Nonlinear Modeling and Investigating the Nonlinear Effects on Frequency Response of Silicon Bulk-Mode Ring Resonator

Transcription

1 Nlea Melg a Iesgag he Nlea Effecs Fequecy Respse f Slc Bulk-Me Rg Resa A. Bja*, S. H. Kesh* a W. Wabuee** Absac: Ths pape peses a lea aalycal el f slc cechacal g esas wh bulk-e bas. A sbue elee el has bee eelpe escbe he yac beha f he cechacal g esa. Ths el shws he lea effecs a slc g esa fcusg he effec f lage aplues au he esace fequecy, aeal a eleccal leaes. Thugh he cba f geecal a aeal leaes, clse-f expesss f he leay echacal sffess f bulk-e g esas ae bae. Usg he peuba eh a he eh f hac balace, he expesss f escbg he effec f leaes he esace fequecy a sably ae ee. The esuls, whch shw he effec f ayg he AC-e lage, al gap spacg, DC-bas lage a he qualy fac he fequecy espse a esa fequeces, ae scusse eal. The lea el uces a apppae eh he fel f bulk-e g esa esg f acheg suffce pwe halg a lw al essace. Keyws: Mcechacal g esa, Nleay, Bulk-e, Fequecy espse, Pwe halg. Iuc Deelpe f cechacal esas a fles wh hgh qualy fac, hgh pwe halg capably a lw al essace, s cuely e f he eesg subjecs c-cuca applcas []. The slc cechacal esas ue he sall sze, lw cs a cpably wh egae ccu (IC echlgy ae a psg aleae suface acusc wae (SAW a quaz cysal esas. Hwee, lw al essace a hgh pwe halg ake he ffcul hale wh leay a sall sze. A, ue he sall sze, hese esas ca se hgh eegy a, heefe, hey shul be e a hgh exca alue whch causes he be easly e lea eges []. Mee, he s ec ehs f lweg he al essace cechacal esas, lke scalg w he Iaa Jual f Eleccal & Elecc Egeeg,. Pape fs ecee Aug. a ese f Oc.. * The Auhs ae wh he Depae f Eleccal Egeeg, Faculy f Egeeg, Fews Uesy f Mashha (FUM, 9775-, Ia. E-als: a.bja@gal.c a kesh@u.ac.. ** The Auh s wh he Schl f Eleccal Egeeg, Isue f Egeeg, Suaaee Uesy f Techlgy (SUT, Nakh Rachasa, Thala. E-al: Eleccal.su@gal.c. elece esa gap a asg he DC-bas lage, ecease he leay []. The ably accuaely el leay a esgae s effec fequecy espse s, heefe, a key equee pu esg f slc cechacal esas. Thee ae se echacal a eleccal leaes slc cechacal esas. Depeg he esa esg a peag cs, ffee leaes ay be a a esul haeg sfeg beha he yac beha f cechacal esa []. A l f eseach has bee cuce elg he lea effecs cechacal esas. Gu e al. [5] esgae he lea effecs he peface f a c-bge, usg Raylegh s eegy eh, a shwe he epeecy f he hyseess ce he qualy fac, peag cs, geec a aeal ppees f he cechacal esa. Mes e al. [] sue he fequecy espses a he lea yac ppees f clape-clape bea esa a pece he haeg beha. They als cpae he aalycal esuls wh he esuls f expees a fu a easable ageee. Alasal e al. [] pesee a ey useful suy he lgual e esas wh espec echacal a eleccal leay. Assug a hgh qualy fac, se f Iaa Jual f Eleccal & Elecc Egeeg, Vl., N., Mach 5

2 he afeee wks hae ge apg ceffce calculag he shf esace fequecy cause by leaes. Mee, he suy he leaes bulk-e cechacal esas s aequae, a peus wks hae ly fcuse he lgual a squae exesal e esas [7]. Ths pape eals wh he effecs f leaes fequecy espse f slc bulk-e g esas. Fs, a cpehese lea el f he esa s ee. The el clues he effec f lage aplues au he esace fequecy, aeal a eleccal leaes. The, he effec f key paaees lea fequecy espse s ealuae applyg peuba echques a hac balace eh. Fally, he aly f he el s efe by cpas wh he expeeal aa bae by e e al. [] lea ege, a w aalycal els pesee by Zhag e al. [9] a Kaajaka e al. [], [] lea ege. Bulk-Me Rg Resa Ag slc cechacal esas, bulke g esas ffe lwe al essace a hghe qualy fac ue he hgh sucual sffess, g geey a hag fu quas-al ps a he ue pephey se axsyec bulk-es lke we glass a exesal we glass. Theefe, hey ae e exesely eelpe RF ascee f-e achecues []. I he bulk-e g esas whch ae shw Fg., assug ha he wh f he g s uch lage ha s hckess (R -R >>, he -D lea equas geg he ba f a g, whu by fce a eal hea suce ca be ge by [], []: E A E A u u ρa υ u = ( ( + υ whee E, υ, ρ a A ae Yug s ulus, Pss s a, esy f sucual aeal a asuc aea f he esa, especely. The splacee ec u=xe +we θ s efe es f he aal (x a ccufeeal splacees (w pla caes hugh he e a e shape fucs as fllws: x (, θ = ( cs( θ, w (, θ = W ( s( θ ( whee ( ( = cs( q, W ( = W cs( q q q q= q= whee a he aual esace fequecy f =h (E/ρ(-υ, he aal splacee a e a ue aus ca be assue as: x (, θ = ( cs( θ, x (, θ = ( cs( θ ( a appxaely, ( = U cs(, ( = U cs( (5 whee, U =U =R a U =U =R ca be expesse by fllwg equa: θ Fg. The scheac ews f he bulk-e shapes f he g esa a we glass b exesal we glass. NODAL SOLUTION STEP= SUB = FRE=.E+9 USUM (AVG RSYS= DM =99 SMN = SM =99 uas-al ps MN Fg. ANSYS sula f EWG e shape g esa. A B U = J( h + Y ( h + h A ( C D J( h + Y ( h A A I he abe equas, J a Y ae Bessel fucs f he fs a sec k, especely. h a k ae e csas f -axsyec e shape f (,, whle k s elae h by k /h = /(-υ. I shul be e ha he elae csas f elasc waes (B /A, C /A, B /A ca be fu by slg he equa f e(m =. The elee f M was explae eal Ref. [], []. I he es f he pape, he exesal we glass (, e g esa wh he specfcas pesee Table has bee use ealuae he fequecy espse cause by lea effecs. Theefe, he subscp s e a he subscp = epeseg he sec-e e ae use he fllwg equas. Fg. peses he e shape a esace fequecy f he exesal we glass esa usg ANSYS sfwae. Melg Appach Sce bh acua a capace eec f he g esa ae ealze usg he e a ue eleces, ca be assue as a w sepaae g Y Z M Iaa Jual f Eleccal & Elecc Egeeg, Vl., N., Mach

3 esas aache gehe a he aus f (R +R / as shw Fg.. The, each g esa s ele as a sbue elee. Cseg a fesal elee, he gap spacg aas capace asuces ae assue alg he aal ec. Thus, he geg equa f a sec-e echacal syse (ass-spg-ape f a fesal elee f he g esa ca be expesse as: ( ( ( θ x + b θ x + k θ x (7 + k x x = f ( θ + f ( θ ( ( c s ( θ x + b ( θ x + k ( θ x ( ( ( θ ( θ + k x x = f + f c s whee x epeses he aal splacees f he effece lupe ass f a b, k a k c ae apg ceffce, echacal sffess a cuplg sffess, especely. The subscps a ee he e a ue g esas, especely. The effece asses f fesal elee e a ue esas ae ge by: ( R R + R R + R ρ R θ (9 U U ρ U U ( θ =, ( = Assug ha he fs e s he a e f he syse, he e ue splacee a ca be expesse as: x (, θ U γ x (, θ U = ( Table The elae EWG e paaees f slc g esa. Paaee Value U Ie aus (R. μ Oue aus (R 5 μ Thckess ( μ Elece agle (θ e 5 eg Resace fequecy (f MHz Lea Yug s ulus (E 7 GPa Pss a (υ. Desy (ρ Kg - Fs-e cecs (E -. Sec-e cecs (E -. Subsug Eqs. ( a ( Eqs. (7 a (, a cbg he gehe esuls he fllwg expess: ( ( θ + ( θ γ cs( θ ( + b ( θ + b ( θ γ cs( θ ( + ( whee ( ( k ( θ + k ( θ γ cs( θ ( = f ( θ ( ( s s f ( θ = f ( θ + f ( θ + f ( θ + f ( θ ( Ipu eleces θ e (R +R / f (θ (θ (θ Oupu eleces f (θ Fg. a The scheac ew f he fesal elee b The equale ass-spg-ape syse f he g esa. Melg he Ogs f he Nleaes Nleaes cechacal esas geeally ase f eleccal a echacal gs. The eleccal leaes clue he elecsac fce leay cause by he aable gap capace asuces a he fgg effecs. A lage sucual efa ca be cbue geecal a aeal leaes; classfe as echacal leaes.. Eleccal Nleay I ay cechacal bulk-e esas, he al gap spacg bewee eleces a he esa s eglgble as cpae he hckess f sucue (sall aspec a a heefe, he fgg fels ae cseable. Hece, he elecsac fce leay ca be ele usg he paallel plae capac appxa alg wh he cec e f C f epeseg fgg effecs as fllws: ( f ( θ + f ( θ = (-a C ( θ C ( θ ( V P ( + x x C ( θ C ( θ ( f s ( θ + f ( s θ = V P + x x (-b s whee C, ( θ CfC, ( θ β = β + x, + x, + x ( s C ( θ C C ( θ = + x + x + (5, f,,, x whee C (θ=εr / a C (θ=εr / ply he capacace e he ue a e gaps whe he ue a e aal splacees ae equal ze, a s he cespg al gap spacg. Base he sese ( e eleces cfgua, he alue f β wul be equal - as he sese ( e eleces ae place a he sae se ppse se, especely. The cec e f capacaces f he fgg effecs epes he ess f he sucue as he fllwg equa [5]: Bja e al: Nlea Melg a Iesgag he Nlea Effecs 7

4 +. λ ; < λ <.5 C f = +.7λ +.97 ;.5 < λ <.5 ( λ ;.5 < λ whee λ=/ s he al gap spacg hckess a f he g sucue.. Mechacal Nleay Mechacal (aeal a geecal leaes ae ceae by he sesses eelpg se he esa sucue ue lage splacees. Depeg he pea e, he aeal geecal leaes ca be a cechacal esas. Ulke he eleccal leaes, whch ca be easly epesee by Tayl sees wh espec splacee, he echacal leaes ca be appxae by efa aalyss f he bulk-e g esa. F hs pupse, he echacal leay s fs ele by cseg he hghe e es he echacal sffess as fllws [], []: k ( θ = k ( θ + k x + k x (7-a k (,,,,,, ( θ = ( θ (7-b,, I e cse he geecal leaes, he geecal efa (Fg. cause by lage aal splacee fesal elee ca be as: A = A( θ θ ( θe ΔR x A( θ = R θ = A( θ υ (9 R Mee, he lage splacee eelps eal sesses se he sucue f esa a heefe, lea elasc beha f slc esul lea Yug s ulus as fllws []: x x E = E + E + E ( whee E a E ee he fs-e a sec-e cecs lea Yug s ulus f E, especely. The alues f E a E ae lse Table f bulk-e slc ee alg <> []. Subsug Eqs. ( a ( Eq. (, ulplyg by cs(θ, a he egag bh ses f θ= π esuls he appxae expesss f h-e leay echacal sffess, k a k, as: R R + R ( R + R Π ( Π R k =, k R = ( R + R U R ( U + R Θ Θ( R U U ( υ υ Π ( = U E ( + E U U U + ( E Eυ + ( Fg. The geecal aa fesal elee f he g esa. U U U Θ ( = U + + ( υ ( I fac, he sec-e leay e cause by syec sucue f he g a e shape s e. Usg he self-we uecal ces MATLAB sfwae, he alues f k a k f he case suy f hs pape wee calculae be -. - N - a -. - N -, especely. 5 Aalyss f he Nlea Effecs Base he elecsac a echacal leaes a ulplyg Eq. ( by cs(θ a he egag e he age f π, he geg equa f a sec-e echacal syse f he cechacal g ca be ewe as: ( + ( + ( +Ω ( ( +Ω ( = g + ( g + g ( + g ( ( The as use he abe equa ae pesee Table. Eq. ( s calle Duffg s equa, whee, a θ e ae he esace fequecy cause by eleccal leay, echacal qualy fac a elece-esa elap agle, especely. The DC e Eq. ( has effec he lea aalyss f he fequecy espse a ca be ge as fllws: ( + ( + ( = α (5 + α ( + α ( + α ( ( whee g ( α = g (, α = ( ( g ( Ω Ω α =, α = The appxae aalyc eh ca be use sle he Eq. (5. Assug weak leaes, hs pble ca be sle by peuba echque. Ths eh assues ha he esace fequecy alg wh he slu aes as a fuc f peuba es a he slu s ge by: = ( = ( + ( (7 Iaa Jual f Eleccal & Elecc Egeeg, Vl., N., Mach

5 Table Defs use he Eq. (. Def ( K k e M = K em K π ( K + γk K e V P ( γc C ( s( θe + θe π K, k ( cs ( θ θ θ, ( B MK e B π b ( θ + b ( θ γ cs ( θ θ ( g V P M ( β + ( C C s( θe g V P M ( C C s( θe g V P M ( γc C ( s( θe + θe g V M ( C C ( + Ω γ cs ( θ s( θ P e e V P M ( β ( γ C C ( θe + π Ω ( γ + ( C C = cs ( s( θ M K k + K k V P γ s( θe cs( θe + + θe = + ( The sec e appxa f hs slu ca be use achee a e exac ealua as: ( = ( + ( (9 = + ( Subsug Eqs. (9 a ( Eq. (5 a gupg he es pwe f, he w fllwg expesss ae bae: ( + ( ( + = α ( ( + ( ( + = ( + ( + α ( ( + α ( + α ( Whe he AC-e lage f (= cs( s apple, he slu f ( wul be as: j ( = Re( g e H( ( = g ( H cs( H s( whee e H( = = H + jh ( + j whee H a H ee he eal a agay pas f he asfe fuc f H(, especely. Subsug Eq. ( he gh ha se f Eq. ( a seg he secula es ze, he expess f s appxaely ge by: αg ( H + H = (5 Thus, by subsug Eq. (5 (, he esace fequecy cause by echacal a eleccal leaes, ώ, s expesse as fllws: = + + Ω g ( H + H ( As shw he Eq. (, ώ s a fuc f he aplue f he fs-e appxa f he slu. By Subsug Eq. ( (, he slu f ( s calculae a, heefe, ( ca be expesse as fllws: ( = g ([ G cs( G s( ] + [ G cs( G s( ] (7 + [ G cs( G s( ] whee G = g ΩH (-a G = H + gg H (-b G = H ( gh gωh H (9-a G = H ( gω H H + gh (9-b G = g H ( gω H H + gh (-a G = g H gω H H + gh (-b whee H a H (=,, ee he eal a agay pas f he asfe fuc f H(, especely. Subsug Eq. (7 (5, he upu cue f fesal elee f cechacal g esa ca be expesse usg he fllwg equa as: V P x (, θ (, θ = β ( C ( θ + γc ( θ + ( + + ( + ( C γ C x(, θ β C γ C x(, θ Bja e al: Nlea Melg a Iesgag he Nlea Effecs 9

6 Mulplyg by cs(θ a he egag bh ses, f π, he al upu cue ue he AC-e lage a he esace fequecy s fally ee as: ( = cs( q + ψ ( q q q = The expeeal esuls f he suy cuce by e e al. [] wee use expeeally efy ee expess f pesee el lea ege a eleccal sffess. As shw Fg. 5 a 5, he fequecy espse s easue usg he xg appach []. T aap hs appach he ppse el, he equas f =( LO RF / a P =(R L /, (R L =5 Ω [7] ae use he ee expesss. I ca be see f Fgs. 5 a ha he fequecy espse a esace fequecy chage f he lea el agee well wh expeeal aa. Hwee, he lw ffeece bewee he aplue a esace fequecy ay be ue he paasc capacace a essace expeeal easuees. Accg he expess f eleccal sffess, K e, whe DC-bas lage (V P, ceases he al gap spacg bewee he eleces esa ( eceases, he esace fequecy cause by eleccal leay (, shfs w as shw Fg.. I e aess he lea effecs he fequecy espse, assug ha he fs e s he a e a usg he fs-e appxa, he slu s assue as fllws: ( = cs( ( = g H + H ( Thus, he phase ffeece bewee he AC-e lage (, a slu (, s aae as he phase f apple lage a s fxe as he phase f slu as fllws: ( = cs( ϕ = cs( + s( (5 Subsug Eqs. ( a (9 (5 a usg he eh f hac balace, he fllwg equas ae bae: ( Ω + ( =, = g + g g + g ( ( Subsug Eq. ( + =, leas he ela bewee he aplue f AC-e lage a ba aplue as: ( Ω + ( + = g + g g + g ( (7 T suy he effecs f e lage he fequecy espse, he DC-bas lage V P, s assue Pwe (B Pwe (B Expeal [] lea el [] Nlea el Expeal [] lea el [] Nlea el Fg. 5 The fequecy espse f plyslc EWG e g esas a. MHz b 5. MHz. (f -f /f (pp (f -f /f (pp - - Expeeal [] - Aalycal [] Aalycal (Ths wk DC apple lage (V x -7.5 (.5 9 7Vp (V Fg. The facal esace fequecy chage cause by eleccal leay f a Plyslc EWG g esa wh f =. MHz b Slc EWG e g esa (as Table 5 5 Iaa Jual f Eleccal & Elecc Egeeg, Vl., N., Mach

7 csa a he e lage aes. I Fg. 7, s shw ha as e lage ( ceases, he esa fequecy espse chages f a als lea cue a cpleely lea e (hyseess. I fac, hghe e lage leas lage bas a eeually esuls a jup fequecy espse. Ths beha s ee whe hee ae w aplues f ba f a ge fcg fequecy a hgh e lage. Mee, he peak fequecy ls a lwe fequecy as he ba aplue ceases a he g esa, heefe, exhbs a sfeg beha. I ca als be see f Fg. ha a cease f he V P a ecease, ls he esace peak e, a he sfeg beha f he cechacal g esa beces e puce. ualy fac s a fuaeal paaee esg f cechacal esas f MEMS-base fles wh a lw se lss. Thee exs seeal sc a exsc eegylss echass he bulk-e esas lke a apg, ach lss a heelasc apg (TED; f a bulk-e esa peag hgh acuu, he a apg echas ca be ge. Als, hese esas, he heelasc apg s eglgble as cpae he ach lss a heefe, ach lss s he a eegy-lss echas []. I s esae ha, ach lss s sgly epee he supp bea ess, a ca be euce by echacally slag he supp beas f he subsae a pu esgg f he ess [9], []. As shw Fg. 9, he lea effecs fequecy espse bece e appae by ceasg qualy fac. (x - ώ = = =5 = ϕ (egee = = =5 = Fg. 7 The effec f AC-e lage fequecy espse f EWG g esa wh =, =9, V P = V. (x - V P =9 V P = V P = V P = = =9 = = Fg. The effecs f DC-bas lage a al gap spacg aas fequecy espse f EWG g esa wh = a =9 a =5 VPP b V P = V a =5 V PP. (x = = = = c =5. c =. = = = = c =5. c =7.7 Fg. 9 The effec f -fac a Fequecy espse f EWG g esa wh = V PP, =9 a V P = V b Ccal ba aplue ( C f a EWG g esa wh =9 a V P = V. The geaes ba aplue befe hyseess, calle he ccal ba aplue, c, ca be use esae he l f pwe halg as ge by E c =(K c / []. Whee E c s he axu sable eegy se he esa. I Fg. 9, s shw ha ue he sae cs, a hghe qualy fac eceases he ccal ba aplue a heefe, lwes axu sable eegy se. T efy he pesee el, he esuls f lea beha f he g esa wee cpae wh w aalycal els. Zhag e al. [9] use a eh f w-aable expas aalyze he Duffg s equa whe he g fequecy s clse he esace fequecy f. Mee, hey ppse a effece h-e sffess (K eff as a lea paaee, whch he as f hs paaee f pse egae wll chage he lef ha se bfuca gh ha se bfuca f he esa fequecy espse. Accg he waable expas eh, he effece h-e sffess was bae f cechacal g esa as fllws: ( Λ +Λe K eff = ( (( γc C ( s( θe + θe whee Λ = π K k + γ K k V (9 ( P Λ e = ( γ C C (+ cs( ζ (5 s( θe ( cs( θe + + θ e whee, ξ ca be calculae by uecally slu f Eqs. (5 a (5: s( ξ = (5 ( g Θ ( + cs( ξ Θ= (5 Ω g cs( ξ As shw Eq. (, Λ a Λ e ee he lea paaees ue h-e echacal a eleccal leay especely. F Fg., s Bja e al: Nlea Melg a Iesgag he Nlea Effecs 5

8 fu ha, he sg f K eff s fxe f ffee alue f DC-bas lage. Ths s ffee f flexual-e esas, whee exhb haeg beha a he sg f K eff ca be chage wh DC-bas lage. Kaajaka e al. [], [] use a eh f successe appxas ba a slu Duffg s equa assug he cechacal esa wh hgh qualy fac. Hwee, se effecs f elecsac fce Duffg s equa wee ake accu. Nlea Paaee. -5.x 7 -.x -.5x -.x -.5x Λ Λ e DC-bas lage (V Fg. The lea paaees esus DC-bas lage f EWG g esa wh =, =9 a =5 V PP. (x - Ths wk Successe appxas [] Tw-aable expas [9] Ths wk Successe appxas [] Tw-aable expas [9] Fg. The cpas bewee he esul f aalycal ehs f EWG g esa wh =, =9 a =5 VPP (ash le a = V PP (sl le wh V P = V b V P = V (ash le, V P = V (sl le wh =5 V PP. (x - Ths wk Successe appxas [] Tw-aable expas [9] c ( 5 Ths wk Successe appxas [] Tw-aable expas [9] ualy fac Fg. The cpas bewee he esul f aalycal ehs f EWG g esa wh V P = V a Effec f al gap spacg, =9 (ash le a = (sl le wh = a =5 V PP b Effecs f qualy fac wh =9. As shw Fgs. a, he aalycal esuls f he pape ae g ageee wh he esuls f successe appxas eh. Hwee, waable expas eh, he esace fequecy shfs w less ha he ehs wh ceasg DCbas lage a eceasg al gap spacg. Mee, he esuls f he aalycal els cae ha he g esa exhb sfeg beha lea ege. Cclus Ths pape eals wh he lea elg f slc cechacal g esas wh elecsac acua a eec bh e a ue aus. The gs f leaes he cechacal esas wee cpleely ele as a sbue elee usg Tayl sees a efa aalyss. Base he ee expesss f h-e leaes echacal a eleccal sffess, he expess f he esace fequecy was bae usg he peuba eh. The lea effecs fequecy espse wee aesse eals a he esuls f he pape wee cpae wh w aalycal els, as well. I was shw ha he cechacal g esa exhbs he sfeg beha. Mee, hee s a ae-ff bewee he ceal ehs euce al essace a sably f he fequecy espse cechacal g esas. Whle he DC-bas lage s cease he al gap spacg s ecease, he g esa beces e suscepble lea effecs. I a, ceasg he esa qualy fac was shw l he peak fequecy wa lwe fequeces a ecease he axu eegy se. The pesee el a he esuls f hs pape allw esges pze he esg f cechacal g esas a pe he peface f MEMS-base fles a scllas. Refeeces [] Fahpu M., Refa M. H. a Ebah S. M., Desg f a esa suspee gae MOSFET wh egae chael pg, Iaa Jual f Eleccal & Elecc Egeeg, Vl., N., pp. 77-, Jue. [] Mes R. M. C., Fey R. H. B. a Njeje H., Phase feeback f lea MEM esas sclla ccus, IEEE/ASME Tasacs Mechacs, Vl., N., pp. -, Aug. 9. [] Dec M. U., Aheleu M. A. a Nguye C. T. C., Mechacally ce-cuple squae cesa aay f euce sees al essace, Jual f Mcelecechacal Syses, Vl. 5, N., pp. 9-, Dec.. [] Mes R. M. C., Fey R. H. B., Va Beekb J. T. M., Phab K. L. a Njeje H., Mellg he 5 Iaa Jual f Eleccal & Elecc Egeeg, Vl., N., Mach

9 yacs f a MEMS esa: Sulas a expees, Sess & Acuas A: Physcal, Vl., pp. -5, Ap. 7. [5] Gu C., Legebeg R., Tlas H. A. C., Flua J. H. J. a Elwespek M., Nleay a hyseess f esa sa gauges, Jual f Mcelecechacal Syses, Vl. 7, N.,, pp. -7, Ma. 99. [] Alasal A. T. a Kaajaka V., Th-e eula celecechacal fles cuple wh capace asuces, Jual f Mcelecechacal Syses, Vl. 5, N., pp. -, Feb.. [7] Sha L. C., Nu T. a Palaapa M., Nleaes a hgh- SOI Lae-e bulk esa, Jual f Mcechacs a Mcegeeg, Vl. 9, pp. -, Ju. 9. [] e Y., L S. S., L Y. W., Re Z. a Nguye C. T. C.,.5-GHz cechacal exesal we-glass e g esas, IEEE Tasac Ulascs, Feeleccs, a Fequecy Cl, Vl. 55, N., pp. 9-97, Ap.. [9] Zhag W., Baskaa R. a Tue K. L., Effec f cubc leay au-paaecally aplfe esa MEMS ass ses, Sess & Acuas A: Physcal, Vl., pp. 9-5, Aug.. [] Kaajaka V., Mala T., Lpsae A. a Oja A., Nlea echacal effecs slc lgual e bea esas, Sess & Acuas A: Physcal, Vl., pp. -7, Dec.. [] Kaajaka V., Mala T., Khaak J., Kaelus H., Oja A. a Seppa H. Nleaes sglecysal slc cechacal esas, The Ieaal IEEE Cfeece Sl sae Sess, Acuas a Mcsyse, pp ,. [] Ha Z., Pukaal S. a Fakh Ayaz., VHF Sgle-Cysal Slc Ellpc Bulk-Me Capace Dsk Resas-Pa I: Desg a Melg, Jual f Mcelecechacal Syses, Vl., N., pp. -, Dec.. [] Sa M. H., Elascy - They, Applcas, a Nuecs, E, Bulg, Acaec Pess, 9. [] Taka T., Haa H. a Tkawa Y., Aalyss f -axsyec ba e pezelecc aula plae a s applca a ulasc, IEEE Tasac Ulascs, Feeleccs, a Fequecy Cl, Vl. 7, N., pp , N. 99. [5] Maques F., Casell R. C. a Shkel A. M., Mellg he elecsac acua f MEMS: sae f he a, IOC-DT-P, Vl., pp. -, Sep. 5. [] Kaajaka V., Mala T., Lpsae A., Oja A. a Seppa H., Nlea ls f sgle-cysal slc cesas, Jual f Mcelecechacal Syses, Vl., N. 5, pp. 75-7, Oc.. [7] Wag, J., Re, Z. a Nguye, C. T. C.,.5- GHz Self-Alge bag cechacal sk esa, IEEE Tasac Ulascs, Feeleccs, a Fequecy Cl, Vl. 5, N., pp. 9-97, Dec.. [] Ha, Z. a Ayaz, F., Supp lss cechacal sk esas, The Ieaal IEEE Cfeece Mc Elec Mechacal Syses, pp. 7, 5. [9] Lee J., Ya J. a Sesha A. A., Suy f laeal e SOI-MEMS esas f euce ach lss, Jual f Mcechacs a Mcegeeg, Vl., pp. -, Ma.. [] Khe L. a Palaapa M., Hgh- bulk-e SOI squae esas wh sagh bea achs, Jual f Mcechacs a Mcegeeg, Vl. 9, pp. -, Ja. 9. Ablfazl Bja was b Bja, Ia 9. He ecee B.S. egee elecuca egeeg a M.S. elecc egeeg f Fews Uesy f Mashha (FUM, Ia 5 a 7, especely. He s cuely PhD caae elecc egeeg a he Depae f Eleccal Egeeg, Faculy f Egeeg, Fews Uesy f Mashha. Hs eseach eess clue cechacal esas, fles a lea effec MEMS-base eces. He als k pa a yea j cllaba a he Sych Lgh Reseach Isu (SLRI, Nakh Rachasa, Thala whee he wke LIGAbase cechacal esas. Sayye-Hsse Kesh ecee hs B.Sc. egee Physcs f Mashha Uesy 99, M.Tech. f Buel Uesy (L, UK 97, a Ph.D. egee f The Pesylaa Sae Uesy (Uesy Pak, USA 9. He sae wk Fews Uesy f Mashha 97 fs Physcs Depae, a lae was asfee he Eleccal Egeeg Depae. He s cuely a pfess f Eleccal Egeeg. Hs eseach eess clue esg a fabca f phlac sla cells, MEMS eces, aspae-cucg (TC fls, sucual-efec passa slc a TC fls, ullaye h-fl pcal fles, a h-fl gas sess. Bja e al: Nlea Melg a Iesgag he Nlea Effecs 5

10 Wa Wabuee was b R-e, Thala 9. He ecee he B.S. a M.S. egees he eleccal egeeg f Suaaee Uesy f Techlgy (SUT, Nakh Rachasa, Thala 5 a 7, especely. He has bee wh Sych Lgh Reseach Isue (SLRI, Nakh achasa, Thala as a ebe f Reseach Saff SUT-MEMS Labay Sce 5. He s cuely wkg wa he Ph.D. egee a Suaaee Uesy f Techlgy sce 7. Hs eseach eess clue esg, aalyss f c-eces such as cb-e acua a RF swch, a eelpe f -ay lhgaphy pcess. 5 Iaa Jual f Eleccal & Elecc Egeeg, Vl., N., Mach