Design Considerations for Achieving ZVS in a Half Bridge Inverter that Drives a Piezoelectric Transformer with No Series Inductor

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1 Design onsideaions fo Achievg ZS a Half Bidge Invee ha Dives a iezoelecic Tansfoe wih No Seies Induco Svelana Bonse and Sa Ben-Yaaov* owe Eleconics aboaoy Depaen of Elecical and opue Engeeg Ben-Guion Univesiy of he Negev.. Box 653, Bee-Sheva 8405, ISAE hone: ; Fax: ; Eail: sby@ee.bgu.ac.il; Websie: Absac A geneal pocedue fo aag sof swichg duco-less half-bidge piezoelecic ansfoe (T) vee was analyzed by applyg he equivalen cicui of he T device. Sof swichg capabiliy of he T was deleaed and deailed guideles ae given fo he load and fequency boundaies, volage ansfe funcion and he oupu volage ha will eep he opeaion unde ZS condiions. The analysis aes o accoun he axiu powe dissipaion of he T, which is used o bd he peissible powe ansfe hough he device. The analyical esuls fo he half-bidge duco-less T vee whee veified by siulaion and expeiens fo a adial vibaion ode T. I. INTDUTIN As iezoelecic Tansfoe (T) echnology is developg, Ts ay becoe a viable alenaive o agneic ansfoes vaious applicaions [, ]. owe supplies ha eploy Ts, ahe han he classical agneic ansfoes, could be ade salle size - an aibue ha is ipoan a nube of applicaions such as baey chages, lapop copues supplies, fluoescen lap dives ec. Howeve os of ealie designs of T based convees/vees used addiional seies ducos o achieve Zeo olage Swichg (ZS) condiion [3-7]. By his, he T advanages of sall size wee adveenly los. I was aleady shown [8] ha by usg specific chaaceisics of he T, ZS could be achieved wihou any addiional eleens. This can be accoplished when he cicui is opeag a a fequency ha is highe han he esonance fequency of he T and sufficien enegy is available o chage and dischage he pu capaciance of T dug he swichg dead ie. Thus, by uilizg he chaaceisics of he T, he swiches of he vee will opeae unde ZS condiions educg significanly he un-on swichg - wihou he need o clude a seies duco. In addiion, he heen pu capaciance of he T wos as a un-off snubbe fo he powe swiches. This fuhe deceases he un-off volage spies and hus he un-off losses of he swiches. This pape pesens a copehensive analysis of he of heen sof swichg capabiliy of Ts. losed fo equaions esiae he load and he fequency boundaies ha allows sof swichg powe vee/convee buil aound a given T. D GS GS D D I Z i() Fig.. Equivalen cicui of a half bidge vee divg a T aound he esonan fequency. II. ANAYSIS AND DESIGN F ZS T WE INETE A. Analysis of ZS ondiion fo Half-Bidge Invee The analysis is caied ou on a half bidge vee shown Fig.. I cludes wo bi-diecional swiches and cludg ani-paalleled diodes D, D, and a T, ha is epesened by an equivalen seies-paallel esonan cicui n. he paaees,, epesen he echanical behavio of he T, is he pu capaciance of T plus he oupu capaciance of he swiches, is he efleced n oupu capaciance, whee is he oupu dielecic capaciance and n is he ga, n is he efleced load esisance [3]. The swiches and (Fig. ) will noally be powe MSFETs and will clude an heen ani-paallel diodes D and D. The swiches ae diven alenaely by ecangula volages GS and GS wih a sufficienly long dead ie. Fig. depics seady-sae cuen and volage wavefos he vee fo an opeag fequency ha is highe han he esonance fequency. The chagg pocess of he capacio is consideed wih efeence o Fig.. A he san he dive volage GS uns FF. Tansiso is sill ep he FF sae by he dive volage GS. Boh diodes ae evesed biased and ea he FF condiion. o o *oespondg auho

2 GS GS I i() Fig.. The seady-sae cuen and volage wavefos of he ZS T vee. Assug ha he of he newo is high, he susoidal cuen wavefo of he esonan cicui can be epesened by: i() I s( ψ) () whee I and ψ ae he cuen pea and he iial phase especively (efeed o he phase of he fis haonic of he pu volage). When ansiso is uned FF a he san 0 his cuen is diveed fo ansiso o he capacio. Thus, he cuen hough he shun capacio dug 0 < < is: i () i() I s( ψ) () This cuen chages he capacio and he volage acoss he capacio (and hence acoss he swich ) gadually ceases fo zeo o D. If he cuen i S hough ansiso is foced o dop quicly o zeo (by a pope gae dive) swichg losses he ansiso will be low. A, he volage acoss he capacio eaches D, heefoe he diode D uns N and he cuen i() is diveed fo he shun capacio o he diode D. The volage acoss he op swich becoes zeo. The diode D conducs dug he eval. When he volage deceases o D a he san, he dive volage GS uns he uppe ansiso N. The ansiso is N dug he ie eval 3. A 3, i uns FF aga. Sce ansiso sill eas FF, he cuen of he esonan cicui dischages he shun capacio, deceasg DS and heeby ceasg DS. The dischagg pocess of is ag place dug he ie eval fo 3 o 4. When he volage acoss eaches zeo, he diode D sas o conduc a 4 and he volage acoss he op swich S becoes zeo. Sce he chaggdischagg pocess aes place when he swich cuen is zeo (boh swiches ae FF) he swichg losses could be ade sall. In fac, he capacio wos as a un-off snubbe fo he swiches and of he half-bidge vee. B. The Ma Assupions The analysis is caied ou unde he followg appoxiaions [9]: ) The capacio chagg ie is shoe han he swichg dead ie. ) The capacio is chaged by a consan cuen. 3) The pu volage () is assued o be a syeical ecangula wavefo (sead of apezoidal). (I can be seen, ha his assupion is elevan because he diffeence beween he fis haonic apliude of he ecangula and apezoidal wavefos is sall). 4) The powe losses on T ae liied o 5-0% of he oupu powe. In ode o ensue ZS fo he swiches, he pu capacio has o be chaged-dischaged wih he swichg dead ie which duaion is less han T/4, whee T is he peiod of he esonan cuen ha developed dug he dead ie (see below). The chagg pocess begs a 0. If he chagg ie is uch shoe han he cycle T/f, he chagg cuen can be assued o be consan and given appoxiaely by: I i (0) I s ψ (3) The chagg pocess ends when he capacio volage eaches D. Hence, he chagg ie is appoxiaely [9]: D π ()p I s ψ I s ψ π Z < T s ψ 4 whee ()p is he fundaenal coponen of he ecangula wavefo, and Z is he pu ipedance of he esonan an (no cludg ). In ode o ansfe sufficien enegy o he oupu he vee has o opeae close o he fequency of axiu oupu powe and unde high efficiency condiions [8]. The powe dissipaed by he T has o be liied o 5-0% of he oupu powe, o achieve efficiencies he ode of 90-95%. Fo exaple, if he powe dissipaion of T is liied o be W, he oupu powe of 0W will obaed wih 90% efficiency (assug hee a lossless vee).. Noalized Model fo Sof Swichg T Invee In ode o genealize he analysis, we developed a noalized odel fo T vee ha is applicable o any T ha can be descibed by he esonan newo of Fig.. All paaees of he vee consideed his sudy ae noalized as follows: The a iial paaees ae defed as: a ; b ; o ; The noalized pu ipedance () Z is defed as he aio of he pu ipedance of he T - Z o he efleced load esisance : (4) (5)

3 Z Z A + jb + j + j + j + + j a A + a whee: a a B + The noalized chagg ie is defed as he aio of he chagg ie o he swichg peiod T. (Noe ha has o be less han ¼ - [8]-[9]): π Z Z b (7) T T s ψ 4 s ψ whee ψ is he noalized pu ipedance phase angle (ha is opposie o he iial cuen phase (): Z ψ ag (8) The volage ansfe aio o is he aio of he oupu volage ou o he pea of he fis haonic of he pu volage ()p (Fig. ): ou o (9) ()p + Z The noalized powe dissipaed by he T, is defed as he aio of he T powe dissipaed by he o he oupu powe ou : a + (0) ou The vee efficiency is he aio of he oupu powe ou o he pu powe : (6) ou Z η o () cos( Z ) The axiu oupu volage is eached a he equivalen esonan fequency. Sce he equivalen esonan fequency is close o he seies esonan fequency one can eplace he noalized esonan fequency by he faco + ε, whee ε is a sall nube ha epesens he deviaion fo he noalized seies esonan fequency. By ag he deivaive of (9) and equag i o zeo we oba an appoxiae expession fo ε: ε a + () The noalized opeag fequency (he aio of he opeag fequency o he seies esonan fequency ) can now be expessed as: ( + ε) (4) whee he noalized fequency faco / is he aio of he opeag fequency o he fequency of he axiu oupu powe. D. Design guideles Given: he T vee oupu volage ou and he T paaees -,,,,, n o. To be evaluaed: he fequency ange, he oupu powe and he load boundaies fo sof swichg. The geneal design seps: ) n he basis of he specificaions of he given T we calculae he paaees a, b, (5). ) Fo diffeen we plo () (6), (7), (3), (4). 3) Fo he sae we calculae () (0). 4) Sof Swichg is achieved he ange whee () < 0.5. The uppe bounday fo is saed by he equieen () 0. 5 and he lowe bounday fo is bounded by he T powe dissipaion lii. 5) Fo he paaee and paaees of T we calculae he load esisance : (5) 6) Based on he sof swichg boundaies of he noalized fequency faco, he seies esonan fequency and he noalized load faco, we calculae he fequency boundaies fo ZS: f + (6) π a + Fo cons one can calculae he ansfe funcion o f ( ) o fo cons - he ansfe funcion o f (). Exaple. Given: The T is a adial vibaion ode piezoelecic ansfoe (T-, Tansone ) [0], he powe dissipaion of T is liied o 0% and he equied pea oupu volage is ou(p) 30.

4 To be evaluaed: he fequency ange, he pu volage ange and he load ange ha ensues sof swichg. This T has one laye a he pu side and one laye a he oupu side. The diaee of he T is 9; he hicness of he pu laye is.5, he hicness of he oupu laye is.9. Applyg he H4395A Ipedance Analyze, he paaees of he siplified elecical equivalen cicui fo naow fequency ange aound is echanical esonan fequency wee esiaed o be: M.6Ω,.9nF,.547nF, 0pF, 5.H, f es 8.3Hz, n Fo hese cicui paaees he noalized odel paaees ae calculaed o be: a.9, b.46, As a pepaaion fo he design we geneae he followg plos: a) Fig. 3, based on equaion (7), shows he plos of he noalized chage ie as a funcion of he noalized fequency faco fo diffeen noalized load faco. I can be seen ha he uppe lii fo o coply wih < 0. 5 is The lowe bounday fo he load faco is deeed by < 0. ( 0. 3 ) (0). b) Fig. 4, based on equaion (9), shows he ansfe ou funcion o as a funcion of he noalized fequency faco fo he sae noalized load facos. These plos ae hen used o calculae he pu volage ange and powe ange fo which ZS can be achieved ag o accoun he design consas and he axiu powe dissipaion on T. Fo any given load () he coespondg plos fo Fig. 3 and Fig. 4 can be cobed o a sgle plo. Fo exaple Fig. 5 is fo 0. 5 (The sae plos can be buil fo diffeen values, o cove he desied powe ange). In his case sof swichg fequency boundaies ae.003 < <.05 (o, fo (7), 8770 < f < 360Hz ). Fo his fequency egion he ansfe funcion o ha can be achieved is 0.8 > o > 0. appoxiaely. The ange of ou(p) he pea pu volage (p) will hus be o 37.5 < < 36 especively (Fig. 6). Exaple. Given: he sae T as he Exaple, he powe dissipaion on T is liied o 0% of he oupu powe, he pea pu volage (p) 50 and load esisance 30Ω. To be evaluaed: he boundaies of he oupu volage and oupu powe fo sof swichg opeaion , η 97% 0.5, η 94.5% 0.3, 90.5% Fig. 3. Noalized chagg ie as a funcion of he noalized fequency faco fo diffeen noalized load facos he ange 0.3 o Daa is fo T-, Tansone [0]. o Fig. 4. olage ansfe funcion o as a funcion of he noalized fequency faco fo diffeen noalized load facos he ange of 0.3 o The T unde he calculaions is (T-, Tansone ) [0]. o o Fig. 5. olage ansfe funcion o and he noalized chagg ie as a funcion of he noalized fequency faco fo noalized load faco 0.5 ( 30Ω ). The T unde he calculaions is (T-, Tansone ) [0]

5 ( p) ou( p) 30 30Ω Fig. 6. ea pu volage (p) as a funcion of he noalized fequency faco fo he consan oupu pea volage ou (p) 30 and he load esisance 30Ω. Daa is fo T-, Tansone ) [0]. ou ( p) 40 30Ω ou ou ou Fig. 7. The pea oupu volage ou(p) and he oupu powe ou as a funcion of he noalized fequency faco fo pea pu volage (p) 50 and load esisance 30Ω. Daa is fo T-, Tansone ) [0]. GS IN The fequency boundaies fo sof swichg is avaluaed fo Fig. 5 o be.003 < <. 05 (o, fo (7), 8770 < f < 360Hz ). The powe dissipaion of he T fo his load faco and his fequency ange is 9% appoxiaely The powe dissipaion of he T fo his load faco and his fequency ange is 9% appoxiaely. The ansfe funcion o ha coesponds o his fequency egion is 0.8 > o > 0. (he sae as Exaple.). oncequenly, he ange of pea oupu volage ha can be obaed (unde sof swichg condiions) ou(p) o is 40 > ou (p) >, and he ange of he oupu powe ou(p) ou will be 6.W > ou > 0.46W especively (Fig. 7). The sae possedue can be caied ou fo diffeen load esisences he sof swihg ange o oba he whole ange of oupu volages and powes. III. SIMUATIN AND EXEIMENTA ESUTS The poposed odel was veified by siulaions and expeiens. Fig. shows he swichg ig diaga of he half-bidge vee (Fig. ) obaed by siulaion. The opeaion fequency was assued o be f 0Hz (.04) and he load esisance 30Ω (0.5). The calculaed noalized chagg ie was 0. 6 while he siulaed noalized chagg ie was 0.67 (Fig. ). T Fig. 8 shows he expeienal volage cuves unde he sae condiions as above. The expeienal noalized chagg ie was found o be T I. NUSINS This pape pesens a copehensive analysis of he of heen sof swichg capabiliy of Ts. losed fo equaions, developed his sudy, esiae he load and he fequency boundaies ha allow sof swichg powe vee buil aound a given T. A geneal pocedue fo aag sof swichg duco-less half-bidge piezoelecic ansfoe vee was sudied analyically and veified by he siulaion and he expeien. The analyical esuls wee found o be a good ageeen wih siulaion and expeien. Fig. 8. Expeienal volage wavefos of he half-bidge duco-less T vee: GS (uppe plo), IN (lowe plo). peag fequency f0hz, load esisance 30 h. Daa is fo T-, Tansone ) [0]. EFEENES []. Y. and F.. ee, iezoelecic Tansfoe and Is Applicaions, oceedgs of E Sea, pp.9-36, 995. []. Y. and F.. ee, Design of a iezoelecic Tansfoe and Is Machg Newos, oceedgs of IEEE ES 94 ecod, pp

6 [3]. Y., Design and Analysis of iezoelecic Tansfoe onvees, h.d. Disseaion, igia Tech. July 997. [4] T. Zaisu, T. Inoue, M. Shoyaa, T. Noiya, F.. ee, and G.. Hua, iezoelecic Tansfoe peag Thicness Exensional ibaion and is Applicaion o Swichg onvee, oceedgs of IEEE ES 94 ecod, pp , 994. [5] H. Kaedhashi, T. Hidaa, T. Noiya, M. Shoyaa, H. gasawaa and Y. ha, Eleconic Ballas Usg iezoelecic Tansfoes fo Fluoescen aps, oceedgs of IEEE ES 98 ecod, pp. 9-35, 998. [6] T. Noiya, M. Shoyaa, T. Zaisu, T. Inoue, Zeo-olage-Swichg Techniques and Thei Applicaion o High Fequency onvee wih iezoelecic Tansfoe, oceedgs of IEN 94, pp , 994. [7] M.J ieo, J. Diaz, J.A. Ma, F. Nuno, A ey Siple D/D onvee Usg iezoelecic Tansfoe, oceedgs of IEEE ES 00 ecod, pp , 00. [8] ay., Fed. ee, Eic M. Bae and Dan Y. hen, Induco-less iezoelecic Tansfoe Ballas fo ea Fluoescen aps, ES owe Eleconics Sea oceedgs, pp , 000. [9] M. K. Kazieczu and D. zaowsi, esonan owe onvees, John Wiley & Sons, Inc., 995, pp [0] Face o., A, USA

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