Phas-Variabl Control of Paralll Synchronizd Tril Bias-Flis Intrfac Circuit towards Broadband Pizolctric Enrgy Harvsting Bao Zhao, Junrui Liang, and Kang Zhao School of Information Scinc and Tchnology ShanghaiTch Univrsity, Shanghai 11, China Email: {zhaobao, liangjr, zhaokang}@shanghaitch.du.cn Abstract This ar introducs a nw has-variabl switch control for th aralll synchronizd tril bias-fli (P-S3BF) intrfac circuit, towards th broadband and high-caability izolctric nrgy harvsting (PEH) systms. By using th hasvariabl P-S3BF (PV-P-S3BF), both th lctrically inducd daming and lctrically inducd mass/stiffnss can b tund to a crtain xtnt in oration, such that to simultanously mak th dual tasks of broadband and high-caability in PEH. Th joint dynamics and harvstd owr of th PEH systms using th PV- P-S3BF circuits ar thoroughly discussd basd on th harmonic analysis and imdanc modling. Th availabl rang of PV-P- S3BF is rationally shown in th comlx imdanc lan. Th xrimntal rsults obtaind with a PCB-lvl rototyd circuit show agrmnt with th analytical rsults. Th nw PV-P-S3BF circuit ons a romising futur towards th lctrically in-situ tunabl broadband and high-caability PEH systms. I. INTRODUCTI Th izolctric nrgy harvsting (PEH) tchnology rovids solutions for convrting th ambint kintic nrgy into usful lctricity, such that to nabl som highly distributd Intrnt of Things (IoT) dvics, which orat in vibrational nvironmnts, to bcom nrgy-slf-sufficint. Th two most significant rsarch targts in this ara ar: 1) to nhanc th nrgy harvsting caability in rsonanc, and ) to broadn th bandwidth of th harvstr; in ordr words, to nhanc th off-rsonanc harvsting caability. Th circuit solutions hav shown significant contributions for making th first goal [1]. On th othr hand, th scond goal has bn xtnsivly invstigatd by adoting diffrnt mchanical dsigns []; lctrical nginrs contributd littl towards th broadband task for long. Th rason is du to th wakly or modratly couling fatur of most izolctric structurs. Th rvrs izolctric ffct was not strong nough to intrvn th mchanical vibration without advancd circuit solutions. Nw intrfac circuits k bing roosd during th last dcad sinc th first synchronizd switch harvsting on inductor (SSHI) [3]. Shu t al. [] hav ointd out that, by using th synchronizd switch circuit solutions, a wakly could PEH systm might bcom a modratly or strongly could systm. Th dynamic tuning now is ossibl to b ralizd to som xtnt by using th circuit solutions with highr PEH caability. Rcntly, som solutions hav invstigatd how to nhanc th off-rsonanc rformanc by introducing i q (t) Pizolctric quivalnt C R U v Harvsting branch D 1 C r D 3 R L V r D GL1 Bias-fli branch L i D D R1 D R3 D R GR1 M GR3 GR R1 M R3 M R C b D L1 GL3 M L1 M L3 M L V 1 U θ/ω V i q v Bias voltags ML U 1 MR3 V U 3 V 3 D L3 D L U 1 GL V 3 U 3 V U V 1 V Tim Tim Tim (b) (c) (d) Fig. 1. P-S3BF (also PV-P-S3BF) intrfac circuit [7]. Circuit toology. (b) Wavforms of P-S3BF (th in-has switch cas of PV-P-S3BF). (c) Enlargd viw of th downstairs instant. (d) Enlargd viw of th ustairs instant. a switching dlay in SSHI [5] or th synchronous charg xtraction (SCE) circuits [6]. Such tchnology is rfrrd to as PV-SSHI and PV-SCE in short in th following arts of this ar. This ar xlors th broadband rformanc of th PEH systms basd on an u-to-dat and mor caabl PEH intrfac circuit, th aralll synchronizd tril bias-fli (P- S3BF) [7]. By introducing a scond tunabl variabl, i.., th switching dlay, to P-S3BF, th nrgy harvsting bandwidth can b furthr broadnd byond othr xisting circuit solutions. II. P-S3BF INTERFACE CIRCUIT [7] Th P-S3BF circuit is a scial imlmntation of th synchronizd multil bias-fli (SMBF) conction [8]. Th basic ida of SMBF is to maximiz th owr xtraction from th izolctric sourc with minimum dissiativ ffort. Such comromis can b ralizd by sohisticatdly combining MR ML3 978-1-5386-881-/18/$31. 18 IEEE
i q (t) L v q (t) R i q (t) L v q (t) i h R C i h R R d or R C R d (b) V r V, ϕ r X C R h X C R h SEH, P-SSHI, S-SSHI, P-S3BF, tc. Z PV-P-SSHI, PV-S-SSHI, PV-P-S3BF, tc. Z Fig.. Equivalnt imdanc ntworks of PEH systms. With singlvariabl tunabl circuits. (b) With doubl-variabl tunabl circuits X ω C (nondimnsionalizd Im[ Z ] ) Largr quivalnt mass ngativ stiffnss Largr quivalnt stiffnss Largr quivalnt daming (th gross ffct of nrgy harvsting and dissiation) 6 8 1 ( Rh + Rd ) ωc (nondimnsionalizd R[ Z ]) PV-P-S3BF (two-dimnsional rgion) PV-P-SSHI (two-dimnsional rgion) Rsistiv load (on-dimnsional trajctory) SEH (on-dimnsional trajctory) S-SSHI (on-dimnsional trajctory) P-SSHI (on-dimnsional trajctory) P-S3BF (on-dimnsional trajctory) Short circuit (a singl oint) On circuit (a singl-oint) Fig. 3. Th attainabl rangs of quivalnt imdancs of diffrnt intrfac circuits. (γ =.5) multil small voltag-changing sts (for lss dissiatd nrgy) through switching transints, such that to roduc a larg voltag jum (for mor xtractd nrgy) at ach synchronizd instant. Th circuit toology and th orating wavforms of P-S3BF, i.., th aralll and M = 3 vrsion of SMBF, is shown in Fig. 1. Th izolctric quivalnt is comosd of a currnt sourc i q, which is roortional to vibration vlocity, C th izolctric clamd caacitanc, and R th lakag rsistanc rrsnting th ffct of dilctric loss, as shown in Fig. 1. Whn i q crosss zro from ositiv to ngativ, th MOSFET switchs tak actions by conducting th (M R1 and M L ), M L1, and (M R3 and M L1 ) in succssion (ach for half of an L i C cycl), such that to chang v th voltag across th izolctric lmnt in a tril-st downstairs sha, as shown in Fig. 1(c). On th othr hand, whn i q crosss zro from ngativ to ositiv, th rcirocal switchs ar turnd on in succssion for making a tril-st ustairs chang of v, as shown in Fig. 1(d). Through thos switching actions, v is mad in has with i q and its magnitud is boostd to a much highr lvl, as shown in Fig. 1(b); thrfor, th xtractd nrgy in ach cycl is largly incrasd. On th othr hand, small voltag sts hl liminat th switching loss. In gnral, P-S3BF outrforms SSHI rgarding nt harvstd owr undr th sam vibration xcitation. Or simly uts, P-S3BF has highr nrgy harvsting caability [7]. Enhancing th harvsting caability is th major, if not th only, goal of intrfac circuit dvlomnt sinc th arly studis on th PEH intrfac circuit [9]. Such targt was ralizd by incrasing th lctrically inducd daming in th wakly could PEH systms. Or, xrssing in an lctrical way, to incras th quivalnt load rsistanc obsrvd from th quivalnt currnt sourc i q. It was obsrvd through th imdanc modling that, SSHI outrforms th standard nrgy harvsting (SEH) bridg rctifir circuit bcaus it can nlarg th quivalnt ral art, i.., th rsistiv comonnt, of th quivalnt imdanc of th lctrical art in a PEH systm. Likwis, P-S3BF outrforms SSHI bcaus it furthr nlargs th quivalnt ral art of such imdanc [7]. III. PV-P-S3BF TOWARD BROADBAND PEH No mattr in SEH, aralll SSHI (P-SSHI), sris SSHI (S-SSHI), or P-S3BF, thr is only on tunabl variabl, i.., th rctifid voltag across th filtr caacitor, lik V r in Fig. 1. Fig. shows th gnral quivalnt imdanc ntwork of th singl-variabl tunabl circuits [1]. In th imdanc ntwork, th sris connctd R, L, and C form th rsonant ath, whos rsonanc frquncy corrsonds to th short-circuit izolctric structur; X, R h, and R d ar th lctrically inducd ractanc, rgnrativ rsistanc, and dissiativ rsistanc, rsctivly. Th lctrical art in Fig. is consistd of ths thr comonnts and C, which also influnc th quivalnt imdanc Z [11]. Th valus of X, R h, and R d dnd on th scific ty of intrfac circuit in us. Thy can b idntifid and quantifid with th harmonic analysis and imdanc modling [11]. Bsids, a lakag rsistanc R, which is connctd in aralll with C and th circuit, rrsnts th dilctric loss ffct in ractical izolctric matrials [1]. In th singl-variabl tunabl PEH circuits, th valus of X, R h, and R d ar functions of th nondimnsionalizd rctifid voltag Ṽr. Changing V r maks thir sum Z mov along th corrsonding on-dimnsional trajctory in th twodimnsional comlx imdanc lan [11]. Th trajctoris of som xtnsivly discussd circuits ar shown in Fig. 3. Sinc most of th trajctoris ar clos to th ral axis, all th xisting singl-variabl tunabl solutions can hardly roduc comarativ lctrically inducd mass (corrsonds to inductiv X ) or stiffnss (corrsonds to caacitiv X ) to countract th imaginary sourc imdanc at off-rsonanc conditions. In othr words, thir rsonanc-tuning caabilitis ar wak. Th adjustmnt of th quivalnt imaginary art can b mad by introducing th scond tunabl variabl, th switching has. It is ralizd by making lad or lag to th switch instants without changing th circuit toology. By tuning two circuit variabls, th availabl rang of th quivalnt imdanc bcoms a two-dimnsional ara in th comlx imdanc lan. Fig.3 shows th availabl rgions of Z in hasvariabl SSHI (PV-SSHI) and has-variabl P-S3BF (PV- 978-1-5386-881-/18/$31. 18 IEEE
Voltag and currnt (a.u.) iq v Availabl imdanc rang of PV-P-SSHI Availabl imdanc rang of PV-P-S3BF v, f Equivalnt imdanc of th corrsonding xamls ϕ θ ϕ= θ Phas (b) Phas (c) X ω C ϕ θ Phas 5 1 5 1 5 1 (d) ( Rh + Rd ) ωc () ( Rh + Rd ) ωc (f) ( Rh + Rd ) ωc Fig.. Wavforms and imdanc icturs of PV-P-S3BF undr diffrnt switching has lag ϕ (γ =.5). -(c) Wavforms with ngativ, zro, and ositiv ϕ, rsctivly. (d)-(f) Th corrsonding quivalnt Z oints of th -(c) cass, rsctivly. P-S3BF). Comard to othr xisting solutions, PV-P-S3BF not only allows th largst xtnt of quivalnt rsistanc so far (corrsonds to daming in th mchanical domain) towards highr nrgy harvsting caability, but also nlargs th availabl rang of quivalnt ractanc (corrsonds to mass/stiffnss in th mchanical domain) towards bttr rsonanc-tuning caability. Such conct is illustratd in th quivalnt imdanc ntworks in Fig. (b). Fig. shows th dtaild wavforms of PV-P-S3BF in thr cass with switch has lad, in-has condition, and switch has lag. Th has lag btwn th switching instant and th zro-crossing instant of i q is dnotd as a nw variabl ϕ. Thrfor, Fig. -(c) corrsond to th ngativ, zro, and ositiv ϕ cass, rsctivly. Th corrsonding ositions of Z in th thr cass ar shown in Fig. (d)-(f), rsctivly. Thir valus can b quantifid with th harmonic analysis and imdanc modling [11]. As w can obsrv from Fig., ngativ ϕ maks v lad i q, which roducs ositiv X in Fig. (d). It introducs an additional mass to th mchanical vibrator and dcrass its rsonant frquncy. On th contrary, ositiv ϕ maks v lag i q, which roducs ngativ X, i.., an additional stiffnss for incrasing th rsonant frquncy. Thrfor, by introducing th switching has ϕ as a nw tunabl variabl, th tunabl rang of Z has bn xtndd vrtically towards a largr imaginary art for tuning th rsonanc of th PEH systm. IV. IMPEDANCE MODELING This sction quantifis th valu of Z, as wll as its dtaild constitutiv comonnts, i.., X, R h, and R d, in PV-P-S3BF by harmonic analysis and imdanc modling. Th harmonic analysis bgins from assuming sinusoidal i h, th currnt flowing through Z, 1 i.., i h (t) = I h sin(ωt), (1) 1 Thr is a subtl diffrnc btwn i q and i h. i q = i h whn R = Mor information about th ffct of dilctric loss can b rfrrd to [1]. whr ω is th vibration frquncy, I h is th magnitud of i h. W dfin th has diffrncs from th switching oint and rctifir-conducting oint to th zro-crossing oint of i h as ϕ and θ rsctivly, as illustratd in Fig. -(c). Whn ϕ [ /, ] and θ [ ϕ, + ϕ], th switch lad condition is shown in Fig.. By assuming th bias-fli actions tak much lss tim than a vibration cycl, th izolctric voltag v can b formulatd with th icwis quations as follows v (t) = V oc Ṽ3 + cos ϕ cos(ωt), ϕ ωt < θ; Ṽ3 + cos ϕ cos θ, θ ωt < + ϕ; () Ṽ 3 cos ϕ cos(ωt), + ϕ ωt < + θ; Ṽ 3 cos ϕ + cos θ, + θ ωt < + ϕ; whr Ṽ3 = V 3 /V oc is th nondimnsionalizd V 3, nd voltag of th downstairs actions, whos maning is illustratd in Fig. 1(c); V oc = I h /(ωc ) is th nominal on-circuit voltag. Th valu of Ṽ3 can b obtaind by solving th following linar quations 1 1 Ṽ cos ϕ cos θ γ 1 γ 1 Ṽ 1 γ 1 Ṽ =, (3) 1 1 1 1 Ṽ 3 whr γ is th fliing factor of ach voltag bias fli [8]. For th switch lag condition, whr ϕ (, /] and θ [ cos 1 ( cos ϕ 1), ], v (t) = V oc Ṽ3 + cos ϕ cos(ωt), ϕ ωt < θ; Ṽ3 + cos ϕ cos θ, θ ωt < ; Ṽ3 + cos ϕ cos(ωt) cos θ 1, ωt < + ϕ; Ṽ 3 cos ϕ cos(ωt), + ϕ ωt < + θ; Ṽ 3 cos ϕ + cos θ, + θ ωt < ; Ṽ 3 cos ϕ cos(ωt) + cos θ + 1, ωt < + ϕ; () whr Ṽ3 can b obtaind by solving th quations as follows 1 1 Ṽ cos ϕ cos θ 1 γ 1 γ 1 Ṽ 1 γ 1 Ṽ =. (5) 1 1 1 1 Ṽ 3 With th icwis xrssion of v, w can furthr obtain its fundamntal harmonic v,f by doing th Fourir analysis [11]. Th icturs of v,f undr th lading, in-has, and lagging conditions ar also shown in Fig. -(c). Th quivalnt imdanc can b formulatd from th frquncy xrssions of V,f and I h, i.., Z (jω) = V,f (jω) I h (jω) = R h + R d + jx. (6) Z is a function of ω, θ (rlatd to th nondimnsionalizd rctifid voltag Ṽr), and ϕ. Thrfor, givn any dviation 978-1-5386-881-/18/$31. 18 IEEE
TABLE I SPECIFICATIS OF THE EXPERIMENTAL PEH SYSTEM. Paramtr Valu Paramtr Valu Fig. 5. Prototyd circuit of th PV-P-S3BF xrimnts [7]. R 57.1 kω L i 7 mh L.65 kh C r 1 µf C.7 nf C b.7 µf C 57.83 nf ω 59.8 Hz R 679.96 kω Acclration.9 m/s γ.5 MOSFET Vishay Si59DY driving th systm off th rsonanc, th systm can b rtund to som xtnt by adjusting th two variabls θ (or quivalntly V r ) and ϕ in PV-P-S3BF. Th circular rgion shown in Fig. 3 can b rovd by analyzing thir imdanc xrssions, th quivalnt imdanc has maximum magnitud whn R L =, i.., th bridg rctifir is always blockd undr stady stat. At this oint, th quivalnt imdanc of PV-P-S3BF is formulatd as follows Z,PV-P-S3BF = 1 ωc [ 6 1 γ 1 + γ j + 6 1 γ (cos ϕ j sin ϕ) 1 + γ ]. Th attainabl rang of quivalnt imdanc of PV-P-S3BF has a largst xtnt, as shown in Fig. 3. According to (7), th ( attainabl ) ara is in a circl sha, whos cntr is at 6 1 γ 1+γ, j and radius is 6 1 γ 1+γ. Bsids th gross ffct of Z, its scific dtaild of X, R h, and R d, can also b quantifid according to [1]. Morovr, givn th quivalnt imdanc of th mchanical art Z m = R + jωl + 1 jωc, (8) and considring th countractiv ffct of R against th PEH nhancmnt [1], th harvstd owr can b thortically obtaind according to th quivalnt imdanc ntworks in Fig., i.., P h = V qr h (7) R Z m R + Z m Z + Z R. (9) Th thortical rdiction on harvstd owr nds to b validatd by xrimnts on ractical PEH systms. V. EXPERIMENTAL VALIDATI Th xrimntal PV-P-S3BF intrfac circuit is imlmntd by carrying out th has-variabl switch control on an stablishd P-S3BF rototyd circuit [7]. Th imrovmnt in nrgy harvsting bandwidth by using PV-P-S3BF is chckd in th xrimnt. Fig. 5 shows th rototyd circuit for th PV-P-S3BF xrimnts. Th switching squnc is dlivrd by six MOSFET switchs, as shown in Fig. 1. Th lctronic switchs ar controlld by a Txas Instrumnt MSP3 microcontrollr, as shown in Fig. 5. A izolctric cantilvr, whos aramtrs ar shown in Tabl I, is xcitd by a shakr. An lctromagntic snsor mountd at th fr nd of th P h.6.. SEH thory PV-P-S3BF (ϕ = 3 ) thory PV-P-S3BF nvlo SEH xrimnt PV-P-S3BF (ϕ = 3 ) xrimnt PV-P-S3BF (ϕ = 3 ) thory PV-P-S3BF (ϕ =, i.., P-S3BF) thory PV-P-S3BF (ϕ = 3 ) xrimnt PV-P-S3BF (ϕ =, i.., P-S3BF) xrimnt SR = HM =.55 Hz 55 6 65 HM = 8.919 Hz SR = 11.85 Hz 55 6 65 (b) Fig. 6. Harvstd owr P h. SEH. (b) PV-P-S3BF. cantilvr snss th vibration vlocity for th synchronization uros. Fig. 6 shows th maximum harvstd owr P h undr diffrnt vibration frquncis and switching has ϕ in th SEH and PV-P-S3BF cass. Th ϕ = cas is just P-S3BF. Th maximum P h in PV-P-S3BF is th nvlo of th owr curvs undr diffrnt ϕ. It can b obsrvd from Fig. 6 that th half-maximum-owr bandwidth ω HM (also rfrrd to as th 3 db bandwidth in [5]) of PV-P-S3BF is 16.3% broadr than that of P-S3BF, and is 96.% broadr than that of SEH. Th bandwidth broadning ffct is mor ronouncd if w tak th half of th maximum owr in SEH as th baslin rfrnc. Th SEH rfrncd bandwidth ω SR of PV-P-S3BF is 16.7% broadr than that of SEH, as shown in Fig. 6(b). Exrimntal rsults agr with th thory in gnral. Th bandwidth broadning ffct of PV-P-S3BF is succssfully validatd. VI. CCLUSI A nw circuit solution, th has-variabl aralll synchronizd tril bias fli (PV-P-S3BF) intrfac circuit was introducd in this ar for broadning th nrgy harvsting bandwidth of th izolctric nrgy harvsting (PEH) systms. Th working rincil and imdanc modling ar rovidd for bttr undrstanding and quantification of th lctromchanical joint dynamics and harvstd owr by using PV-P-S3BF. Exrimnts ar carrid out for validating th thortical analysis. Th roosd solution and analysis rovid a nw insight towards th dsigns of broadband PEH systms. 978-1-5386-881-/18/$31. 18 IEEE
ACKNOWLEDGMENT Th work dscribd in this ar was suortd by th grants from National Natural Scinc Foundation of China (Projct No. 61177) and ShanghaiTch Univrsity (Projct No. F-3-13-3). REFERENCES [1] G. D. Szarka, B. H. Stark, and S. G. Burrow, Rviw of owr conditioning for kintic nrgy harvsting systms, IEEE Trans. Powr Elctron., vol. 7, no.,. 83 815, 1. [] L. Tang, Y. Yang, and C. K. Soh, Toward broadband vibration-basd nrgy harvsting, J. Intll. Matr. Syst. Struct., vol. 1, no. 18,. 1867 1897, 1. [3] D. Guyomar, A. Badl, E. Lfuvr, and C. Richard, Toward nrgy harvsting using activ matrials and convrsion imrovmnt by nonlinar rocssing, vol. 5,. 58 95, 5 5. [] Y. Shu, I. Lin, and W. Wu, An imrovd analysis of th sshi intrfac in izolctric nrgy harvsting, Smart Matr. Struct., vol. 16, no. 6,. 53, 7. [5] P.-H. Hsih, C.-H. Chn, and H.-C. Chn, Imroving th scavngd owr of nonlinar izolctric nrgy harvsting intrfac at offrsonanc by introducing switching dlay, IEEE Trans. Powr Elctron., vol. 3, no. 6,. 31 3155, 15. [6] E. Lfuvr, A. Badl, A. Brns, S. Sok, and C.-S. Yoo, Powr and frquncy bandwidth imrovmnt of izolctric nrgy harvsting dvics using has-shiftd synchronous lctric charg xtraction intrfac circuit, J. Intll. Matr. Syst. Struct., vol. 8, no.,. 988 995, 17. [Onlin]. Availabl: htts://doi.org/1.1177/15389x17791 [7] Y. Zhao and J. Liang, Synchronizd tril bias-fli circuit for izolctric nrgy harvsting nhancmnt: Oration rincil and xrimntal validation, in 16 IEEE Enrgy Convrsion Congrss and Exosition (ECCE). IEEE, s 16. [8] J. Liang, Synchronizd bias-fli intrfac circuits for izolctric nrgy harvsting nhancmnt: A gnral modl and roscts, J. Intll. Matr. Syst. Struct., vol. 8, no. 3,. 339 356, fb 17. [9] G. K. Ottman, H. F. Hofmann, A. C. Bhatt, and G. A. Lsiutr, Adativ izolctric nrgy harvsting circuit for wirlss rmot owr suly, IEEE Trans. Powr Elctron., vol. 17, no. 5,. 669 676,. [1] J. Liang, H. S.-H. Chung, and W.-H. Liao, Dilctric loss against izolctric owr harvsting, Smart Matr. Struct., vol. 3, no. 9,. 91, 1. [11] J. Liang and W.-H. Liao, Imdanc modling and analysis for izolctric nrgy harvsting systms, IEEE/ASME Trans. Mchatron., vol. 17, no. 6,. 115 1157, 1. 978-1-5386-881-/18/$31. 18 IEEE