme o a minimum. he proposed converer srucures and ZVS modulaion schemes come a he expense of resricions on he inpu-o-oupu volage conversion raio and oupu power range, as i will be explained in deail in Secion II. he design of he boos inducance and he calculaion of he iming inervals on, off and (cf. Fig. and ) are presened in Secion III. In addiion, wo converer operaing modes, eiher offering a variable or consan swiching frequency operaion are analyzed and compared. In Secion IV, he conroller implemenaion is explained for boh converer ypes and in Secion V, he experimenal verificaion of he ZVS operaion and he proposed operaing modes is presened. In addiion, a - efficiency comparison for he differen - M converer ypes is given in he same secion. oncluding remarks are given in Secion VI. II. MOUION SHEME ypical inducor curren waveforms for he considered - M converer operaion a minimum and maximum oupu power are shown in Fig. and respecively. maximum oupu power, he -M operaion corresponds o he M operaion, i.e. he clamp swich is unused. he inducor curren has a riangular shape wih a negaive inducor curren I,min a he end of ime inerval off ha allows for ZVS of he low-side swich a he beginning of he subsequen ime inerval on. ligh load condiions, he clamp-swich allows o inroduce a free-wheeling sae for he inducor curren afer he urn-off of swich and hence, allows o srech he swiching period as i is shown in Fig.. s a resul, he swiching frequency variaion can be conrolled depending on he oupu power and on he volage conversion raio. he maximum swiching frequency f max occurs always a he maximum volage conversion raio, whereby he maximum feasible operaing frequency is mainly limied by he ime delays in he measuremen and conrol circui, as he swiching ime inervals need o be calculaed and synchronized o he zero-crossings of he inducor curren, as explained in deail in Secion IV. he ZVS modulaion scheme proposed in his paper allows o reduce he number of acive swiches in he circui opology and is explained in he following. However, as already menioned, he reduced hardware complexiy comes a he expense of a resricion on he inpu-o-oupu volage conversion raio in order o achieve ZVS for all swiches, and, neglecing he forward volage drop of he diodes, can be expressed by 3 +, () which reduces o if 3 = applies. Where 3 and denoe he parasiic oupu capaciance of swich and he juncion capaciance of diode respecively. Noneheless, a unidirecional operaion and volage sep-up raios according o () are common in numerous applicaions, such as in module inegraed converers for phoovolaic sysems [] [7], fuel-cell based backup energy sysems and uninerrupible power supplies [8], [9] as well as in auomoive applicaions [], []. he main focus of his paper is on he operaion of he 3-swich -M converer opology shown in Fig.. However, he ZVS modulaion scheme can be exended o a -swich -M operaion as well, where he high-side swich is replaced by a diode. his ype of operaion and he ZVS condiions are explained laer in his secion. opyrigh 7 IEEE. Personal use is permied. For any oher purposes, permission mus be obained from he IEEE by ing pubs-permissions@ieee.org.

3 his is he auhor's version of an aricle ha has been published in his journal. hanges were made o his version by he publisher prior o publicaion. he final version of record is available a hp://dx.doi.org/.9/pe Noe ha boh converer opologies allow o use a boosrap gae drive power supply for he clamp-swich (cf. Fig. ), which simplifies he hardware complexiy significanly.. 3-Swich -M Operaion Firs, he deailed principle of operaion and ZVS modulaion scheme is explained for he 3-swich -M converer, based on he operaing saes and he corresponding inducor curren and swich-node volage waveform shown in Fig.. useful represenaion for he analysis of he ZVS operaion of he converer is provided by he sae-plane diagram [], [3], which in his case displays he swich-node volage wih respec o he inducor curren scaled by he characerisic impedance of he resonan circui formed by he inducor and he parasiic oupu capaciances of he swiches and diodes, as shown in Fig. 3. ssuming consan parasiic capaciances, he resonan volage and curren ransiions are described wih Z () =Z I,i cos (ω )+( U sw,i ) sin(ω ) () = ( U sw,i ) cos(ω )+Z I,i sin(ω ) () which represens a circle wih he cener locaed a Z = and =. he beginning of he resonan ransiion, he inducor curren has he value I,i and he swich-node volage is U sw,i. he radius of he circle can be expressed wih R = ( U sw,i ) +(Z I,i ), wih Z =, (3) o where o is he oal capaciance of he resonan circui. espie of he non-lineariy of he parasiic capaciance of he swiches and diodes, he analysis provided in his paper considers consan capaciances only, in order o simplify he formalism and o give a meaningful insigh ino he operaion of he converer. he analysis however could be exended o non-linear capaciances as well, as i is shown in [], [3], []. Furher i is assumed ha he seady sae inpu and oupu volage and are consan, which is ensured by proper inpu and oupu filer design. he diode forward volage drops are denoed wih u F,x and x [, ] and he urn-off process of each swich is considered o be free of power losses. Saring wih he firs ime inerval [, ], swich is urned on and he body diode of swich is blocking he inpu volage and prevens a shor circui of he inpu capacior. Hence, he inducor curren rises linearly. he inducor curren zero crossing is deeced a in swich and is used o synchronize he swiching imes and he gae drive conrol signals s i o he acual inducor curren waveform as described in Secion IV. Hence, he remaining inducor curren build-up ime inerval on (cf. Fig. ) and he ime inerval off are calculaed such ha he required average inducor curren and he curren I, needed a o allow for ZVS of he swiches in he following ime inervals, are achieved. When he inducor curren reaches he value I, a ime, swich is urned off and he inducor curren sars o charge he parasiic oupu capaciance of swich, while, () R Z,R I,min 7 Z,R I, u F, Z,R I, = 8 [, ] u,3 3 u F, R u, 3 [, ] 3 R 3 R u F, Z,R I, Z () Z,R I, Z,R I,max Figure 3: sae-plane diagram, showing he scaled inducor curren Z () wih respec o he swich-node volage () for he 3-swich -M converer operaion. - Operaing saes of he converer during he ime inerval [, ] and [, ] respecively. discharging he oupu capaciance of. Iniially, he volage across he parasiic capaciance,3 is ( u F, ) and he volage across diode is u F,. Hence, he parasiic oupu capaciance of swich is discharged and he juncion capaciance of is charged, as shown in Fig. 3. ue o he series connecion of 3 and, he oal capaciance ha needs o be charged by he inducor curren is o,r = /( 3 + ). he resonan ransiion is described in he sae-plane diagram wih a circle around he cener locaed a = and =and a radius given by R = +(Z,RI, ), and Z,R = o,r. () he maximum inducor I,max = R /Z,R is reached as soon as he swich-node volage is equal o he inpu volage. ime, he swich-node volage a which he volage across approaches zero volage and is body diode 3 sars o conduc, can be calculaed according o, = 3+ ( + u F,3 u F, ), () 3+ if u F,3 u F, applies. Noe ha if 3, he body diode of will sar o conduc as soon as approaches, where he inducor curren reaches is maximum curren I,max. In conras, if 3 >, he capaciance 3 can be discharged o zero only if ( + u F, ),, which is equal o () if he forward volage drop of he diodes are negleced. If he condiion () is no me, sof-swiching of swich canno be achieved in he following operaing saes. s soon as he body diode of sars o conduc, he oal capaciance of he resonan circui changes o o,r = + +, as i is shown in Fig. 3. Hence, he opyrigh 7 IEEE. Personal use is permied. For any oher purposes, permission mus be obained from he IEEE by ing pubs-permissions@ieee.org.

4 his is he auhor's version of an aricle ha has been published in his journal. hanges were made o his version by he publisher prior o publicaion. he final version of record is available a hp://dx.doi.org/.9/pe characerisic impedance of he resonan circui decreases, which appears as a disconinuiy in he sae-space rajecory as shown in Fig. 3. he inducor curren a ime is given by I, = R Z (, ), (),R and hence, using Z,R = / o,r, he radius R can be calculaed according o ( R = (, ) + Z,R I,). (7) If i is assumed ha u F,3 u F, and 3 =, he swich-node volage a ime is, = and he inducor curren is I, = I,, and hence, equaion (7) is reduced o R + (Z,R I,). (8) In his case, if he iniial inducor curren I, is large enough, is charged up o he volage ( ), assuming ha he diode and he body diode of swich have he same forward volage drop. ime, he body diode of swich sars o conduc and clamps he volage across o he diode forward volage drop u F,. If he diode volage drop u F, is negleced, he condiion for ZVS operaion of swich follows from R ( ), and using (8), he condiion can be expressed wih I, u ( ), for ( > ). (9) Z,R If condiions () and (9) are me, swich can be urned on a 3 a nearly zero volage and since he parasiic oupu capaciance of was discharged compleely during [, ], swich can be urned on a any ime beween 3 and wihou causing losses. he criical operaing poin, where ZVS of swich could be los is a minimum oupu power and maximum oupu volage. uring ime inerval [ 3, ] swich is in on-sae and he inducor curren is supplied o he oupu and is decreasing linearly and reverses is flow direcion a ime 3., swich is urned off and he negaive inducor curren I, sars o discharge he parasiic capaciances of swich and diode, while charging he oupu capaciance of swich. Hence, during [, ], he oal equivalen resonan capaciance is o,r = o,r = + + and he resonan ransiion is described in Fig. 3 as a circle wih a radius given by R = ( ) + (Z,R I, ). () s soon as he volage reaches a value of ( u F, ) a, he diode sars o conduc and he inducor clamping ime inerval [, ] is iniiaed. uring his inerval, he inducor curren is free-wheeling in he clamp-swich and no energy is delivered from he inpu o he oupu of he converer. Hence, he clamping ime inerval can be used as a degree of freedom o conrol he swiching period and he amoun of power delivered o he load. ue o he forward volage drop of he diode, he inducor curren is increasing wih a slope of d /d = u F, /, if he ohmic losses in he inducor curren loop are negleced. his needs o be aken ino accoun, specifically if he clamping ime inerval is large, since he inducor curren ampliude a, denoed wih I,, could increase o a value where ZVS of swich could no be achieved anymore a ime 8. he negaive inducor curren I, a he urn-off of swich a can be calculaed wih good approximaion according o I, I,min + u F, and I,min = R. () Z,R uring [, 7 ], he inducor curren coninues discharging he parasiic oupu capaciance of swich and charges he parasiic oupu capaciance of. he oupu capaciance of swich is charged as well by par of he inducor curren flowing hrough diode. Hence, he oal equivalen resonan capaciance changes o o,r = and he radius R in Fig. 3 is given by R = F, (Z +,R I,), and Z,R =. o,r () s soon as he swich-node volage reaches a volage of u F, a 7, he parasiic oupu capaciance of swich is charged up o he inpu volage and he diode sops conducing. he same ime, he body diode of swich sars o conduc and he inducor curren again sars o rise linearly as shown in Fig. in he ime inerval [ 7, 8 ]. he swich can hen be urned on a nearly zero volage as long as he inducor curren is negaive, since is body diode would preven a curren flow in he reverse direcion and he parasiic oupu capaciance of would be charged again as soon as he inducor curren ges posiive. he condiion for ZVS operaion of swich follows direcly from condiion R and is given by I, Z,R u F,, (3) Z,R which is mainly dependen on he inducor curren I, and he duraion of he clamping ime inerval, if he inpu and oupu volage are consan. Noe ha if applies and considering radiional M operaion only, i.e. =, a zero volage ransiion of he swich-node volage in he ime inerval [ 3, 7 ] can always be achieved, even when saring wih an inducor curren I, =. his allows o reduce he converer hardware complexiy furher, by replacing he swich by a single diode as shown in Fig.. his modificaion allows o increase he converer reliabiliy as he number of acive componens in he circui is reduced. However, he conducion losses are increased as well, bu compared o he power losses occurring in he case of a hard-swiched boos converer soluion, he addiional diode conducion losses are accepable. he operaion principle, he limiaions and he condiions for ZVS operaion of he -swich -M converer are explained in he following, based on he sae-plane diagram shown in Fig., which depics he resonan ransiion during he ime inervals wih negaive inducor curren. opyrigh 7 IEEE. Personal use is permied. For any oher purposes, permission mus be obained from he IEEE by ing pubs-permissions@ieee.org.

5 his is he auhor's version of an aricle ha has been published in his journal. hanges were made o his version by he publisher prior o publicaion. he final version of record is available a hp://dx.doi.org/.9/pe i Z,R I,min Z,R I, () R 7 R u F, = 8 3 = u F, ZVS HSW Z () Oupu Power Range (W) 3 i ZVS HSW 8 khz i R R khz lines of consan boos inducance ZVS boundary f p = khz ZVS boundary f p = khz khz khz = V 3 3 Oupu Volage (V) Figure : -swich -M converer opology. ssociaed sae-plane diagram showing he resonan ransiion during he ime inervals wih negaive inducor curren. Region of Zero- Volage-Swiching (ZVS) and Hard-Swiching (HSW) operaion for he -swich -M converer wih respec o oupu power, for he converer designed for differen oupu volages and swiching frequencies f p in he range of khz o 8 khz. B. -Swich -M Operaion he saes of operaion during [, ] are he same as for he 3-swich -M converer. If condiion (9) is me, diode sars o conduc a and he inducor curren sars o decrease linearly. Swich can be urned on a any ime beween and 3, wihou causing swiching losses. 3 =, when he inducor curren reverses is flow direcion, sops o conduc naurally and he resonan ransiion is iniiaed. he inducor curren sars o charge he juncion capaciance of and as soon as he swich-node volage reaches a value of ( u F, ), close o he minimum inducor curren I,min, he clamping ime inerval is sared. he decrease of he swich-node volage, as a resul of blocking a curren flow in he reverse direcion, can be deeced easily. Hence, also he sar of he clamping ime inerval a can be deeced wihou he need for an addiional inducor curren zero crossing deecion and allows o simplify he conroller implemenaion, as i is explained in deail in Secion IV. fer he clamping ime inerval, swich is urned off and he inducor curren furher discharges he parasiic oupu capaciance of swich. If he he negaive inducor curren I, a is large enough, he volage across is reduced o zero and a 7 is body diode sars o conduc. Hence, swich can be urned on a nearly zero volage a ime 8. Since he inducor curren I, a he beginning of he resonan volage ransiion a is zero and canno be conrolled, he ZVS operaion of swich a 7 depends on he inpu-o-oupu volage raio, he characerisic impedance of he resonan circui and on he duraion of he clamping ime inerval, and hence also on he oupu power of he converer. he radius R of he circle describing he resonan ransiion in he sae-plane diagram in Fig. is given by R =( + u F, ) and hence, he minimum inducor curren I,min can be expressed wih I,min = R Z,R, and Z,R = + +. () he radius R of he circle describing he resonan ransiion afer he clamping ime inerval (cf. Fig. ) is given in (), using o,r = In order o allow for ZVS for swich a ime 8, he condiion R mus be fulfilled. By aking () for he inducor curren I, and assuming ha F, ( Z Z,R I,) applies in (), he ZVS condiion for can be expressed wih ( + u F, ) u F, Z,R. () Z,R If i is furher assumed ha ( + u F, ) ( ) and Z,R = Z,R = Z, i.e. if 3 =, condiion () is simplified o + Z u F,. () Noe ha if he clamping-ime inerval =, i.e. a maximum oupu power, expression () is reduced o he condiion, which is equal o he ZVS condiion of he radiional M operaion wih, =[]. s an example, Fig. shows he ZVS boundary according o (), where he -swich -M converer is designed according o (7)-(), as described in Secion III-, for a fixed inpu-o-oupu volage conversion raio, a maximum oupu power of = 3 W, and a swiching frequency f p ranging from khz o 8 khz. I is eviden ha a a volage conversion raio of =, he -swich - M converer allows ZVS operaion only a he specified maximum oupu power, which corresponds o he radiional M operaion, and as soon as he oupu power is reduced, he inroducion of he clamping ime inerval leads o hard-swiching immediaely. his is a main limiaion of he -swich -M converer. However, a larger volage conversion raios, he oupu power range allowing for ZVS operaion is exended significanly, and is highly dependen on he specified swiching frequency and inpu volage of he converer, as hese parameers deermine also he value of he boos inducance. However, he 3-swich -M converer allows for ZVS operaion even in he hard-swiching region of he -swich -M converer, since i allows o adjus he negaive inducor curren I, accordingly in order o achieve zerovolage-swiching. III. OPERING MOES In his secion, wo operaing modes of eiher he -swich or 3-swich -M converer are oulined and equaions for he calculaion of he boos inducance value and he swiching ime inervals on, on, off and are provided. opyrigh 7 IEEE. Personal use is permied. For any oher purposes, permission mus be obained from he IEEE by ing pubs-permissions@ieee.org.

6 his is he auhor's version of an aricle ha has been published in his journal. hanges were made o his version by he publisher prior o publicaion. he final version of record is available a hp://dx.doi.org/.9/pe f p,max f p,min (max) I,rms (min) I,rms () I,max I,min P min Pmin B B B u,min,min,max,max f p,cons (d) (max) I,rms (min) I,rms (e) () I,max P min Pmin I,min B p,min p,max I,min (f) p,cons B B I,max u,min,min,max,max Figure : Swiching frequency variaion, inducor RMS curren variaion and inducor curren waveforms for variable swiching frequency operaing - and for consan swiching frequency operaion (d)-(f).. Variable Swiching Frequency Operaion he main objecives of he firs mode of operaion is he minimizaion of he swiching frequency variaion and he simulaneous minimizaion of he inducor RMS curren for a variable oupu power P [P,min,P,max ] and a variable oupu volage [,min,,max ]. I is assumed ha he inpu volage has a consan value. s explained above, he clamping ime inerval is used as an addiional degree of freedom o conrol he swiching frequency variaion of he converer. onsidering he ypical inducor curren waveforms shown in Fig. and, i is beneficial o emulae M operaion a maximum oupu power, i.e. by reducing he clamping ime inerval o zero [8], and hence reducing he inducor RMS curren o a minimum, while mainaining ZVS operaion. his however implies, ha if he minimum inducor curren I,min is fixed, he swiching frequency will vary wih changes of he inpu and/or he oupu volage, due o he changing slopes of he inducor curren. In conras, if he erminal volages are fixed and he oupu power is varied, he swiching frequency can be mainained consan by inroducing he clamping ime inerval. he inducor RMS curren could be reduced only by increasing he swiching frequency, while approaching he M operaion again, which is no desirable in his case. s repored in [8] for consan swiching frequency operaion, and assuming a lossless operaion of he converer, i.e. P = P, he inducor mus be designed according o = (,min ),min f p,min (P,max / I,min ), (7) in order achieve M operaion a maximum oupu power and minimum oupu volage,min. If, as described in he following, a variable swiching frequency is allowed, he converer operaes always a or above he minimum swiching frequency f p,min. For an accurae calculaion of he swiching ime inervals on, on, off and, he increase of he minimum inducor curren I,min o I, = I,min + u F,, (8) during he clamping ime inerval canno be negleced. his is specifically he case for he operaion a low oupu power and low oupu volage when he clamping ime inerval is large. ssuming ha he resonan volage ransiion ime inervals are much shorer han he swiching period, he ime inerval on can be calculaed for a desired average inpu curren I,avg = P / using ( ) on = P,max I,avg I,min + I,min I,min uf,, (9) which is independen of he oupu volage variaion. he swiching ime inervals labeled wih off and (cf. in Fig. and ) are calculaed according o off = on (u F, ) p,p(max) u F,, u F, () = p,p(max) on off, () using he swiching period p, evaluaed for he nominal inpu power P,max, which follows from (7) and is given by p,p(max) = (P,max / I,min ). () ( ) fer he clamping ime inerval, he inducor curren sars rising from I, and a he curren zero crossing a, he remaining on-ime inerval on is se by he conrol circui, which is calculaed wih on = on + I,min + u F,. (3) Noe ha he swiching ime inervals are calculaed ieraively, since he clamping ime inerval is no known iniially. Hence, saring wih =in (9), he swiching ime inervals (9)-() and (3) can be calculaed wihin few ieraions. In order o furher improve he accuracy of he inducance and swiching ime inerval calculaions, he - efficiency η P(max) a maximum oupu power can be esimaed in advance and hence, he prediced maximum inpu power P,max = P,max /η P(max) can be used in (7) and (9)- (). Using (7) and (), he maximum swiching frequency can be calculaed according o f p,max = f p,min u,min (,max ),max (,min ), () which is obained a maximum oupu volage and is independen of he oupu power. Noe ha for large inpu o oupu volage conversion raios, he swiching frequency variaion is very small, i.e. f p,min f p,max. opyrigh 7 IEEE. Personal use is permied. For any oher purposes, permission mus be obained from he IEEE by ing pubs-permissions@ieee.org.

7 his is he auhor's version of an aricle ha has been published in his journal. hanges were made o his version by he publisher prior o publicaion. he final version of record is available a hp://dx.doi.org/.9/pe B. onsan Swiching Frequency Operaion Generally, a varying swiching frequency operaion is no desired in EMI sensiive applicaions as i spreads he noise emissions over a wide specral range and herefore complicaes he filer design. herefore, he second mode of operaion allows o mainain a consan swiching frequency by adjusing he clamping ime inerval and/or he minimum inducor curren [8]. Noe ha his mode of operaion canno be achieved wih he -swich -M converer, since he magniude of he minimum inducor curren I,min mus be conrollable. he boos inducance can be calculaed according o (7) wih he desired consan swiching frequency f p,cons. In order o mainain he swiching frequency while he oupu volage is allowed o vary, he minimum inducor curren I,min needs o be adjused during he converer operaion according o I,min = u ( )+f p,cons P,max f p,cons. () he swiching ime inervals on, on, off and can hen be calculaed by insering () ino (8)-(3) and p,p(max) = /f p,cons ino ()-(). In order o ouline he differences of he variable and he consan swiching frequency operaion, he swiching frequency variaion, he RMS inducor curren - which gives an indicaion for he converer power losses - and he ypical inducor curren waveforms are illusraed in Fig. -(f) for boh modes. he -M converer is operaed wih variable oupu volage and variable oupu power, and is designed for he same minimum swiching frequency. Fig. shows he variaion of he swiching frequency for he firs operaing mode. he swiching frequency is kep consan for a fixed volage conversion raio and increases wih increasing oupu volage. In conras, he RMS inducor curren remains consan for a fixed oupu power and variable oupu volage and is increasing almos linearly wih increasing oupu power and fixed oupu volage, as i is shown in Fig.. he inducor curren waveforms for he converer operaing poins labeled wih ()-() are shown in Fig.. he consan swiching frequency operaing mode of he -M converer (cf. Fig. (d)) comes a he expense of an increased RMS inducor curren a higher volage conversion raios, as i is shown in Fig. (e). Hence, he converer power losses are increased a high oupu volage, due o he larger peak-o-peak inducor curren ripple shown in Fig. (f), which is necessary o mainain he consan swiching frequency. herefore, his mode of operaion should be used only for applicaions which inherenly limi he variaion of he inpu and oupu volage o a narrow range or which have a large volage conversion raio. In he following secion, he conroller implemenaion for he -M converer operaed a variable swiching frequency is explained in deail. IV. ONROER IMPEMENION. 3-Swich -M onrol he inducor curren zero crossing deecion is he key feaure ha is required o implemen he digial conrol of i R c < on i i en = c < dead, u m R zc c < off u zc,ref 3, i, i R on, off, u zc,ref c < SP FPG () on off c < dead, i en = c < blank s s ou? en = yes ou == no updae on, off, ou == u * i * on iming calc. off i R F FSM (d) curren zero crossing deecor oupu signal and enable signal. Figure : Realizaion of he conrol circui and curren zero crossing deecion for he 3-swich -M converer. 3-swich -M curren waveforms, modulaor saes and modulaor sae machine. (d) 3-swich -M oupu volage conrol wih load curren feed-forward. he 3-swich -M converer. n effecive implemenaion of he zero crossing deecion is shown in Fig., where he low-side swich curren i is sensed in order o deec he curren zero crossing a he rising edge of he inducor curren, as i is illusraed in Fig.. he iming values on, off and are calculaed by a igial Signal Processor (SP) and are ransmied o a Field Programmable Gae rray (FPG), which implemens he modulaor Finie Sae Machine (FSM) shown in Fig. and which generaes he gae conrol signals s i, i [, 3]. couner c wihin he FPG is used o se he duraion of he swiching ime inervals. fer he on-ime on in sae has expired, he curren zero crossing deecor is disabled and he modulaor eners sae, which ses he firs dead-ime inerval dead, for he swiches. In sae 3, swich and are enabled and wih he expiraion of off, he modulaor eners he clamping ime-inerval in sae, followed by he second dead-ime inerval in sae. fer he dead-ime, swich is urned on and he curren zero crossing deecor is enabled. However, is oupu is blanked in he firs place in order o preven he deecion of an erroneous curren zero crossing due o he charging of he boo-srap capaciors of he high-side gae drivers or due o a hard-swiching even a he urn-on of swich. fer he blanking ime inerval, which can be as shor as ns, he curren zero crossing deecor oupu signal is evaluaed. If he deecor oupu is indicaing ha he inducor curren is already posiive, he sae machine coninues wih sae in order o reduce he inducor curren unil is value is below zero when exiing opyrigh 7 IEEE. Personal use is permied. For any oher purposes, permission mus be obained from he IEEE by ing pubs-permissions@ieee.org.

8 his is he auhor's version of an aricle ha has been published in his journal. hanges were made o his version by he publisher prior o publicaion. he final version of record is available a hp://dx.doi.org/.9/pe i, i, i R () s SP on, off, on en = u m FPG ou 3 updae on, i R c < on c < dead, en = ou == 3 c < en = c < dead, clamping inerval deecor oupu and enable signal. Figure 7: Realizaion of he conrol circui for he -swich - M converer. -swich -M curren/volage waveforms, modulaor saes and modulaor sae machine. sae. If he inducor curren is negaive a he end of sae, he modulaor eners sae 7 and wais for he deecion of he curren zero crossing, which hen riggers he sar of he modulaion sequence from he beginning. very simple and effecive implemenaion of he oupu volage conrol of he converer is shown in Fig. (d). single PI-conroller and a load curren feed-forward is used o se he inpu curren arge i. Since he inducor curren can be conrolled direcly cycle by cycle, he converer allows for a highly dynamic operaion. However, since he evaluaion of he iming values is compuaionally expensive, he values on, off and may be updaed only every n-h cycle, i.e. he modulaor sae machine runs wih he same se of iming values for few swiching cycles unil he values are updaed a he beginning of he firs sae (cf. Fig. ). Furher noe ha for he conroller implemenaion i is no necessary o calculae he iming values ieraively for every updae, since he ieraion process is performed wihin he periodic conrol sequence, using he las clamping ime inerval as iniial condiion for he nex iming calculaion. noher soluion o deermine he iming values is o generae a look-up able wih pre-calculaed iming values and o inerpolae he acual values online, according o he lookup able and he measured inpu and oupu volage and he inpu curren se-poin. B. -Swich -M onrol he realizaion of he conrol circui of he -swich - M converer is shown in Fig. 7. In his case, he synchronizaion of he modulaor sae machine o he inducor curren can be realized wih very lile hardware effor. s shown in Fig. 7, if he curren in reaches zero wihin he falling edge of he inducor curren, sops o conduc and he swich-node volage sars o decrease. s soon as he swich-node volage falls below he inpu volage, sars FPG Parameer 7.8 mm Inducance iz wire Number of urns ore maerial.3 mm inpu power source connecor gae driver SP inpu capacior 7. mm inducor connecor ore oal air gap Power densiy clamp swich main swiches load connecor oupu capacior auxiliary power supply Value 7. µh 3 x µm 9 N87 x EEP. mm. W/cm 3 Figure 8: Hardware prooype of he -M converer including he FPG/SP conrol board. Realizaion and echnical specificaions of he inducor used for he measuremens. o conduc and iniiaes he clamping ime inerval. s a main advanage of he -swich opology, he sar of he clampswich ime inerval can be deeced easily by comparing he swich-node volage wih he inpu volage, as shown in Fig. 7, using a comparaor circui wih a propagaion delay as small as ns and a very low hardware effor. he modulaor sae machine is shown in Fig. 7. fer he pre-calculaed on-ime on and he firs dead-ime inerval have expired, he clamping inerval deecor is enabled and swich is enabled. he decreasing inducor curren is supplied o he oupu via diode and he modulaor sae machine wais in sae 3 for he rising edge of he deecor oupu signal, indicaing ha he clamping inerval is iniiaed. fer he clamping ime inerval has expired, is urned off and afer a shor dead-ime inerval, he conrol sequence sars from he beginning. he oupu volage conrol of he -swich -M converer can be implemened as shown in Fig. (d). In he following secion, he operaing modes and he ZVS operaion of he -M converer are verified experimenally using a hardware prooype. V. MESUREMENS Fig. 8 shows he hardware prooype of he -M converer. he EP GaN FEs are used for he swiches -, operaed wih he half-bridge gae driver M3. For he diode he Schoky diode MBRHSF3G was used because of is low forward volage drop and is also placed in ani-parallel configuraion wih each GaN FE. Noe ha he prooype includes a GaN FE in parallel o as well, in order o allow for he -swich -M operaion presened in [3], which however is urned off permanenly during he -swich and 3-swich -M converer measuremens. he converer is conrolled wih a SP/FPG board comprising a opyrigh 7 IEEE. Personal use is permied. For any oher purposes, permission mus be obained from he IEEE by ing pubs-permissions@ieee.org.

9 his is he auhor's version of an aricle ha has been published in his journal. hanges were made o his version by he publisher prior o publicaion. he final version of record is available a hp://dx.doi.org/.9/pe Inducor urren () 8 = V = V = V Inducor urren () 8 = V = V = V. u P min u m d,gd d,gd. d,gd P min s s, - i,zvs ime (µs) ime (µs) ime (ns) (d) ime (ns) Volage (V) 3 P = V = 8 V = W,ZVS,ZVS... urren () Volage (V) u m u F, P s = V = 8 V = W Figure 9: Measuremen of he inducor curren waveform for he variable swiching frequency operaion and consan swiching frequency operaing mode of he 3-swich -M converer. -(d) Verificaion of he ZVS operaion of he swiches, and respecively. urren () exas Insrumens MS3F833 SP and a aice FXP- E FPG. he specificaions and he realizaion of he inducor used for he measuremens are shown in Fig. 8. uring he measuremens, he converer was operaed in open-loop mode and he iming values for he modulaor sae-machine are calculaed offline. he inpu volage is se o a consan value of V. he oupu volage range is se o - V, wih a nominal oupu volage of 8 V, as ypical e.g. for elecom applicaions, and he oupu power range is se o -3 W. Fig. 9 shows he inducor curren waveform for he variable swiching frequency operaing mode of he 3-swich -M converer. I can be seen ha he swiching frequency varies only by a facor. beween 7 khz and 99 khz, which is due o he large volage conversion raio. In Fig. 9, he inducor curren waveforms are shown for consan swiching frequency operaion and he increased peak-o-peak inducor curren ripple a he higher oupu volage is clearly eviden. In his case however, he RMS inducor curren is only a facor of.3-.3 higher compared o he variable frequency operaing mode. he ZVS operaion of he swiches - is shown in Fig. 9 and (d) for an oupu volage of 8 V and a minimum oupu power. In Fig. 9 he resonan volage ransiion of he swich-node volage is shown a he maximum inducor curren. he volage ransiion is iniiaed wih he urn-off he swich afer a gae drive propagaion delay d,gd of approximaely 7 ns. he inducor curren is large enough o discharge he parasiic oupu capaciance of swich well wihin he dead-ime inerval of ns. he oupu capaciance of swich is discharged even faser as indicaed by he clamp-swich midpoin volage u m. Hence, he wo swiches and can be urned on simulaneously afer he deadime inerval wihou causing swiching losses. he end of he clamping ime inerval shown in Fig. 9(d), he resonan volage ransiion is iniiaed wih he urn-off of swich. he negaive inducor curren discharges he parasiic oupu capaciance of swich unil is diode sars o conduc. ccordingly, swich can be urned on a nearly zero volage afer he dead-ime inerval of ns. he resuls for he -swich -M converer operaion are shown in Fig. for a fixed inpu and oupu volage of V and 8 V respecively. Fig. shows he measured inducor curren waveforms for variable oupu power and Fig. shows he verificaion of he calculaion of he swiching ime inervals according o () and (9)-(). urren () ime (us) Volage (V) meas. calc Oupu Power (W) Oupu Power (W) Oupu Power (W) P ou = W - - P ou = 3 W ime (µs) Volage (V) 3 = V = 8 V P,max = 3 W P,min = W - - ime (µs) on off meas. calc. P meas. calc. Figure : Measuremen of he inducor curren waveforms for he -swich -M converer operaion for fixed inpu/oupu volages and variable oupu power. Measured and calculaed swiching ime inervals on, off and. Measured waveforms of he swich-node volage and he inducor curren waveform for minimum and maximum oupu power. In order o simplify he calculaion, i is assumed ha he converer causes no power losses and ha he capaciances, and, used in (), have a value of 3 pf, which is he oal charge equivalen capaciance [] of he EP GaN FE in parallel o he Schoky diode a an oupu volage of 8 V. For he diode forward volages a value of. V is used, which is he ypical forward volage drop of he Schoky diode MBRHSF3G a 3 m and. he measured waveforms of he swich-node volage and urren () urren () opyrigh 7 IEEE. Personal use is permied. For any oher purposes, permission mus be obained from he IEEE by ing pubs-permissions@ieee.org.

10 his is he auhor's version of an aricle ha has been published in his journal. hanges were made o his version by he publisher prior o publicaion. he final version of record is available a hp://dx.doi.org/.9/pe M operaion: -swich 3-swich -swich. I,max I,rms = V I,min u. = 8 V Oupu Power (W) Oupu Power (W) Oupu Power (W) -swich -M operaion according o [] and [3]. Efficiency (%) Power oss (W) Figure : - Measured - efficiency and power loss a variable oupu power, for he proposed -swich and 3-swich - M operaion as well as for he -swich -M operaion explained in [], [3]. Noe ha hese measuremens do no include he consan power loss of he SP/FPG conrol board. Measured minimum, maximum and RMS inducor curren. he inducor curren are shown in Fig. for minimum and maximum oupu power. he measured - efficiency and he power loss of he proposed converer operaions are shown in Fig. and respecively. he inpu and oupu power is calculaed, based on he measuremen of he erminal volages and currens using gilen 3 mulimeers. he power loss caused by he curren and volage measuremen circuis, which amoun o 37. mw and he gae-drive power losses are measured separaely and are included in he oal power loss and efficiency calculaion. However, he measuremens do no include he consan power loss of 99 mw caused by he SP/FPG conrol board, since i is no opimized for he hardware prooype a hand and i could be designed wih significanly reduced fooprin and power loss. s shown in Fig., a maximum efficiency of 97. % was obained for he 3-swich -M operaion a maximum oupu power. he efficiency of he -swich operaion is almos. % lower compared o he 3-swich operaion, which is due o he conducion losses caused in diode. I is imporan o noe, ha he diodes used in he hardware prooype are inended o lower he volage drop across he GaN swiches during he shor dead-ime inerval and are no suied o carry he inducor curren for a much longer ime. herefore, a more suiable diode such as he VP-M3 Schoky recifier diode could be used for o improve he efficiency of he -swich -M converer. In order o provide a complee comparison, he - efficiency is measured as well for he -swich -M converer operaion proposed in [3]. I can be seen in Fig. ha he -swich -M converer achieves a higher efficiency a low oupu power when compared o he 3-swich operaion, which is due o he decreased power losses occurring during he clamping ime inerval. However, a maximum oupu power, he -swich -M converer shows a lower performance, because of he increased diode conducion power loss during he dead-ime inervals. he minimum and maximum inducor curren, as well as he RMS inducor curren is shown in Fig. for each converer operaion. he minimum inducor curren canno be urren () conrolled for he -swich -M converer operaion and herefore, he same negaive curren was chosen for he 3- swich and -swich -M converer operaion, in order o achieve he same operaing frequency, which is in a range of 87-9 khz. s expeced, he maximum and he RMS inducor curren do no significanly differ among he differen -M converer operaions. Hence he main differences in he power loss measuremen mainly arise from he differen diode conducion losses and also from he differen gae-drive power losses, as he number of acive swiches varies for he differen -M converers. VI. ONUSIONS he -M - boos converer allows for ZVS of all swiches and offers a significanly reduced swiching frequency variaion when compared o he radiional M operaion [3], which in urn simplifies he filer design in EMI sensiive applicaions and relaxes he requiremens for he digial conrol. In his paper, wo -M boos converer opologies wih reduced hardware complexiy and is ZVS modulaion schemes are proposed. ddiionally, he limiaions for ZVS operaion, he iming calculaions and he conroller implemenaion are presened and analyzed in deail for boh converer opologies. he reduced complexiy of he -M converer hardware and modulaion scheme, however, comes a he expense of a unidirecional power flow and a resricion on he minimum inpu-o-oupu volage conversion raio, which is required o ensure ZVS operaion for all he swiches. In addiion o he ZVS modulaion schemes, wo operaing modes of he -M converer are compared in his paper. he firs operaing mode allows for minimum swiching frequency variaion and a minimized RMS inducor curren, which is achievable wih boh he -swich and he 3-swich -M converer. he second mode of operaion allows for consan swiching frequency operaion and is achieved wih he 3-swich -M converer only, because i allows o conrol he negaive inducor curren. However, he consan swiching frequency operaion has limiaions regarding he converer efficiency, since he RMS inducor curren increases as he oupu volage is increased. Hence, his mode of operaion is inended mainly for applicaions requiring a small inpu or oupu volage operaing range or a high volage conversion raio. I is imporan o noe ha he modulaion scheme and he operaing modes presened in his paper are no limied o - M boos converers only, bu could be adaped easily for an unidirecional buck-ype -M converer operaion as well. Furher noe ha he -M converer opologies presened in his paper and in [3] deliver heir benefis specifically in applicaions wih higher oupu volage and higher oupu power, where he conrol power losses are negligible. KNOWEGMEN he auhors graefully acknowledge he financial suppor by he Baugaren foundaion. his work is par of he Zurich Hear projec under he umbrella of Universiy Medicine opyrigh 7 IEEE. Personal use is permied. For any oher purposes, permission mus be obained from he IEEE by ing pubs-permissions@ieee.org.

11 his is he auhor's version of an aricle ha has been published in his journal. hanges were made o his version by he publisher prior o publicaion. he final version of record is available a hp://dx.doi.org/.9/pe Zurich/Hochschulmedizin Zürich. Furher hanks goes o ndrés ao for he design of he hardware prooype in he course of his semeser projec. REFERENES [] X. Huang, F.. ee, Q. i, and W. u, High-frequency high-efficiency GaN-based inerleaved RM bidirecional buck/boos converer wih inverse coupled inducor, IEEE rans. Power Elecron., vol. 3, no., pp. 33 3,. []. Marxgu, F. Krismer,. Boris, and J. W. Kolar, Ulrafla inerleaved riangular curren mode (M) single-phase PF recifier, IEEE rans. Power Elecron., vol. 9, no., pp ,. [3]. Gerber and J. Biela, Inerleaving of a sof-swiching boos converer operaed in boundary conducion mode, IEEE rans. Plasma Sci., vol. 3, no., pp ,. [] S. G. Yoon, J. M. ee, J. H. Park, I. K. ee, and B. 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Oliver Knech (S ) received he M.Sc. degree in elecrical engineering from he Swiss Federal Insiue of echnology (EH) Zurich, Zurich, Swizerland, in 3, where he is currenly working oward he Ph.. degree a he Power Elecronic Sysems aboraory. uring his sudies he focused on power elecronics, conrol sysems and microwave elecronics. His curren research ineress include he analysis, design and conrol of inducive power ransfer sysems for medical applicaions. ominik Boris (M 8) received he M.Sc. degree in elecrical engineering and he Ph.. degree from he Swiss Federal Insiue of echnology (EH) Zurich, Swizerland, in and 8, respecively. In May, he joined he Power Elecronic Sysems aboraory (PES), EH Zurich, as a Ph.. suden. From 8 o, he has been a Posdocoral Fellow and from o a Research ssociae wih PES, co-supervising Ph.. sudens and leading indusry research projecs. Since January r. Boris is heading he newly esablished research group dvanced Mecharonic Sysems a PES. Johann W. Kolar (F ) received his Ph.. degree (summa cum laude) from he Vienna Universiy of echnology, usria. He is currenly a Full Professor and he Head of he Power Elecronic Sysems aboraory a he Swiss Federal Insiue of echnology (EH) Zurich. He has proposed numerous novel PWM converer opologies, and modulaion and conrol conceps and has supervised over Ph.. sudens. He has published over 7 scienific papers in inernaional journals and conference proceedings, 3 book chapers, and has filed more han paens. He has presened over educaional seminars a leading inernaional conferences, has served as IEEE PES isinguished ecurer from hrough, and has received IEEE ransacions and onference Prize Paper wards, he IEEE Power Elecronics Sociey R. avid Middlebrook chievemen ward, he IEEE William E. Newell Power Elecronics ward, he IEEE PEM ouncil ward, and he EH Zurich Golden Owl ward for excellence in eaching. He has iniiaed and/or is he founder of EH Spin-off companies. he focus of his curren research is on ulracompac and ulra-efficien Si and GaN converer sysems, wireless power ransfer, Solid-Sae ransformers, Power Supplies on hip, as well as ulrahigh speed and ulra-ligh weigh drives, bearingless moors, and energy harvesing. opyrigh 7 IEEE. Personal use is permied. For any oher purposes, permission mus be obained from he IEEE by ing pubs-permissions@ieee.org.