Review of energy harvesting techniques and applications for microelectronics

Re iew o Ene gy Ha es ing Techniques and Applica ions o Mic oelec onics Lo e o Ma eu and F ancesc Moll Uni e si a Poli `ecnica de Ca alunya Dep . o Elec onic Enginee ing Ba celona, Spain ABSTRACT The ends in echnology allow he dec ease in bo h size and powe consump ion o complex digi al sys ems. This dec ease in size and powe gi es ise o new pa adigms o compu ing and use o elec onics, wi h many small de ices wo king collabo a i ely o a leas wi h s ong communica ion capabili ies. Examples o hese new pa adigms a e wea able de ices and wi eless senso ne wo ks. Cu en ly, hese de ices a e powe ed by ba e ies. Howe e , ba e ies p esen se e al disad an ages: he need o ei he eplace o echa ge hem pe iodically and hei big size and weigh compa ed o high echnology elec onics. One possibili y o o e come hese powe limi a ions is o ex ac (ha es ) ene gy om he en i onmen o ei he echa ge a ba e y, o e en o di ec ly powe he elec onic de ice. This pape p esen s se e al me hods odesignanene gyha es ing de ice depending on he ypeo ene gya aliable. Keywo ds: Ene gy ha es ing, wea able de ices, wi eless senso ne wo ks 1. INTRODUCTION One o he mos impo an ends in he elec onic equipmen echnology om i s o igins has been he educ ion in size and he inc ease in unc ionali y. Nowadays small, handheld, hough e y powe ul de ices a e comme cially a ailable ha allow he use o play music, o wi elessly communica e o o compu e p ac ically e e ywhe e o , in o he wo ds, ubiqui ously. In he nex yea s he e will be new p oduc s a ailable p o iding ision and o he ex ended unc ions o he wea e . The size o such de ices is becoming so small ha ins ead o po able de ices hey a e becoming wea able de ices ha can be in eg a ed in e e yday use objec s like wa ches, glasses, clo hes, e c.1 All hose uni s, based on oday’s mic oelec onic echnology, need an ex e nal powe supply. The size o he elec onic ci cui and he ene gy needed o pe o m a single (bina y) ope a ion2has been d as ically educed du ing he las decades, ollowing Moo e’s Law. The e o e, ad ances in low powe design open he possibili y o ha es ene gy om he en i onmen o powe elec onic ci cui s. This wo k p esen s cu en app oaches o using ene gy ex ac ed om he en i onmen o powe mic oelec- onic de ices. The elec ical ene gy o powe he elec onics is gene a ed om ei he kine ic, elec omagne ic o he mal ene gy. The ob ained ene gy can hen be used o echa ge a seconda y ba e y o , in some cases, o powe di ec ly he elec onics. The ou pu ol age and cu en o he gene a o s is ansien and discon inuous in na u e, and mus be con e ed o a DC signal. The e o e i is necessa y o design a con e e and/o s o age ci cui ha needs o ake in o accoun he ou pu signal o he gene a o and i s impedance. The s uc u e o he pape is as ollows: Fi s , in sec ion 2, he echnology ends o bo h ba e y (ene gy gene a ion) and elec onic de ices (ene gy consump ion) a e b iefly ske ched. Then, ene gy ha es ing de ices a eclassifiedinsec ion3acco ding osou ceand ypeo ene gy. Sec ions 4 h ough 6 e iew he p inciples behind diffe en ypes o ene gy con e sion. In sec ion 7 i is discussed he powe condi ioning needed by elec onic de ices elying on ene gy ha es ing, depending on hei consump ion and ene gy gene a ion possibili ies. Finally, in sec ion 8, he conclusions o he wo k a e p esen ed. Fu he au ho in o ma ion: (Send co espondence o F. Moll) F. Moll: E-mail: [email p o ec ed]c.edu L. Ma eu: E-mail: mlo e [email p o ec ed]c.edu Table 1. Cha ac e is ics o ba e ies. Ba e y ype Vol. Ene gy densi y G a . Ene gy densi y Sel -discha ge Cycle Li e Wh/dm3Wh/kg %pe yea no. Alkaline 300 125 4% 1 Ni-Cd 100 30-35 15-20% 300 Ni-MH 175 50 20% 300 Li-ion 200 90 5-10% 500 2. TECHNOLOGY TRENDS 2.1. Ba e y e olu ion In he g ea majo i y o oday’s wea able o po able de ices, he ene gy necessa y o hei ope a ion is p o ided by ba e ies. Ba e ies a e a significan ac ion o he o al size and weigh o he sys em. As echnology scales down, his ac ion is expec ed o u he inc ease. Also e y impo an is he equi emen o p ope main enance o ba e ies, wi h he need o ei he eplace o echa ge hem. This is a se ious limi a ion o compu ing pa adigms like ubiqui ous compu ing o senso ne wo ks, in which he e a e dozens o hund eds o small sys ems wi h ba e ies o main ain. O cou se, hese incon enien s do no hide he ad an ages o ba e ies as a ese oi ene gy sou ce. Fo example, we can cha ac e ize he ba e ies by hei ene gy densi y, wi h espec o olume and weigh , called olume ic and g a ime ic ene gy densi y espec i ely. Table 1 shows some ypical alues o ene gy densi ies and sel -discha ge alues o comme cial ba e ies. I is seen how he mos mode n ba e ies (Li-ion) p esen be e cha ac e is ics o ene gy densi y, sel -discha ge cu en and numbe o cycles. I is wo h no ing ha hese alues o ene gy densi y a e he bes op ion a ailable oday. Recen ad ances in capaci o echnology ha e led o he de elopmen o he so-called ul acapaci o s, wi h a capaci ance alue o he o de o kF. Such imp essi ely la ge capaci o s, howe e , p esen an ene gy densi y a ound 3 Wh/kg, e y a om a e age ba e y alues.3The main ad an ages o ul acapaci o s is he supplied peak powe , and he numbe o cycles. These cha ac e is ics make hem mo e o ien ed o au omo i e applica ions han o low powe elec onic de ices, whe e ba e ies a e s ill he choice o ene gy s o age. S ill, ba e y echnology has e ol ed e y slowly compa ed o elec onic echnology.4Fo example, while disk s o age densi y has inc eased o e 1,200 imes since 1990, ba e y’s ene gy densi y has inc eased only abou 3 imes. New app oaches a e on he way o e y small size po able ba e ies ha may enable he size and weigh educ ion o wea able sys ems and senso ne wo ks. They a e based on new echnologies as he hin- film Li hium-ion o Li hium polyme cells and some o hem a e s ill unde de elopmen .5One o he mos p omising al e na i es is he uel cell, powe gene a o s ha use chemical uels (i.e. Hyd ogen o Me hanol). The g a ime ic ene gy densi y o uel cells is expec ed o be h ee o fi e imes la ge han Li-ion cells and mo e han en imes be e han Ni-Cd o Ni-MH ba e ies whe eas he olume ic ene gy densi y is six o se en imes la ge han Li-ion.6Howe e , he main enance p oblem is no sol ed; hese cells need o be e ueled o al e na i ely hey ha e o be manu ac u ed ca ying enough uel o sus ain he ba e y ope a ion du ing all i s expec ed li e ime. Seconda y ba e ies a e in p inciple a be e choice o ubiqui ous o wea able sys ems because hey can be echa ged in se e al ways, in many cases wi hou ex ac ing he ba e y om he sys em. Ac ually, one o he possibili ies o echa ge such ba e ies is o use ene gy ha es ed om he en i onmen .7In his sense, ene gy ha es ing is no ying o eplace ba e ies, bu ins ead alle ia ing some o hei d awbacks, especially in ela ion wi h he main enance issue. 2.2. Powe consump ion o mic oelec onic de ices Following Moo e’s law, in eg a ed ci cui echnology e ol es ollowing a ansis o size sh inking end. Toge he wi h his end and because o eliabili y easons he supply ol age (VDD) is also educed. The ne esul is a educ ion in ene gy consump ion due o he educ ion in he size o pa asi ic componen s. Fo a scale educ ion Table 2. Classes o ene gy ha es ing de ices. Ene gy Sou ce Type o Ene gy Human Kine ic, The mal En i onmen Kine ic, The mal, Radia ion wi h a ac o α(α>1), he ene gy consumed by a gi en sh unk ci cui pe o ming a gi en ask is educed by (1/α)3, as dicussed elsewhe e.8 I is also impo an o conside he use model o he elec onic de ice. Fo example, he powe consump ion o a wea able can be scaled ollowing wo diffe en scena ios: 1. Maximum pe o mance use: he imp o emen in echnology allows o educe he ime pe se ice, bu i is used o gi e a highe numbe o se ices. In his case he o al powe consump ion o he p ocessing unc ionsisscaledas(1/α)2. 2. Cons an numbe o se ices: he imp o emen in echnology educes he ime pe se ice and he powe consump ion bu he use does no inc ease he numbe o equi ed se ices. The powe consump ion o he p ocessing unc ions is scaled as (1/α)3. Cu en po able elec onic de ices ha e diffe en low powe o sleep modes o sa e ene gy du ing imes o inac i i y. The managemen o hese modes is e y impo an in ela ion wi h an ene gy ha es ing s a egy, allowing o “ efill” he ene gy ese oi o he sys em du ing hese pe iods o low ac i i y. This means ha gene ally, a discon inuous ope a ion use model is manda o y o he ene gy ha es ing app oach. 3. ENERGY HARVESTING DEVICES Be o e s a ing o discuss he diffe en me hods o ene gy ha es ing, le us look a he defini ion o an ene gy ha es ing de ice as unde s ood in his pape . An ene gy ha es ing de ice gene a es elec ic ene gy om i s su oundings using some me hod o wha is called in he li e a u e Di ec Ene gy Con e sion echniques.9The e o e, he ene gy ha es ing de ices he e conside ed do no consume any uel o subs ance, so ha he main enance p oblem men ioned abo e does no apply. On he o he hand, as he en i onmen ene gy le els a e e y low (a leas o oday’s elec onic de ices equi emen s), he use models men ioned in he p e ious sec ion a e e y impo an . 3.1. Classi ica ion o Ene gy Ha es ing de ices We may classi y he diffe en ene gy ha es ing de ices in wo ways: conside ing who o wha p o ides he ene gy o con e sion, and wha ype o ene gy is con e ed. Table 2 ela es he wo classifica ion schemes. In he fi s classifica ion scheme we can dis inguish be ween wo kinds o de ices. Fi s , de ices ha use pa o he ene gy o he use o he elec onic appliance. I will usually be a human, bu i could be also an animal, o example o a emo e moni o ing de ice. We call his fi s kind o de ices Human Ene gy∗de ices.10 The second kind o ene gy ha es ing de ice ge s i s ene gy om he en i onmen , and hus we call hem En i onmen Ene gy de ices. This classifica ion akes in o accoun ha , ollowing he fi s p inciple o he modynamics, a g ea e amoun o ene gy mus be spen o ob ain a ce ain amoun o elec ical ene gy. In he case o Human Powe i is he use ha in some way o o he p o ides his ene gy and, hough he ene gy le els a e e y small, he effec may p o e no iceable when se e al de ices depend on he ac i i y o a single use . In o de o e alua e he bu den o ene gy ha es ing on use ac i i ies, i is possible o use a simple biomechanical model o calcula e he ene gy in ol ed in a human s ep,11 ob aining a ound 40 J. In compa ison, he ene gy o a sho RF ansmission can be e alua ed in he o de o 100 µW. This means ha he ex a ene gy demanded o ob ain ∗In mos o he li e a u e he e m Powe is used ins ead o Ene gy. We p e e he e m Human Ene gy ins ead o Human Powe because ene gy is a mo e meaning ul magni ude when dealing wi h discon inuous e en s, as discussed in subsec ion 7.1. enough ene gy is e y small o some applica ions, and he e o e i makes sense o conside human beings as a possible ene gy sou ce. The second classifica ion scheme may conside h ee ypes o ene gy: kine ic, elec omagne ic adia ion (including ligh and RF), and he mal. Fo Human Ene gy de ices only kine ic and he mal ene gy a e a ailable. In he case o kine ic Human ene gy, one may dis inguish be ween hose ac ions made specifically o gene a e ene gy and casual mo emen s made du ing no mal beha io . These wo cases a e called by he Human Powe esea ch g oup o he Del Uni e si y o Technology12 Ac i e and Passi e Human Ene gy espec i ely. Following his defini ion, he mal Human Ene gy is always passi e. En i onmen Ene gy sou ces include kine ic ene gy in he o m o ib a ions, adia ion as sola ene gy o RF adia ion, and he mal ene gy. The ene gy ha es ing de ices may pick up ib a ions when loca ed on machines, building elemen s o o he places nea ib a ing sou ces. Radia ion may come om na u al o a ificial sou ces. The mal ene gy depends on he exis ence o a empe a u e g adien . While he ansducing me hods may be simila o he Human Ene gy de ices, he exci a ion magni udes, equency spec a and pe iodici y a e e y diffe en , and he e o e each case mus be s udied sepa a ely. This will also ha e consequences in he elec ical powe condi ioning ci cui . 3.2. Some wo king examples The e a e se e al examples, bo h comme cial and in he esea ch s age ha apply ene gy ha es ing o powe elec onic p oduc s. 3.2.1. Human Ac i e Ene gy This is an old concep ha has e i ed ecen ly, basically imp o ing he a io o ime o use wi h espec o ime o cha ge. De ices in he ma ke using human ene gy as he only ene gy sou ce include adio ecei e s, elec ic o ches and phone ba e y cha ge s.13–15 These de ices use kine ic ene gy p o ided by winding a hand c ank, o shaking he de ice, and hey offe a good a io be ween cha ging ime and use ime.16 3.2.2. Human Passi e Ene gy While Human ac i e ene gy is in e es ing as an indus ial concep , i is Human Passi e Ene gy ha p esen s a eal challenge and is mos a ac i e because i elimina es he powe main enance p oblem in po able and wea able de ices. Among comme cial p oduc s, he fi s de ices we e w is wa ches, because hey ha e a e y low powe con- sump ion. Bo h kine ic and he mal ene gy powe ed wa ches ha e been comme cialized, al hough cu en ly, only he kine ic is being manu ac u ed by se e al companies. Fo kine ic ene gy, he powe ou pu is 5 µWinno mal condi ions, and up o 1 mW when he wa ch is o cibly shaken. Fo he mal con e sion, a ound 1.5 µWo mo e is gene a ed when he empe a u e diffe ence is 1–3◦C.17 Minia u e he moelec ic gene a o s a e also de eloped18 ha con e s body hea flow in o elec ici y. I is claimed ha i can gene a e 40 µW a 3 V wi h a 5 deg ee diffe ence in empe a u e. Po en ial applica ions include a achable medical de ices, elec onic w is wa ches, sel powe ed hea senso s, and mobile elec onics. Ano he applica ion al eady commecialized o ene gy ha es ing is in he emo e con ol a ea. The mechan- ical o ce employed o push down he swi ch is used o bend a can ile e piezoelec ic ce amic.19 This kind o de ices is conside ed as Human Passi e ene gy ha es ing because he same mo emen o pushing he swi ch is used o gene a e he ene gy o a wi eless communica ion. 3.2.3. En i onmen Ene gy Se e al app oaches ha e been made du ing he las ew yea s in o de o ha es ene gy om he en i onmen o powe wi eless senso ne wo ks. Ba e ies a e no a ecommended powe sou ce o wi eless senso s since he powe sou ce would limi he li e ime o he senso . The ene gy needed by a wi eless senso is in he o de o hund eds o mic o wa s. The main powe sou ces s udied o wi eless senso ne wo ks a e sola powe (ou doo s o indoo s) and mechanical ib a ion. Roundy e al.20 analyzed and ab ica ed a bimo ph piezoelec ic (PZT) gene a o wi h a s eel cen e shim. The can ile e s uc u e has an a ached mass. The olume o he o al s uc u e is 1 cm3. A model o he de eloped piezoelec ic gene a o was made and alida ed. Fo an inpu ib a ion o 2.25 m/s2a abou 120 Hz, powe om 125 µW o 975 µW we e gene a ing depending o he load. The powe eco e ed was analyzed connec ing he gene a o di ec ly o a esis i e load o o a capaci i e load. La e , a DC-DC con e e was included and he gene a o supplied powe o a low powe anscei e . The adio ansmi s a 1.9 GHz and consumes 10 mA a 1.2 V and he ib a ion sou ce was 2.25 m/s2a 60 Hz. 4. KINETIC ENERGY Kine ic ene gy is one o he mos eadily a ailable ene gy sou ce, bo h o Human and o En i onmen ene gy ha es ing de ices. This sec ion b iefly explains he p inciples o he diffe en ansduce s o ob aining elec ical ene gy om kine ic ene gy. 4.1. Types o kine ic ene gy ansduce s The p inciple behind kine ic ene gy ha es ing is he displacemen o a mo ing pa o he mechanical de o ma ion o some s uc u e inside he ene gy ha es ing de ice. This displacemen o de o ma ion can be con e ed o elec ical ene gy by h ee me hods, ha a e explained in subsequen subsec ions: by a piezoelec ic ma e ial (subsec ion 4.2), by elec os a ic ene gy (subsec ion 4.3) and by magne ic induc ion (subsec ion 4.4). Wi h espec o mechanical s uc u es, he e a e wo ypes o possible con e e s. One esponds o he kine ic ene gy wi h a ib a ion o displacemen o a p oo mass. The ene gy ob ained will depend on his mass, and he e o e we will call his fi s class Ine ial con e e s. Mi cheson e al.21 ha e classified ine ial con e e s in unc ion o he o ce opposing he displacemen o he p oo mass as Vol age Damped Resonan Gene a o s (VDRG), app op ia e o desc ibe magne ic induc ion ansduce s, Coulomb Damped Resonan Gen- e a o s (CDRG), which desc ibe ib a ing elec os a ic ansduce s, and Coulomb Fo ce Pa ame ic Gene a o s (CFPG) ha co espond o displacemen elec os a ic gene a o ype. The e a e also ine ial con e e s based on piezoelec ic, in which an accele a ed mass causes a de o ma ion o a piezoelec ic ma e ial, ei he by impac o ib a ion. Many ine ial con e e s a e based on a sp ing-mass sys em ha esona es a a pa icula equency. When he mechanical s imulus ib a es a ha esonance equency, he ene y ob ained is maximum. Howe e , as he con e e s a e minia u ized o in eg a e hem on mic oelec onic de ices, he esonance equency inc eases, and i becomes much highe han cha ac e is ic equencies o many e e yday mechanical s imuli. Fo example, ypical accele a ion equencies o he human body in mo emen a e below 20 Hz.22 As was ecognized by Mi cheson e al.21 o such cases, ei he a CFPG ype o con e e , o a non ine ial con e e is bes sui ed. In he second case (Non-Ine ial con e e s), an ex e nal elemen applies p essu e ha is ans o med as elas ic ene gy, causing a de o ma ion ha is con e ed o elec ical ene gy by a piezoelec ic ma e ial. In his case, he ob ained ene gy does no depend on he mass o he con e e , bu gene ally, on he a e o de o ma ion, hus gi en by mechanical cons ain s like Young’s modulus o geome ic dimensions.23 4.2. Piezoelec ic gene a o The piezoelec ic effec was disco e ed by Jacques and Pie e Cu ie in 1880. Cu ie’s b o he s ound ha ce ain ma e ials, when subjec ed o mechanical s ain, suffe ed an elec ical pola iza ion ha was p opo ional o he applied s ain. This is he piezoelec ic effec used o mechanical o elec ical ene gy con e sion. The phenomenon o piezoelec ici y is desc ibed by he ollowing equa ions: {Si}={1 Yc,ij }{Tj}+{dik}{Ek} {Dl}={lm}{Em}+{dln}{Tn} o j, n =1,...,6andi, k, l, m =1,2,3(1) Table 3. Subsc ip s o he educed no a ion o piezoelec ic cons i u i e equa ions. Reduced no a ion Co esponding di ec ion o axes 1Longi udinal in xdi ec ion 2Longi udinal in ydi ec ion 3Longi udinal in zdi ec ion 4Shea y-z 5Shea z-x 6Shea x-y C'p T 1:-1/(dYc) SD E 1/Yc C'm S T 1:-d/ε D Cp E (a) (b) Figu e 1. Piezoelec ic coupling ci cui s, ela ing mechanical and elec ical magni udes. In hese equa ions, subsc ip s co espond o he 6 di ec ions o he axes, h ee ca esian di ec ions plus he shea a ound he h ee axes, as shown in Table 3. Repea ed subsc ip s in he p oduc s imply a summa ion o e he diffe en componen s: T, applied mechanical s ess [N/m2]. E, applied elec ic field [N/C]. d, piezo s ain enso [(C/m2)/(N/m2)]. , pe mi i i y enso [F/m]. D, elec ic displacemen [C/m2]. S, mechanical s ain [m/m]. Yc, Young’s modulus enso [N/m2]. A piezoelec ic ma e ial mechanically s essed a a low equency can be modelled elec ically by a ime- dependen cha ge sou ce, ha is accumula ed in a capaci o . I he piezoelec ic cons i u i e equa ions a e ans o med o he Laplace domain, he ollowing equa ions a e ob ained: ˙ S=jω T Yc+jωdE ˙ D=jωTE+jωdT (2) This ela ionship is ep esen ed by he piezoelec ic coupling ci cui o Figu e 1(a). The ans o me ela es mechanical magni udes (s ess) and elec ical magni udes (elec ic field). C p=T1−d2Yc T=T(1 −k2)(3) Ano he possibili y o he ep esen a ion o he piezoelec ic coupling ci cui is shown in Figu e 1(b), whe e capaci o s C mand Cpa e gi en by: C m=1 Yc1−d2Yc =1 Yc(1 −k2);Cp=TA (4) The wo mos common ypes o piezoelec ic ma e ials a e PVDF, poly inylidene fluo ide, and PZT, lead zi cona e i ana e. The e a e h ee diffe en ways o exci e a piezoelec ic ma e ial in o de o gene a e elec ical ene gy: by comp ession, slap and bending. Fo he analysis o he piezoelec ic esponse, i is assumed ha elec ical e minals a e loca ed along di ec ion 3, pa allel o he poling axis ( he di ec ion o he pola molecules ha o m he piezoelec ic effec ). The wo mos common ways o employ piezoelec ic ma e ials a e modes 31 and 33. In mode 31, he s ess is applied in Table 4. Vol age V3and cha ge q3ob ained applying a mechanical s ess in di ec ion 1, mode 31, and in di ec ion 3, mode 33. Cons an s gij a e de ined as dij /. Mode 31 Mode 33 V3g31 F1 Wg33 F3 WLH q3d31 F1L Hd33F3 di ec ion 1 whe eas he elec ic field ( ol age mode) o he elec ic displacemen (cha ge mode) a e in di ec ion 3. In mode 33, he s ess is applied in di ec ion 3. Table 3 gi es he ob ained ol age o cha ge esul ing om an applied o ce in a ce ain di ec ion, F1o F3 o each mode. I he same o ce is applied in di ec ion 3 and in di ec ion 1 o e a piezoelec ic ma e ial wi h simila dimensions in leng h L,wid hWand hickness H, mode 33 exci a ion can gene a e mo e cha ge and ol age han mode 31 because d33 is usually la ge han d31. Howe e , he geome ical dimensions o he ma e ial play a e y significan ole. Fo example, in a hin PVDF film, he a io L/H is on he o de o 1000, while d31 =23·10−12m/V and d33 =−33 ·10−12m/V .24 I i is conside ed again ha F1is equal o F3, heob ained alue o V3and q3 o he mode 31 will be on he o de o 700 imes g ea e han o he mode 33. The e o e, he mechanical s uc u e mus ake in o accoun bo h he geome y and he mechanical coupling in o de o apply he de o ma ion in he op imum way. Piezoelec ic hin films a e used o se e al sys ems due o hei adap abili y. In his case, he mos ad an- ageous way o exci a ion is by bending piezoelec ic ma e ials configu ed in can ile e -like s uc u es. The e a e diffe en kinds o suppo , and diffe en e ical s uc u es o he ma e ial ha is going o be ben . The combina ion o hese s uc u es gene a es se e al op ions.23 When se e al piezoelec ic elemen s a e p esen in he s uc u e, hey can be connec ed ei he in pa allel o in se ies. In a pa allel connec ion, he cha ge gene a ed by he piezoelec ics is added whe eas in a se ies connec ion, he cha ge gene a ed co esponds o he s ain o one o he piezoelec ic elemen s connec ed, and he ol age o he piezoelec ic elemen s is added. In o de o adequa ely connec he piezoelec ic elemen s in se ies o pa allel, he o ien a ion o he poling axis has o be aken in o accoun . In summa y, piezoelec ic con e e s ha e mos o he ad an ages o induc i e and elec os a ic gene a o s, and hey a e also e y obus . On he o he hand, piezoelec ic con e e s a e difficul o implemen on mic omachined p ocesses, and he e o e o minia u ize.20 4.3. Elec os a ic ene gy gene a o The p inciple o elec os a ic gene a o s is ha he mo ing pa o he ansduce mo es agains an elec ical field, hus gene a ing ene gy. Meninge e al.25 o MIT p esen ed an elec os a ic gene a o ha employs a a iable mic omachined ca- paci o . Two diffe en designs we e s udied: a pa allel capaci o ope a ed wi h a cons an cha ge and a comb capaci o ope a ed wi h a cons an ol age. These gene a o s a e also called Coulomb-damped esonan gene - a o s (CDRGs) because hey a e based on elec os a ic damping. I he cha ge on he capaci o is main ained cons an while he capaci ance dec eases (e.g. educing he o e lap a ea o he pla es o inc easing he dis- ance be ween hem), he ol age will inc ease. I he ol age on he capaci o is main ained cons an while he capaci ance dec eases, he cha ge will dec ease. Figu e 2 illus a es he p ocess o cha ging and discha ging he capaci ance ollowing cons an cha ge (pa h A-B-D-A) o cons an ol age (pa h A-C-D-A) app oaches. The ene gy enclosed by he o al pa h is he ene gy ex ac ed in he p ocess. The cha ge cons ained con e sion cycle s a s when he mic omachined capaci ance (gi en by he slope o he Q-V cu e) is maximum. A his momen , a ol age sou ce cha ges he MEMS capaci o o an ini ial ol age, Vs a , ha has a smalle alue han Vmax, and he e o e he cycle con e sion goes om poin A o poin B. The pa h B-D co esponds o he pla es mo ing om maximum capaci ance, Cmax, o minimum capaci ance, Cmin cmax cmin Vol age-cons ained cycle Cha ge-cons ained cycle V Q Vs a Vmax A B C D Qa Figu e 2. Diag am explaining elec os a ic ene gy con e sion. Adap ed om Meninge e al.25 wi h cons an cha ge, Q0. As he capaci o dec eases and cha ge is main ained cons an , he ol age inc eases i s alue. The cha ge is e u ned o he ese oi in pa h D-A. The ne ene gy ou is equal o he a ea A-B-D. The ol age cons ained con e sion cycle s a s when he mic omachined capaci ance is maximum. A his momen , a ol age sou ce cha ges he MEMS capaci o o an ini ial ol age, Vmax, and he e o e he cycle mo es om poin A o poin C. The pa h C-D co esponds o he pla es mo ing om maximum capaci ance, Cmax, o minimum capaci ance, Cmin. Pa h D-A shows he discha ge o he capaci o . The mechanical ib a ion ha akes place in pa h C-D is con e ed o elec ical ene gy wi h a cons an ol age. The ne ene gy gained co esponds o he a ea A-C-D. The ene gy gained in he con e sion p ocess is pumped om he MEMS capaci o along pa h DA o bo h cha ge and ol age cons ained cycle. As shown g aphically, he mechanical ene gy con e ed in o elec ical ene gy is g ea e i he ol age ac oss he capaci o is cons ained han i he cha ge ac oss he capaci o is cons ained. Howe e , he ini ial ol age sou ce needed has a smalle alue o he cons an cha ge case. A way o inc ease he elec ical ene gy o he cha ge cons ained me hod is o add a capaci o in pa allel, Cpa wi h he MEMS capaci o , CMEMS. The disad an age o his solu ion is ha he ini ial ol age sou ce has o inc ease i s alue. As explained, he p ope ope a ion o he swi ches, o when he cha ges a e ans e ed, is c i ical o a good efficiency. The ope a ion o he swi ches mus be synch onized wi h he mechanical oscilla ion. The equency o he mechanical oscilla ion depends on he esonance equency o he mechanical s uc u e. Fo bes esul s, hen, he mechanical sou ce mus ha e a ib a ion wi h a equency close o ha o he esonance equency o he ansduce , which is in he o de o kHz o minia u ized componen s. O he app oaches use non- esonan s uc u es21 ha a e mo e sui ed o mechanical exci a ions a lowe equencies. 4.4. Magne ic induc ion gene a o The magne ic induc ion ansduce is based on Fa aday’s law. The a ia ion in magne ic flux, Φm h ough an elec ical ci cui causes an elec ic field. This flux a ia ion can be ealized wi h a mo ing magne whose flux is linked wi h a fixed coil o wi h a fixed magne whose flux is linked wi h a mo ing coil. The fi s configu a ion is p e e ed o he second one because he elec ical wi es a e fixed. As he ele an magni ude he e is he magne ic flux h ough a ci cui , he size o he coil is in e sely ela ed o he ob ained elec ic field and he e o e, o he gene a ed ene gy. This means ha big ansduce s wi h la ge m k Bm y( ) z( ) R L Rc - + m V Z ksBms 1 m 2++ c RRLs BlRs ++ R Bl e (a) (b) Figu e 3. Magne ic induc ion ansduce model. Adap ed om Ching e al.26 a ea coils will pe o m be e han smalle ansduce s, unless a la ge ime de i a i e is in ol ed wi h he small scale gene a o s. We b iefly p esen he analysis o a simple gene a o .26 When he gene a o ib a es, he oscilla ing mass has a ela i e displacemen wi h espec o he housing. The magne ic induc ion gene a o con e s his ela i e displacemen in o elec ical ene gy. The ansduce is modelled as a damped sp ing-mass sys em, since he ene gy ex ac ion damps he mass mo emen wi h a ac o Bm.Themassm, hemagne ,whichisjoined oa sp ing wi h a sp ing cons an kmo es h ough a cons an magne ic field, B, when he gene a o oscilla es. The ela i e displacemen , z( ), is ela ed o he ol age ac oss he coil by a fi s o de sys em as can be shown in Figu e 3(a). Lis he induc ance o he coil, Rcis he pa asi ic esis ance o he coil, lis he leng h o he coil, and Ris he load esis ance. Figu e 3(b) shows he ans e unc ion block diag am ha ela es he mechanical inpu o ce wi h he ou pu ol age. The cu en induced in he coil gene a es an elec omechanical o ce, e ha dampes he mo emen o he magne . F om he New on’s second Law o mo ion, he ans e unc ion be ween he inpu mechanical o ce, m, and he ela i e displacemen o he mass can be ob ained. A e some algeb a, he ans e unc ion ha ela es he ou pu ol age V, ac oss he load esis o wi h he inpu mechanical o ce mis: V(s) m(s)=(BlR)s (Ls +R+Rc)(ms2+Bms+k)+(Bl)2s(5) The hi d o de sys em can be simplified o a second o de sys em by assuming ha he elec ical ime cons an is much smalle han he mechanical ime cons an . Wi h his assump ion, he ans e unc ion is exp essed as: V(s) m(s)= (Bl)s m (s2+2ζωns+ω2 n)(6) whe e ζand ωna e he damping ac o and he sp ing na u al equency, espec i ely. ωn=k m(7) ζ=BmR+(Bl)2 2R√mk =Bm 2ωnm+(Bl)2/R 2ωnm=ζm+ζe(8)