doi: 1.7/cc-13-9 13 / 3 Conductd of Switching Frquncy Modulatd Boost Convrtr Dniss Stpins (Rsarchr, Riga Tchnical Univrsity) Abstract In this papr conductd lctromagntic intrfrnc () of boost convrtr with itching frquncy modulation (SFM) is thortically analyzd in dtails. In th analysis lin impdanc stabilization ntwork paramtrs, powr inductor and input filtring capacitor paramtrs ar takn into account. Th analysis shows that th conductd attnuation du to th us of SFM dpnds not only on modulation indx as it is assumd in numrous rsarch paprs, but also on cntral itching frquncy. Usful xprssions to numrically calculat SFM boost convrtr conductd spctrum and attnuation du to th us of triangular and sawtooth modulation wavforms ar drivd. Additionally xprimntal vrification of th thortical rsults is prformd using a suprhtrodyn spctrum analyzr. Morovr a procdur for th choic of optimum SFM paramtrs (modulation wavform, frquncy dviation and modulation frquncy) to gt maximum conductd attnuation is proposd. Kywords Elctromagntic intrfrnc, itchd-mod powr supply, frquncy modulation. I. INTRODUCTION Nowadays itch-mod powr convrtrs (SMPC) ar oftn usd in many lctronic dvics to convrt lctric powr with high fficincy. High lvls of lctromagntic intrfrnc () both conductd and radiatd ar still on of th major disadvantags of SMPC. Thus, much attntion is usually focusd on rduction whn dsigning a SMPC [1-3]. To supprss, filtring, shilding, soft-itching tc. ar usually usd in practic. Howvr, ovr th last dcad so calld sprad-spctrum tchniqu has bn xtnsivly studid by rsarchrs all ovr th world and usd for th rduction in SMPC including powr factor corrctors (PFC), lighting quipmnt lctronic ballasts, invrtrs, tc. [-7]. Noticabl supprssion of pak lvls can b simply obtaind by th modulation of itching frquncy f using simpl priodic modulating wavforms (such as sin, triangl, sawtooth, tc) thus sprading th spctrum of SMPC voltags and currnts [],[9]. Switching frquncy modulation (SFM) can rduc not only conductd but radiatd as wll [11]. Although numrous rsarch paprs [-11] ar dvotd to SMPC conductd rduction with priodic SFM, usually th analysis includs only th invstigation of spctra of rctangular puls trains (rprsnting powr componnt voltags) or powr componnt currnts (such as powr inductor currnt). Howvr th conductd nois voltag wavforms highly diffr from th powr componnt voltags and currnts wavforms [1]. Thus th analysis prsntd in th paprs can omit svral important dtails of th ffct of SFM paramtrs on conductd attnuation. In this papr a comprhnsiv thortical analysis of conductd of SFM SMPC is prsntd. In th analysis th ffct of lin impdanc stabilization ntwork (LISN) and input filtr paramtrs is also takn into account. Morovr th xprssions to calculat SFM SMPC spctrum and attnuation du to th us of triangular and sawtooth modulation wavforms ar drivd. Additional xprimntal vrification is prformd and a procdur for th choic of optimum SFM paramtrs to gt maximum attnuation is proposd. II. THEORETICAL ANALYSIS OF OF SMPC WITHOUT SFM In this chaptr th conductd spctrum without SFM will b considrd first. It is rathr wll known from th powr lctronics that for masurmnts LISN and spctrum analyzr ar usd as shown in Fig.1. A spctrum analyzr with spcifid rsolution bandwidth (RBW) and dtctor typ is connctd to th LISN radio-frquncy masurmnt output to analyz conductd spctrum in th spcifid frquncy rang (.g. 9kHz-3MHz). During th dsign procss it is of importanc to prdict spctrum thortically. Thortical analysis and prdiction of conductd of SMPC without SFM has bn prformd in various paprs,.g. [1] - [1]. Usually is analyzd using computr simulation and fast Fourir transform (FFT) to calculat spctrum. Howvr svral paprs [1], [1] propos simpl analytical modls for analysis and prdiction in SMPC without SFM. In this papr a boost DC-DC convrtr oprating in continuous conduction mod (CCM) is chosn for th analysis. In Fig. boost SMPC with input filtring capacitor C in and LISN is shown. To simplify th analysis only nonidalitis of C in and powr inductor will b takn into account. Sinc conductd is of intrst, LISN radio-frquncy masurmnt output voltag V LISN will b analyzd in th frquncy domain. V ns should b drivd first in ordr to calculat V LISN spctrum transfr function K (f) btwn V LISN and an quivalnt nois sourc [1], [1]. Fig.1. Typical conductd masurmnt stup. 1
13 / 3 Fig.. Boost SMPC schmatic diagram with LISN. Fig.3.(a) simpl boost SMPC modl (slightly modifid vrsion takn from [1]), (b) quivalnt nois sourc voltag wavform. For this purpos a slightly modifid simpl modl takn from [1] is usd as shown in Fig.3(a). Using th modl th transfr function btwn V ns and V LISN can b drivd: 5 K ( f ) 5, (1) C5 Ch ( L ) whr Th transfr function K (f) for diffrnt valus of parasitic capacitanc C h btwn MOSFET drain and a groundd hatsink is shown in Fig.. -1-5 / ) (5 ) /(55 ), ( C5 L3 C5 L3 but /( j f ), Ch C 5 1 C5 1/( j f Ch ) and L 3 j f L3, ral input capacitor complx impdanc 1 jfc in jfl r and ral powr inductor complx impdanc [17] L p L p () rl jfl (3) 1 (f ) LC jfr C -3 - -5 - -7 1 5 1 1 7 Fig.. Transfr function K (f) for diffrnt C h. 13
13 / 3 1 1 1 (a) 1 3 5 7 9 x 1 5 1 (b) 1 1 1 1 1 1 x 1 (c) Fig.5. Spctrum of unmodulatd and SFM V LISN : (a) f =khz, f m =1kHz, Δf =3kHz; (b) f =khz, f m =1kHz, Δf =1kHz; (c) f =5kHz, f m =1kHz, Δf =3kHz. Othr paramtrs: D=.5, V in =V, m(t) is sawtooth. Thus V LISN spctrum can b calculatd as SVLISN ( f ) SVns ( f ) K ( f ), () whr V ns spctrum S Vns (f)=d n (whr d n ar Fourir sris complx cofficints) according to d 1 T j nf t n vns ( t) dt T DT T 1 jnf t jnf B dt B1 T DT t jnd jn jnd 1 B dt B 1, (5) jn whr D is duty ratio, T is itching priod, f is itching frquncy. For boost SMPC B =V out -V in and B 1 =-V in [1]. Th calculatd conductd (V LISN spctrum) whn D=5% is shown in Fig.5. It can b sn that th spctrum consists of discrt harmonics of f. Th 1 st harmonic amplitud is th highst..5 1 1.5 x 1 Fig.. Spctrum of unmodulatd and SFM V ns : (a) f =15kHz, f m =khz, Δf =khz, m(t) is sawtooth; (b) f =khz, f m =1kHz, Δf =3kHz, m(t) is sawtooth. Othr paramtrs: D=.5, B 1 = 1V, B = 1V. III. THEORETICAL ANALYSIS OF OF SMPC WITH SFM Whn th SFM is usd thn V ns and V LISN spctra ar mor difficult to calculat. For sinusoidal SFM V ns spctrum can b obtaind using th Bssl functions as follows [7] S Vns n ( f ) d [ J ( n ) ( f nf ) J ( n ) n o k1 k f nf kf ) ( 1) ( f nf kf ) ], () ( m m whr J k is kth ordr Bssl function, β is th modulation indx and f m is modulation frquncy. For othr modulation wavforms.g. sawtooth, triangular, tc. th spctrum calculation is mor difficult [11]. Usually to calculat th spctrum of SFM signal, FFT is usd as it was don.g. in [9]. Howvr, as such FFT rquirs a lot of computation tim and powr. Thus in this papr simpl xprssions to calculat spctrum ar drivd. For this purpos Fourir sris can b usd, assuming that whn T m /T is an intgr numbr thn SFM signal is priodic with modulation priod T m [11]. k 1
13 / 3 1 1 1 1 1 1 3 x 1 1 3 x 1 1 1 1 1 1 3 x 1 7 5 3 1 1 3 x 1 1 1 1 1 1 3 x 1 Fig.7. A and A vrsus Δf for diffrnt m(t) and f. 1 3 x 1 15
13 / 3 Complx Fourir sris cofficints for SFM V ns Fig.3(b). d sn t t3 jnf mt B dt B1 Tm t1 t 1 jnfmt tk1 jnf t m B dt... B tk N / tn 1 jnf mt 1 tn dt B jnfmti jnfmti1 [ ] jn i1 N / dt... B1 jnfmti 1 jnfmti [ ] jn (7) i1 whr an intgr numbr N=f /f m. t k ar th tim instants at which V ns crosss zro Fig.3(b). Thy can b calculatd by solving trigonomtric quation [11] cos( t ( t)), () f whr th tim dpndnt phas angl [] is t ( t) f m( ) d, (9) but m(t) is th modulation signal with unitary amplitud. Solution of () with rspct to t producs a st of simpl analytical xprssions of t k calculation for sawtooth SFM min f f f k Tm t min ( 1) / k f / Tm (1) and for triangular SFM f min f min f k / Tm f / Tm at t Tm /, tk k f 3f ( f 3f ) f ( ) f / Tm at Tm / t Tm (11) whr f min =f -Δf and β=δf /f m. Drivd xprssions (7), (1) and (11) can b simply usd to numrically calculat V ns and V LISN spctra in SMPC with triangular and sawtooth SFM. Using th xprssions and Matlab cod th spctra can b calculatd just within a fw sconds. As an xampl unmodulatd and SFM boost SMPC thortical spctra of V ns ar shown in Fig.. In turn, in Fig.5 calculatd conductd spctra (V LISN spctra) ar shown for diffrnt f. As it can b sn from th figurs SFM lads to noticabl dcras in amplituds of unmodulatd f harmonics. It is intrsting to obsrv that whn adjacnt sidbands do not ovrlap thn th sidbands ar symmtrical with rspct to f and its harmonics in V ns spctrum. Howvr in th cas of V LISN spctrum, th sidbands ar asymmtrical whn f =khz. This is bcaus th transfr function btwn V ns and V LISN dpnds on frquncy (Fig.). In fact th sidband asymmtry is also obsrvd in SFM lctronic ballast output currnt [5]. Effctivnss of th us of SFM is charactrizd by a paramtr calld attnuation which is th diffrnc in (db) btwn maximum amplitud of unmodulatd and SFM spctra in th frquncy rang of intrst [9], [1]. In th litratur th rsarchrs usually considr only attnuation (A) of amplituds of unmodulatd f harmonics for rctangular puls trains. This assumption in fact is incorrct bcaus V ns spctrum highly diffrs from V LISN spctrum (s Fig.5 and Fig.). That is why in this papr w will considr not only A but also attnuation (A ) of amplituds of unmodulatd f harmonics for V LISN. So to calculat th attnuations th following quations will b usd A log1 (max SVns ( f ) / max SVns 1( f ) ), (1) A log1 (max SVLISN ( f ) / max SVLISN1( f ) ), (13) whr S Vns and S Vns1 ar unmodulatd and SFM V ns spctra, but S VLISN and S VLISN1 ar unmodulatd and SFM V LISN spctra. To calculat th attnuations for sinusoidal SFM (), (), (1) and (13) should b usd, but for sawtooth and triangular SFM (), (7), (1)-(13) can b usd. Calculatd A and A as a function of Δf (f m =const) for diffrnt f and m(t) ar shown in Fig.7. Th rsults clarly show that conductd attnuation cannot b charactrizd by th paramtr A (as it was don in numrous paprs), bcaus th actual conductd attnuation (A ) highly diffrs from A. Morovr A dpnds only on Δf, f m and m(t), but A dpnds also on f valu. So whn calculating conductd attnuation du to SFM, f should also b takn into account. Morovr A is an incrasing function of Δf, but A incrass, thn it achivs its maximum and thn it vn dcrass as Δf incrass (s Fig.7). Sinc th 1 st sidband amplitud is th highst in SFM V LISN spctrum and f st th location of th sidband in th frquncy rang, thn whn th 1 st sidband is in th rang whr K (f) changs slowly, diffrnc ΔA btwn A and A is minimal (this mainly corrsponds to th high frquncy rang). Howvr whn th 1 st sidband is in th rang whr K (f) changs stply, th diffrnc ΔA is high (this mainly corrsponds to low frquncy rang). Approximat ΔA can b calculatd using th following simpl xprssion K ( f min ) K ( f ) A max, (1) K ( f max ) K ( f ) whr f max = f +Δf. For rathr small valus of Δf (up to 1 khz) A is approximatly qual to A, howvr th highr is Δf th highr also is ΔA. It is intrsting to obsrv from Fig.7 that A for sawtooth SFM is th highst but for sinusoidal it is th lowst, that is why it is bttr to us sawtooth m(t). 1
13 / 3 Fig.. Simplifid schmatic diagram of th xprimntal stup. 7 5 3.5 1 1.5.5 3 3.5.5 x 1 5 7 5 3 (a).5 1 1.5.5 3 3.5.5 5 x 1 5 (b) Fig.9. Exprimntal (a) and thortical (b) spctra of V LISN spctrum with and without SFM. SFM paramtrs: Δf =3kHz, f m =1kHz, f =khz, m(t) sawtooth. Othr paramtrs: C h =pf, V out =V; RBW=Hz. As for th choic of modulation frquncy, it is widly known that to gt accptabl rduction f m should b chosn slightly highr than RBW (which is usually st by a standard,.g. CISPR ) [1]. Th most problmatic SFM paramtr to choos is Δf. Whn dsigning SFM SMPC Δf should b carfully chosn so that A is maximal. Th drivd xprssions can b usd for this purpos. IV. EXPERIMENTAL VERIFICATION A. Exprimntal stup Exprimntal boost SMPC (Fig.) oprating in CCM is tstd in an opn loop mod to vrify th thortical analysis dscribd abov. In th xprimnts a rgulatd DC sourc is connctd to th input of th boost SMPC. Th input voltag of th boost convrtr is V in = V; output load 1Ω and f = khz. For th xprimnts MOSFET IRF53 was usd without xtrnal hatsink, so only diffrntial mod conductd will b considrd in th calculations. To prform SFM, a frquncy modulatd squar wavform signal from an arbitrary wavform gnrator is fd into th drivr controlling th powr MOSFET. Th ncssary SFM paramtrs can b st using th gnrator. B. Exprimntal rsults Conductd (V LISN spctrum) is analyzd using a spctrum analyzr (Agilnt EB) with RBW=Hz and a pak dtctor. Th xprimntal and calculatd V LISN spctra ar dpictd in Fig.9. As it can b sn th diffrnc btwn th rsults is not high. Thus th drivd xprssions can b usd for th conductd calculation. V. PROCEDURE FOR THE CHOICE OF SFM PARAMETERS To gt th maximum attnuation du to th us of SFM for th givn valu of f, SFM paramtrs should b proprly chosn. For this purpos a procdur for th choic of optimum SFM paramtrs to gt maximum attnuation is proposd as follows: stp 1: choos f m slightly highr than RBW; stp : as m(t) choos sawtooth; stp 3: calculat unmodulatd V LISN spctrum using (1)-(5); stp : calculat SFM V LISN spctrum using (1) (), (7), (1); stp : calculat A vrsus Δf using (13); stp 5: find Δf max at which A is at maximum; stp : choos Δf = Δf max ; stp 7: nd. VI. CONCLUSIONS Th comprhnsiv thortical analysis prsntd in this papr shows that th assumption that conductd attnuation (A ) du to th us of SFM dpnds only on modulation indx and modulation wavform (as it was considrd by othr rsarchrs) gnrally is incorrct. A dpnds not only on Δf /f m and m(t), but also on f. This is bcaus in th analysis LISN, input filtr and powr inductor paramtrs should b takn into account. Th drivd xprssions to numrically calculat conductd spctrum and attnuation in SFM SMPC can b vry usful in th dsign procss, bcaus thy rquir lss computation tim than FFT. Th prsntd analysis shows that sawtooth modulation wavform is th bst choic. Th most problmatic SFM paramtr to choos is Δf. Whn dsigning a SFM SMPC Δf should b carfully chosn so that A is at maximum. For this purpos th drivd xprssions can b usd. Th dvlopd procdur for th choic of SFM paramtrs can simplify th slction of optimum SFM paramtrs to gt maximum attnuation for th givn valu of f. ACKNOWLEDGMENTS This rsarch was fundd by a grant (No. 7/1) from th Latvian Council of Scinc. 17
13 / 3 REFERENCES [1] C. R. Paul, Introduction to Elctromagntic Compatibility. Nw Jrsy: John Wily & Sons, nd d.,, pp. 9-9. [] F. ar, issus in modrn powr lctronic systms, IEEE EMC Socity Nwslttr, No.1, pp.-7, 9. [3] K. Mainali, R. Oruganti, Conductd Mitigation Tchniqus for Switch-Mod Powr Convrtrs: A Survy, IEEE Transactions on Powr Elctronics, vol. 5, no. 9, pp. 3-35, 1. [] G. M. Dousoky, M. Shoyama, T. Ninomiya, "Doubl-hybrid spradspctrum tchniqu for conductd- rduction in DC-DC itching rgulators with FPGA-basd controllr," IEEE Tlcommunications Enrgy Confrnc, 9 (INTELEC 9), pp. 1-. [5] S. Johnson and R. an, Custom spctral shaping for rduction in high-frquncy invrtrs and ballasts, IEEE Transactions on Powr Elctronics, vol., no., pp. 199 155, Nov. 5. [] D. Gonzalz, J. Balclls, A. Santolaria, J. Buntl, J. Gago, D. Magnon, S. Brhaut, Conductd Rduction in Powr Convrtrs by Mans of Priodic Switching Frquncy Modulation, IEEE Transactions on Powr Elctronics, vol., no., pp. 71-1, 7. [7] K. Ts, H. Chung, S. Hui, H. So, Comparativ Study of Carrir- Frquncy Modulation Tchniqus for Conductd Supprssion in PWM Convrtrs, IEEE Transactions on Industrial Elctronics, vol. 9, no.3. pp. 1-7,. [] J. Balclls, A. Santolaria, A. Orlandi, D. Gonzalz, and J. Gago, rduction in itchd powr convrtrs using frquncy modulation tchniqus, IEEE Trans. Elctromagn. Compat., vol. 7, no. 3, pp. 59 57, Aug. 5. [9] Santolaria A., SSCG mthods of missions rduction applid to itching powr convrtrs // Ph.D. dissrtation, Elctron. Eng. Dpt., Polytchnic Univrsity of Catalonia, Barclona, Spain, Jul.. [1] F. Lin and D. Y. Chn, Rduction of powr supply mission by itching frquncy modulation, IEEE Trans. Powr Elctron., vol. 9, no. 1, pp. 13 137, Jan. 199. [11] K.B. Hardin, J.T. Fsslr, D.R. Bush, Sprad Spctrum Clock Gnration for th Rduction of Radiatd Emissions, Procdings of IEEE Intrnational Symposium on Elctromagntic Compatibility, August 199, pp. 7-31. [1] P. Musznicki, JL. Schann, P. Granjon, P.J. Chrzan, Bttr undrstanding gnration of powr convrtrs, Procdings of IEEE Powr Elctronics Spcialists Confrnc (PESC5), Rcif, Brazil, Jun 5, pp. 15-15. [13] F. Gizndannr, J. Bila, J. W. Kolar, S. udrll-koch, nois prdiction for lctronic ballasts, IEEE Transactions on Powr Elctronics, vol. 5, no., pp. 133-11. [1] S. Wang, F.C. L, W.G. Odndaal Improving th prformanc of boost PFC filtrs, Procdings of IEEE Applid Powr Elctronics Confrnc and Exposition (APEC 3), Fb. 3, pp. 3 37. [15] L. Yang, B. Lu, W. Dong,. Lu, M. Xu, F.C. L, W.G. Odndaal Modlling and charactrization of a 1 KW CCM PFC convrtr for conductd prdiction, Procdings of IEEE Applid Powr Elctronics Conf. and Exposition (APEC ),, pp. 73 79. [1] K. Mainali, R. Oruganti, Simpl analytical modls to prdict conductd nois in a powr lctronic convrtr, Procdings of th 33rd Annual Confrnc of th IEEE Industrial Elctronics Socity (IECON7), 7, pp. 193 193. [17] K. Kostov, J.-P. Sjöroos, J. Kyyrä, and T. Suntio Slction of Powr Filtrs for Switchd Mod Powr Supplis, Procdings of Nordic Workshop on Powr and Industrial Elctronics (NORPIE ), Trondhim, Norway, Jun, pp. 1-7. [1] L. Barragan, D. Navarro, J. Acro, I. Urriza, and J-M. Burdío, FPGA Implmntation of a Switching Frquncy Modulation Circuit for Rduction in Rsonant Invrtrs for Induction Hating Appliancs, IEEE Transactions on Industrial Elctronics, vol. 55, no.1, Jan., pp. 11. Dniss Stpins rcivd th B.Sc., M.Sc. and Dr.Sc.Ing dgrs in lctronics from Riga Tchnical Univrsity, Riga, Latvia, in, and 11 rspctivly. H is currntly a rsarchr and lcturr in th Dpartmnt of Radiolctronics, Riga Tchnical Univrsity. H has bn involvd in svral rsarch projcts on th xamination of sprad spctrum tchniqu for itching powr convrtrs and improvmnt of powr magntic componnts. His rsarch intrsts includ rduction tchniqus applid to itching powr convrtrs, control of itch-mod powr convrtrs and planar magntic componnts. H is currntly an IEEE mmbr. Postal addrss: Dpartmnt of Radiolctronics, Riga Tchnical Univrsity, LV-1, 1 Azns strt, Riga, Latvia. -mail: dniss.stpins@rtu.lv. 1