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: +97-8-646-1561; Fax: +97-8-647-949; Email: sby@ee.bgu.ac.il; Website: www.ee.bgu.ac.il/~pel 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
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.
C 6 4 R 4 6 4 4 4 6 4 4 6 4 ( C L R + 4C C L R + 4C C L R C C R R x 6 4 3 4CC 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 40-0. 30 0 10 0 f Hz pt Ph( i f max Deg -0.4-0.6-0.8 500k 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 -1 4 3 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 1 0.9999 0.9998 0.9997 0.9996 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
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. 8-10. 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. 1. 4.7 4.7 10k 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.
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. 14 - the fequency f peatin was t f 1 (Fig. 1 while in Fig. 15 - 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 0 180 160 140 10 100 f 1 f A 1 A 3 A 1.76MΩ 80 1.MΩ 60 70 71 7 73 74 75 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.
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