Superheterodyne Amplification for Increase the Working Frequency

Transcription

1 Jurnal f Elctrmagntic Analysis and Applicatins, 7, 9, ISSN Onlin: ISSN Print: Suprhtrdyn Amplificatin fr Incras th Wrking Frquncy Svtlana Kshvaya, Vladimir Grimalsky, Yuriy Ktsarnk, Margarita Tcpytl, Jsus Escbd Autnmus Stat Univrsity f Mrls, Curnavaca, Mxic Hw t cit this papr: Kshvaya, S., Grimalsky, V., Ktsarnk, Y., Tcpytl, M. and Escbd, J. (7) Suprhtrdyn Amplificatin fr Incras th Wrking Frquncy. Jurnal f Elctrmagntic Analysis and Applicatins, 9, Rcivd: March 3, 7 Accptd: May 3, 7 Publishd: May 6, 7 Cpyright 7 by authrs and Scintific Rsarch Publishing Inc. This wrk is licnsd undr th Crativ Cmmns Attributin Intrnatinal Licns (CC BY 4.). Opn Accss Abstract Th amplificatin f micrwavs in n-gaas films has bn widly studid. On th thr hand, using nnlinar paramtric ffcts in micrwav, millimtr, and TH rangs has a larg ptntial. In this papr th rsnant nnlinar phnmna ar invstigatd in activ n-gaas smicnductr and in films n its bas. Th phnmna ar th nnlinar intractins f spac charg wavs, including th frquncy multiplicatin and mixing, and th thr-wav intractin btwn tw TH lctrmagntic wavs and a singl spac charg wav. This thr-wav intractin rsults in th suprhtrdyn amplificatin f TH wavs. Th lctrn vlcity in GaAs is th nnlinar functin f an xtrnal lctric fild. If th bias lctric fild is mr E > E crit 3 KV cm, it is pssibl t btain a ngativ diffrntial mbility (NDM and spac charg wavs). Th spac charg wavs hav phas vlcity f lctrns qual t v = v( E), E = V L, whr V is th vltag, prducing th bias lctric fild E in GaAs film. Th suprhtrdyn amplificatin and th multiplicatin f micrwavs ar vry prmising fr building activ snsrs in tlcmmunicatins systm, radimtrs, and radi tlscps. Th suprhtrdyn mchanism has an advantag rlatd t dcrasing nis bcaus f incrasing f frquncy in th prcss f amplificatin. It is usd in th prcss f amplificatin f lngitudinal spac charg wavs that in turn causs th transfr f nrgy frm lngitudinal wav int transvrs n with incrasing frquncy. This is ralid du t paramtric cupling f tw transvrs wavs and a singl spac charg wav in GaAs. Kywrds Spac Charg Wavs, Suprhtrdyn Amplificatin. Intrductin Vry high frquncis including gigahrt rang ar vry prmising fr building DOI:.436/jmaa May 6, 7

2 S. Kshvaya t al. activ dvics [] []. This articl is dvtd t ida t us crystal GaAs lik vry wid matrial fr btain f high frquncy f vry simpl mthd in mnlithic matrial withut f difficult nanstructur dsign which usually dstryd diffusin prcsss. Thr ar diffrnt ffcts f nnlinar intractin f lctrmagntic wavs which causd th incras f frquncy. Mr frquntly it is using th trminus suprhtrdyn mchanism fr incrasing th frquncis. It is usful t shw hw wrks all mchanisms n simplst cas with analytical dmnstratin f suprhtrdyn amplificatin in cas f GaAs thanks paramtric cnnctin f tw transvrsal wavs and charg wav. It is ncssary t xplain th rl f spac charg wav. Amplificatin f travling spac charg wavs (SCW) f th micrwav rang in n-gaas has bn undr invstigatins fr many yars []. Whn bias lctric filds ar highr than th critical valu fr bsrving ngativ diffrntial cnductivity (NDC), spac charg wavs hav th pssibility t tak nrgy du t ngativ diffrntial mbility. But th critical valu f bias lctric fild in GaAs is E c = 3.5 kv cm that limits th maximum valus f spac charg wavs. Als, th frquncy rang f amplificatin f SCW in GaAs films is f < 5 GH. At frquncis f > 5 GH, it is bttr t us a nw typ f intractin. It is ncssary t us th cnnctin f spac charg wavs with lctrmagntic n. This cnnctin causd t study nnlinar intractin btwn spac charg wavs and lctrmagntic n. First f all it is ncssary t discuss a nw typ f intractin namd suprhytrdyn n, which analyd vry carfully in this articl. In any cas th ngativ mbility f crystal is vry imprtant fr all ur simulatin f nnlinar intractin fr diffrnt cass. Th suprhtrdyn amplificatin is thanks ging f th nrgy f crystal with battry and with currnt t nrgy f lctrmagntic wav f high frquncy in cas f cnnctin f lctrmagntic and spac charg wavs. In rdr t btain a ngativ diffrntial mbility (NDM), th bias lctric E > E, which is diffrnt in diffrnt crystals. fild crit. Ida and Mdl Lt s cnsidr l crystal GaAs In rdr t btain a ngativ diffrntial mbility (NDM) in GaAs, th bias lctric fild E > E crit 3 KV cm shuld b [] []. Thr ar th tw lctrmagntic wavs f TH rang with frquncis and wav numbrs ω, k, ω, k with ppsit dirctins f prpagatin and spac charg wav with Ω, K f th micrwav rang. Th frquncis and wav numbrs ar cnnctd by cupling cnditins ω ω =Ω () κ + κ = K Th wav synchrnism is ralid at th frquncis: Ω ω (), c whr, c ar th lctrn and light vlcitis, is dilctric prmittivity f GaAs. Lt s xplain simplst cas f intractin in th n dimnsinal mdl 44

3 S. Kshvaya t al. = = x y fr analysis f Maxwll s quatins (in abslut units): E 4π rt H = + J c t c H rt E = c t J = n and hydrdynamic quatin f th mtin fr th lctrns v T + ( ) = n υ E+ H (4) t m c nm * whr and m ar th lctrn charg and mass, υ is th cllisin frquncy, n is th lctrn s cncntratin. Fr lctrmagntic wavs th ffctiv dilctric cnstant is ω p, = ω ω ( ιυ ) 4πn with plasma frquncy ω p =. Th intractin f lngitudinal wav m ( E, v, K ) with transvrsal wavs ( Ex, Hy, vx, k, ) is pssibl thanks nnlinar cnnctin btwn wavs. In th cas f lngitudinal wav ( E, v, K ) it is ncssary us (3), and (4) in th cas f frquncy Ω v taking int accunt th diffrntial ngativ mbility f lctrns T n = E ( xh ), (5) mυ mcυ nm υ It is ncssary t us µ ( E) µ ( E E) v µ de mυ = = + = +, E dµ whr v = µ E, µ d = µ + ar th vlcity lctrns and diff- µ de rntial mbility µ d f lctrns, which is ngativ in cas if th fild is mr th critical fild E > E crit 3 KV cm fr GaAs. It is pssibl t tak in calculatins µ = µ lik mbility in first vally f GaAs and n is initial cncntratin f lctrns. Th variabl currnt j is dtrmind frm (5) n J Z = nµ de n + D + nµ ( xh ), (6) c V T T whr D = = is diffusin cfficint. Using (6) and (3) it is pssibl m υ υ btain th quatin fr lngitudinal variabl wav E E E 4π n µ + D + ω ME = { xhy} (7) t c whr th right part is calculatd lik rsnanc part f lngitudinal part, 4πn µ d 4πσd ω = M =, is th rlaxatin frquncy, σ is diffrntial cnduc- d tivity ngativ if fild is mr critical. (3) 45

4 S. Kshvaya t al. Fr transvrs wavs ( Ex, Hy, vx, k, ) frm (3) and (4) it is pssibl btain th wav quatin Ex Ex 4π ω pex = ( nvx) (8) c t c t Th right parts f (7) and (8) dscrib th nnlinar intractin f wavs which is rsnanc () with rspct t th wav quatin. 3. Nnlinar Equatins fr Wavs Th nnlinar intractins f wavs ar with lngitudinal wav and transvrsal lctrmagntic wavs whr,, k x i( Ωy K) i( Ωy K) 3, 3, E = t + t i( ωt k ) i( ωt k ),, E = t + t i( ωt+ k ) i( ωt+ k ) t, t, + + ω ω p =. Th wavs satisfy th paramtric cnditins (). c ω, Th nnlinar right parts in (7) and (8) wr calculatd using Blmbrgn s mthd [3]: Vx = i + i + c. c. mω iψ iψ mω ck ck Hy = + + c. c. ω iψ iψ ω K = + 3 iψ 3 n i c whr ψ ωt k, ψ ωt k, ψ3 t K, ψ ψ ψ3. c. (9) () = = + =Ω = +. Frm (8) w hav tw nnlinar quatins fr transvrs wavs: whr α = v, ω K ckω m ck,, l + = α 3 t = α t 3 = ar grup s vlcitis f lctrmagntic wavs, ω K ckω (a) (b) ω α = and α m α. Frm (7) it is pssibl t b- tain th nnlinar quatin fr lngitudinal wav ωµ K p + + idk + ( + DK ) 3 D = i ωω t 4. Calculatin f Suprhtrdyn Amplificatin (c) W analy amplificatin by mans f using cnstant pumping wav =, 46

5 S. Kshvaya t al. = t tins and ngativ diffrntial mbility µ d <. It is ncssary us th qua- = y =, 3 = fr = t = α3 3 γ + = i 3 () Ω and th cnditins ( ), Ω ωd, whr ω D = is th diffusin frquncy, α =, γ = Frm (a) and (b) it fllw th ωd D Κ ωµ p Κ cmk ωω Γ dcisins, 3 Fr Γ it is pssibl btain th quatin And αγ = Γ = + i Γ = i αγ = ( ) ω M Th suprhtrdyn amplificatin is charactrid by cfficints Γ and Γ : Γ Γ = Γ (3) Γ Γ Γ If w hav ngativ diffrntial mbility ω M < and Γ Γ frm (3) it is fllw ptimal fr amplificatin lngth L f crystal: whr ( L) p max υω c M L Ωω = max =. Fr th nxt paramtrs f GaAs th initial vlum cnnω 4 3 n cm, th cllisin frquncy υ s, 7 v cm s, L cm, absnc f dmain, th frquncis cntratin f lctrns th vlcity ω, 6 s in TH rang and th plasma frquncy ω p s, m Ω s m in th micrwav rang,., whr m is th mass f lc- 47

6 S. Kshvaya t al. trn,, th pumping intnsity is 6 cm v, sg max = and n frquncy Ω π 4 GH th suprhtrdyn amplificatin f abut c S = rg E 8π cm sc ( L) fr th cas f suprhtrdyn intractin. 5. Simulatin f Amplificatin in Gaas Films. This amplificatin is significant Th amplificatin is mr prspctiv fr intgratd systm s it is ncssary t analy amplificatin and multiplicatin fr btain incras f frquncis in GaAs films with spac charg wavs. It is pssibl by mans f cmputr simulatin and cnsidratin f th paramtric intractin f spac charg wavs with matching cnditins is ralid: ω = ω + ω ; k = k + k. (4) 3 3 Th lctrn vlcity in GaAs is th nnlinar functin f an xtrnal lctric fild [4] [5]. Th crdinat systm is chsn as fllws: X-axis is dirctd prpndicularly t th plan f film, th drift bias fild is applid alng Z n, xciting and rciving antnnas ar paralll t Y-axis. Th sis f th film ar L, L y. In ur mdl, it is cnsidrd D mdl f th lctrn gas in GaAs s as ur cnsidratin dscribd th pitaxial film n-gaas and i-gaas substrat. Thus, D lctrn cncntratin is prsnt nly in th plan x = (pitaxial n-gaas), and an influnc f transvrs mtin f carrirs n spac charg wav dynamics is nglctd. Cnsidr spac charg wavs having phas vlcity qual t vlcity f lctrns drift qual t v = v( E), E = V L, whr V is th cnstant diffrnc f ptntial, crating th bias lctric fild E in GaAs film. Th fllwing systm fr dscriptin f nnlinar spac charg wavs in quasi-statinary apprximatin is usd: n + div ( nv D n) = ; v = µ ( E) E ; x= t E = E + E + E xtδ ( x) ; (5) E = ϕ; ϕ = n δ ( x ); y y t t E xt = E j sin ( ω jt) xp xp ; (6) j= y t Th Equatins (5), (6) ar addd by bundary cnditins: ϕ( xy, ; = ) = ϕ( = L) = ; n( y ; = ) = n ( = L) = n ; n n Ey ( x, y =, ) = Ey ( y = Ly) = ; ( y =, ) = ( y = Ly) = y y Hr n n n = + whr n is cnstant tw-dimnsinal lctrn cncntratin, n is its varying part f cncntratin, D is th diffusin cfficint which, 48

7 S. Kshvaya t al. wakly dpnds n a drift fild, is th lctrn charg (th signs ar changd fr th psitiv charg); is unit vctr alng dirctin f axis Z, and is th lattic dilctric prmittivity f GaAs. A dpndnc f Z-cmpnnt f lctrn vlcity v ( E ) is prsntd in a Figur. In th input antnna ( =, y = y), th signal f th lngitudinal lctric fild is prsnt E xt at tw sparat micrwav frquncis ω, ;, y, t ar half-widths f input puls. This signal xcits spac charg wavs in D lctrn gas. First f all, amplificatin at th frquncis ω, ω taks plac in th cas f ngativ diffrntial mbility, NDM. Als, th paramtric intractin f wavs with matching cnditins is ralid lik (4). Th utput antnna is in = >. Th prblm is t gt th ptimal cnditins fr rlasing th utput signal at th sum frquncy in films f finit sis. Fr a small mnchrmatic input signal ( E, n ~xp i ( wt k), ω = ω + iω ) in an unbundd film, it is pssibl t gt th xprssin fr th linar incrmnt f tmpral grwth ω : 4πn dv ω ω = k + Dk ; k = (7) de V In th cas f NDM ( dv de < ), an instability taks plac: ω < in a crtain frquncy rang. A dpndnc f incrmnt ω n carrir frquncy ω is prsntd in a Figur. It is sn that thr xists th maximal valu at an ptimal frquncy. A cmparisn f th valu f incrmnt btaind in lcal fild apprximatin usd hr with calculatin within th mr gnral 5 3 nn-lcal Shur s mdl [4], [5] shws that undr n = cm, th lcal fild apprximatin is valid fr ω < 5 s. Thrfr, th sum frquncy shuld b chsn within this rang. Simulatins f wav mixing in GaAs films dmnstrat a pssibility t gt th Figur. Dpndnc v E ( 5 m/s, 5 V/m). 49

8 S. Kshvaya t al. signal at sum frquncy undr a wid rang f amplituds f input signals. Th spctral distributins f utput signal E ( w ) in films with diffrnt input antnna widths ar prsntd in Figur 3 and Figur 4. Th paramtrs ar: D lctrn cncntratin is n = cm, L = μm, L y = μm ; = μm, =.5 μm, = 9 μm ; y = 5 μm ; y = μm (Figur 3); y = 3 μm (Figur 4). Th input puls duratin is t = 5 ns ; input frquncis ar ω 5 =.4 s, ω =.3 s ; E = 5.4 V m, E = V m, E =. V m. Th utput amplituds f wavs ar ~ 4 3 V m. In th cas f widr input antnna, th spctral lin intnsity crrspnding t sum frquncy is gratr but th additinal backgrund spctrum is prsnt. This can b xplaind in th fllwing mannr. Th main bstacl fr bsrvatin f wav mixing is a transitin f instability int an ssntially nnlinar rgim, whr a lt f xtranus spctral cmpnnts ar prsnt. Fr a widr input antnna, such a transitin taks plac arlir. Thus, thr xists th ptimal width f th input antnna fr bsrving wav mixing. Figur. Dpndnc f incrmnt ω n a frquncy ( s ). Figur 3. Furir spctrum f E (rlativ units) in th utput antnna. 5

9 S. Kshvaya t al. Figur 4. Furir spctrum in th utput fr widr input antnna. A cmparisn f simulatins with xprimnt n wav mixing in GaAs films [6] shws that thr is a cincidnc n th frquncy intrval and pssibl lvls f input signals. 6. Cnclusins It is shwn that suprhtrdyn amplificatin is ralid by ngativ diffrntial mbility in GaAs and nnlinar intractin tw transvrsal and lngitudinal wavs. Th pumping wav f vry small amplitud hlps t mv th nrgy f battry t micrwav. Usually lvl f nis is lw in high f frquncy and absnt f dmains. Th advantag t us f transvrsal wavs is in mving vry asy frm crystal. Th pumping wav may b vry lw amplitud. Th valu f amplificatin is vry big n th lngth L cm withut xciting f dmain. Th cnditin fr xciting dmain nl cm is nt fulfilld. This mchanism f amplificatin is vry prmising in millimtr and submillimtr rangs. In ths rangs it is absnt gd amplifirs rangs. Th mchanism f th mixing and th multiplicatin is a transitin f instability int an ssntially nnlinar rgim. Thr xists th ptimal width f input antnna fr bsrving wav paramtric and multiplicatin ffcts. Cmparisn f simulatins with xprimnt n wav mixing in GaAs films is t shw a cincidnc n frquncy intrval and pssibl lvls f input signals. It is pssibl futur wrk t invstigat sm thr crystal having ngativ diffrntial mbility which it is ralid nw. Fr anthr hand it is pssibl t us th strngly nnlinar matrial lik TiSrO 3 that is dn [7] [8] [9], and th rsults f this invstigatins ar succssful. Only it is n prblm, frm diffrnt matrials including TiSrO 3, it is ncssary t us tmpratur f liquid nitrgn N. It is pssibl t us anthr mthd t incras th frquncy using pridical systms and graphn [] []. Rfrncs [] Dan, R.H. and Matarss, R.J. (97) Th GaAs Travlling Wav Amplifir as a Nw Kind f Micrwav Transistrs. IEEE Trans. MTT, 6, [] Barybin, A.A. and Prigrvskii, V.M. (98) Th Wavs in Thin Layrs f Smicnductr with Ngativ Diffrntial Mbility. Isvstiya VUZ. Fisika (Russian J. f Physics), 4,

10 S. Kshvaya t al. [3] Blmbrgn, N. (966) Nnlinar Optics. Wrld Scintific, Singapr, 44. [4] Shur, M. (987) GaAs Dvics and Circuits. Wily, Nw Yrk. [5] Shur, M., Ed. (996) Cmpund Smicnductr Elctrnics. Wrld Scintific, Singapr. [6] Mikhailv, A.I. () Exprimntal Invstigatin f Paramtric Intractin f Spac Charg Wavs in Thin Layrd Smicnductr Structurs n th Bas f Gallium Arsnid. Tchnical Physics Lttrs, 6, [7] Grimalsky, V., Kshvaya, S., Escbd, J. and Tcpytl, M. (6) Nnlinar Trahrt Elctrmagntic Wavs in SrTiO 3 Crystals undr Fcusing. Jurnal f Elctrmagntic Analysis and Applicatins, 8, [8] Grimalsky, V., Kshvaya, S., Escbd-Alatrr, J. and Rapprt, Yu. (6) Frquncy Multiplicatin f Trahrt Radiatin in Wavguids n th Bas f Paralctrics. 6 IEEE Radar Mthds and Systms Wrkshp, Kyiv, Ukrain, 7-8 Sptmbr 6, -3. [9] Kshvaya, S.V., Grimalsky, V.V., Ktsarnk, Yu.N. and Tcpytl, M. (6) Mdulatin Instability f Transvrsly Limit Elctrmagntic Wavs f Trahrt Rang in Strntium Titanat Paralctric. Radilctrnics and Cmmunicatins Systms, 59, [] Castrjn-M, C., Grimalsky, V.V., Kshvaya, S.V. and Tcpytl-T, M. (4) Amplificatin f Optical Phnns in Narrw Smicnductrs at Lw Tmpraturs. Radilctrnics and Cmmunicatins Systms, 57, [] Rapprt, Yu., Grimalsky, V., Irsh, I., Kalinich, N., Kshvaya, S., Castrjn-Martin, Ch. and Kivshar, Yu.S. (3) Nnlinar Rshaping f Trahrt Pulss with Graphn Mtamatrials. Pis ma v ZhETF, 98, Submit r rcmmnd nxt manuscript t SCIRP and w will prvid bst srvic fr yu: Accpting pr-submissin inquiris thrugh , Facbk, LinkdIn, Twittr, tc. A wid slctin f jurnals (inclusiv f 9 subjcts, mr than jurnals) Prviding 4-hur high-quality srvic Usr-frindly nlin submissin systm Fair and swift pr-rviw systm Efficint typstting and prfrading prcdur Display f th rsult f dwnlads and visits, as wll as th numbr f citd articls Maximum dissminatin f yur rsarch wrk Submit yur manuscript at: Or cntact jmaa@scirp.rg 5