Frequency Tracking to Maximum Power of Piezoelectric Transformer HV Converters under Load Variations

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1 Fequency Tacking t Maximum Pwe f Piezelectic Tansfme HV Cnvetes unde Lad Vaiatins Sam Ben-Yaakv* and Simn Lineykin Pwe Electnics Labaty Depatment f Electical and Cmpute Engineeing Ben-Guin Univesity f the egev P. O. Bx 653, Bee-Sheva 84105, ISRAEL Phne: ; Fax: ; sby@ee.bgu.ac.il; Website: Abstact-The pblem f maximum pwe pint tacking f high utput DC vltage cnvetes that apply Piezelectic Tansfmes (PT and vltage dubles was studied theetically and expeimentally. It was shwn that the peating fequency f the PT, at which maximum vltage gain is eached, is a functin f the lad. Hence, unde lad vaiatins, and t vecme paametes instability, thee is a need f sme mechanism f fequency tacking that will help t lck the peating fequency t the ptimum ne. The ppsed methd t achieve fequency tacking is based n a Phase Lcked Lp (PLL. The PLL inputs ae the phase f the input vltage diving the PT and the phase f the cuent flwing thugh ne f the vltage duble dides. Theetical analysis, veified by expeiments, shws that when the phase shift f the dide cuent elative the phase f the input vltage is ze, the vltage gain f the system is at its maximum pint. By applying this appach, the system peatin can be made independent n input vltage, lad vaiatins, tempeatue (within pemitted ange, and the spead and nn-lineaity f the PT paametes, as well thei dift with time. I. ITRODUCTIO The main advantages f Piezelectic Tansfmes (PTs ae ptential lw cst, small size, lw pfile, gd insulatin capability and the absent f windings and hence magnetic field. In sme specific applicatins, PTs ae supei t electmagnetic tansfmes, making the PT a gd design chice. Amng these is the geneatin f a lw pwe, High DC Vltage (HV. Rsen type (Fig. 1 PTs have a high gain ati that, when cmbined with excellent insulatin ppeties f the PT, make it a gd candidate f the cnstuctin f cmpact HV cnvetes up t few kv. Since the PT is a esnant element, its utput t input vltage gain is stngly dependent n the peating fequency [1]. Hence, t maintain maximum utput vltage unde vaiable peating cnditins (lad vaiatin, tempeatue changes and cmpnents tleances it is necessay t lck the peating fequency t the ne that will ensue highest pssible utput vltage f any given lad. As a peequisite f slving the fequency-tacking pblem, ne needs fist t find a paamete that can be used as a measue f the deviatin fm the desied fequency. Diffeent appaches have been suggested f fequency tacking f PTs dives. In [] the phase angel between input vltage and input cuent was used as a citein while in [3], the phase angel between input and utput vltage was used as a measue f the deviatin fm the fequency f maximum gain. Unftunately, these citeia ae lad dependent and culd be used nly ve a naw lad esistance ange. The difficulty in lcating the ptimum tacking paamete can be appeciated by cnsideing the equivalent cicuit f a typical PT (Fig. a and its seies esnance epesentatin (Fig. b. i in 735pF V in b a V in 01mH C in L C R m C in L i i 4.5pF 63Ω V (a C 1: + - R m V ' i C c 5.5pF d V R R C Fig. 1. Rsen type piezelectic tansfme. (b Fig.. Equivalent cicuit f a PT (a Oiginal equivalent cicuit (b Simplified equivalent cicuit eflecting secnday t the pimay side. Values ae f PXE43, Philips, peating aund 73 khz. *Cespnding auth

2 As can be easily bseved fm Fig. a [1], the angula fequency f the maximum utput t input vltage ati will be between ( C C /( L C C + f high esistance lads (clse t the pen cicuit situatin, lad is negligible and 1 / L C f lw esistance lads, when C is c pactically shted. Thus, the fequency f the maximum utput t input vltage ati is a stng functin f the lad esistance. Hweve, since the seies esnance banch (Fig. b is espnsible f the input t utput pwe tansfe, it stands t easn that maximum vltage gain will be btained when the peating fequency is lcked t this seies esnance. In this study we expled this pssible citein f fequency lcking t maximum pwe and ppse a nvel methd f btaining a eliable bipla signal that is a measue f the deviatin fm the ptimal fequency. It is then demnstated hw this signal can be used t lck the fequency t the ptimal ne. II. THE ROSE TYPE PT I HV APPLICATIOS The Rsen-type piezelectic tansfme 48x1xmm (Phillips [4] was chsen f pesent eseach (Fig. 1. This unit has a lage utput t input vltage ati at the fequency f the maximum utput vltage, elatively high pwe (up t 5 W, and high input t utput insulatin (tens f kilvlts. The equivalent cicuit f a PT peating nea its esnance pint (Fig. a includes a esnant netwk (L, C, Rm that emulates the effect f the mechanical vibatin and dependent suces that expess the mechanical t electical enegy tansfmatin [1]. The mdel als cmpises the physical dielectic capacits (Cin, C that ae fmed by the input and utput electdes. Since the netwk is highly selective it will pass, with easnable gain, nly fequencies that ae in the vicinity f the esnant fequency. T simplify the analysis sme equivalent tansfmatins f the equivalent cicuit can be applied. Fist, eflectin f the utput pat (ight-hand side f Fig. a f the equivalent cicuit t the input side. R and C f the equivalent cicuit ae tansfmed t R and C. Output vltage V is tansfmed t V R R C C (1 ( V V (3 Secndly, the paallel netwk R, C is tansfmed t a seies fequency dependent netwk R, C (Fig. b, whee: R R (4 ( 1+ C R ω ( 1+ C ω R C (5 CR ω The vltage tansfe functin f a PT (in tems f equivalent cicuit paametes is V Vin ( s C R s ( 1+ C R s ( 1+ C ( R + L s s C R s + m As ne can see, the system is f thid de. An analysis f this system is given in [1]. In a typical HV applicatin, ne wuld use a vltage duble t bst the utput vltage. Hence, the utput sectin will be cnstucted as shwn in Fig. 3a, whee C f is the utput filte capacit and is the lad esistance. Assuming that the quality fact (Q f the PT is high, the cuent thugh the pimay seies esnant cicuit i will be sinusidal. This cuent, afte being tansfeed t the secnday, chages and dischages the capacit C f the utput sectin (Fig. 3b. As shwn in [5], the vltage duble and lad sectin can be epesented as an equivalent eactive lad (a esist in paallel t a capacit. Cnsequently, the gain functin (6 is valid f this case t except that the lad esistance R and C in Fig. a need t be eplaced by an equivalent esist and capacit espectively. (6 III. CRITERIA OF MAXIMUM POWER POIT FREQUECY As shwn in [1], taking the deivative f the abslute value f (6 and equating it t ze can be used t deive the fequency f maximum vltage gain. This esults in a thid de equatin f the fm f (7. i V C i D1 i D _ i V L C + - V C d π c θ D (a i D1 i D D 1 C f π θ V L (b Fig. 3. (a Output stage f PT with vltage-duble ectifie. (b Vltage-duble wavefms.

3 C 6 4 R ( C L R + 4C C L R + 4C C L R C C R R x CC L R x 0 whee: x(πf max, f max fequency f the maximum f PT s tansfe functin. The ppsed citein f maximum vltage gain is ze phase-shift between input vltage V in and vitual cuent i f esnant banch f the equivalent cicuit (Fig. b. The atinal f this hypthesis is that maximum utput pwe will be btained when the PT is diven at the seies esnance fequency. This is futhe suppted by the bsevatin made in [1] that the behavi f (6 is like that f secnd de RLC band-pass filte, because within the R ω and naw band aund the esnant fequency, ( C change slwly. Based n the simplified equivalent cicuit f Fig. the i jω is (8. V tansfe functin ( i V in ( jω 1 L C in eq jωceq ω + jωr C whee R eq (ω and C eq (ω ae expessed in (9 and (10 as a functin f the paametes shwn in Fig. : Req Rm + R (9 CC Ceq (10 C + C Fm (8 ne can see that ze phase-shift between i and V in ccus when the imagine pat is ze, i. e: ( ω ω 0 eq eq (8 1 L Ceq pt pt (11 : ω pt 1 LCeq( ωpt (1 Applying (4, (5, (9, (10 and (1 the fequency f ze phase-shift f pt : 50 0 f max - f pt f Hz pt Ph( i f max Deg k 1M 1.5M M.5M 3M 3.5M R Fig. 4. Phase f i when ff max (dashed-line. And diffeence between f max and f pt (slid line m This fequency f seies esnance f equivalent cicuit is nt identical t f max but is vey clse t it [1]. F the expeimental high vltage PT used in this study, the maximum diffeence between f max and f pt is less then 50Hz (less then 0.1% f peatin fequency and phase-shift f the i at f max is less then 1.º (Fig. 4. Fig. 5 shws the ati f PTs utput pwe at f pt t the utput pwe at f maxt. These numeical values clealy pint ut t the fact that f pt is a vey gd appximatin f f max. Hence, the phase shift f i can be used f all pactical pupses as a sense signal f deviatin fm f max. The bjective f the tacking system will thus t ze this phase shift. IV. PROPOSED TRACKIG METHOD The esults f sectin III suggest that the maximum gain is eached when the phase angel between the input vltage V in and i is ze. Unftunately, thee is n diect way t measue this cuent its phase since thee is n physical access t the (vitual seies banch. This is vecme, in ppsed methd, by an indiect measuement that makes use f the bsevatin that cuent f dide D is in fact a sample f the cuent i (Fig. 3b. te, in paticula, that D will stp cnducting when the plaity f the cuent i is evesed. Hence, this plaity evesal instant can be used as an indicat f the phase f the seies cuent. This ppsed sensing methd is demnstated in Fig. 6. Cmp1 and Cmp ae used t geneate tw squae waves; ne is synchnized t V in while the secnd ne is synchnized with i. The phase angel between V in and i. can thus be measued by feeding these tw signals t a phase detect. ( C L C C R C R CCR + C R CL + 4C CL R + (13 πc R 8C L P( f pt P( f max 1M M 3M 4M Fig. 5. The ati between the utput pwe f PT diven at f pt t the utput pwe at f max as a functin f R. R (7

4 V in PT 15V 10k 15V D 4.7k 4.7k CL cmp 1 V R 1 cmp V L V 3 V 4 p(v in p(i d Fig. 6. T phase detect D 1 V ut Ppsed methd f extacting the phase signals f V in and i. V. EXPERIMETAL RESULTS The expeimental cicuit (Fig. 7 included a Phase Lck Lp (PLL fed by the tw phase signals. The digital fequency phase detect f the PLL (CD4046A cmpaes these ectangula wavefms and feeds the VCO by the phase e signal. Typical expeimental wavefms ae shwn in Figs A bias netwk (B was used t slightly shift the ze pint such that fequency lcking is btained when thee is a small phase shift between the Cmp1 and Cmp signal. This was fund necessay f the cmpensatin f the phase shift caused by the paasitic capacitances f the dides used as clamps (Fig. 7. This phase ffset was fund t be cnstant and independent f lad esistance. Pactical designs f this tacking system shuld attempt t minimize this paasitic effect by chsing lw capacitance dides. The fequency tacking system was tested by subjecting it t a lad vaiatin (Fig. 11. Fist, the pen lp utput vltage as a functin f the dive fequency was measued f each lad (Fig. 1. The plt clealy shws that maximum utput vltage is btained at diffeent fequencies f 1 and f, cespnding t 1.MΩ and 1.76MΩ espectively. It is thus expected that when the lad is vaied peidically between the tw values, unde clsed lp, the utput vltage shuld vay between peaks f the cuves with amplitude A 1, Fig. 1 (fm 150.5V t 178.5V. Fig. 13 shws the peatin unde clsed lp cnditins. The utput vltage vaiatins as well as the fequency hpping matched the expected nes (Fig k 10k High vltage 370uH 0.u V in D 1 V ut PT 15v 10k 15v D C L 4.7k 4.7k V 3 V V 1 4 V p(v in p(i d 10.n IR 110 dive Q FF Q B 15v 4.k 1k 1.5k 3.3k 1n f 39k VCO Phase detect CD4046A Fig. 7. Expeimental setup f the ppsed fequency tacking t maximum utput vltage. Fig. 8. V in (uppe tace and V (lwe tace (see Fig. 6 at the seies esnance fequency. Fig. 9. V 1 (uppe tace and V (lwe tace at the seies esnant fequency.

5 V L,V Fig. 10. V 3 (uppe tace and V 4 (lwe tace f the cmpaats utputs (Fig. 6. In figues 14 and 15 the system was diven by fixed fequencies. In Fig the fequency f peatin was t f 1 (Fig. 1 while in Fig the fequency cespnds t f. The amplitudes f the utput vltage steps wee fund t be equal t the expected ne A and A 3 (Fig. 1 espectively. The esults f this expeiment suggest that the expeimental setup is functining as expected. VI. DISCUSSIOS AD COCLUSIOS The ppsed tacking methd ffes a way t lck t the fequency that pvides the maximum utput pwe f any lad. This culd be useful in vaius applicatins that need t geneate high utput vltage (e.g. inizatin equipment. By applying the ppsed appach, the system peatin can be made independent n input vltage, lad vaiatins, tempeatue (within pemitted ange, and the spead and nn-lineaity f the PT paametes, as well thei dift with time. The phase detectin methd ppsed hee can als be used in cases that call f utput vltage egulatin. In such cases, a simple feedback lp via a Vltage Cntlled Oscillat (VCO wuld be ambiguus. If, say, the utput vltage is t lw, shuld the fequency be inceased deceased? This ambiguity can be eslved by applying the phase detectin methd ppsed hee that geneates a clea unequivcal bi-pla signal. The ppsed methd was veified expeimentally and it is demnstated that the cntl cicuity needed f the implementatin is simple and can be easily cnstucted fm ff the shelf cmpnents. V ut 1.M fm geneat 560k f 1 f A 1 A 3 A 1.76MΩ 80 1.MΩ f, khz Fig. 1. Steady state utput vltage as a functin f the peatin fequency f, f tw values f the lad esistance. (V in 0.3V. V ut Fig. 13. The system with PLL cntl. Amplitude f V ut is equal t A 1 f Fig. 1. is vltage n the lp filte, (VCO input, Fig. 7. V ut Fig. 14. The system withut PLL cntl. Dive fequency is f 1 - the fequency f esnance when 1.M. Amplitude f V ut is equal t A f Fig. 1. is the lp-filte vltage, (VCO input, Fig. 7. V ut GD Fig. 11. The vaiable lad. -5v Fig. 15. The system withut PLL cntl. Dive fequency is f - the fequency f esnance with 1.76M. Amplitude f V ut is equal t A 3 f Fig. 1. is the lp-filte vltage, (VCO input, Fig. 7.

6 [1] G. Ivensky, I. Zafany, and S. Ben-Yaakv, Geneic peatinal chaacteistics f piezelectic tansfmes, IEEE PESC 00, vl. 3, pp , June 000. []. Vlket, "DC-DC cnvete with vey high insulatin capability," Eupean Cnfeence n Pwe Electnics and Applicatin EPE 99, pp.1-8, Sep [3] S.akashima, H. Ogasawaa, T. inmiya, and H. Kakehashi, "Piezelectic-tansfme invete with REFERECES maximum efficiency tacking and dimming cntl," IEEE APEC'0, vl. 1, pp , Mach 00. [4] Philips Cmpnents, Applicatin nte Phillips magnetic pducts: Piezelectic tansfmes, ethelands: Philips Cmpnents, [5] G. Ivensky, M. Shvatsas, and S. Ben-Yaakv, "Analysis and mdeling f a piezelectic tansfme in high utput vltage applicatins," IEEE APEC 00, pp , 000.