322 Philips tech. Rev. 32,322-327, 1971, No. 9/10/11/12 YIG filters P. Röschmnn Introduetion A new group of microwve ferrite components hve ttrcted good del of ttention in recent yers becuse of their unique nd very nerly idel chrcteristics. These components, known s "YIG" devices, re now employ.edin vrious pplictions. Smll polished smples of single-crystl yttrium iron grnet (YIG, Y 3Fe5ÛI2), operted t the ferrimgnetic resonnce, re used s resontors for tunble filters [11,for tuning oscilltors nd for low-level limiters. Single-crystl YIG hs n extremely smll ferrimgnetic resonnce linewidth, which gives high unloded Q-fctors (up to 10000). Fig. 1 shows the principle of opertion of YIG resontor in typicl coupling configurtion giving bnd-pss-filter response. The electron spins in the YIG crystl tht re unpired nd re the origin of its ferrimgnetism re ligned by sttic or qusisttic mgnetic field Ho. An r.f. signl t the input coupling loop builds up n r.f. mgnetic field H«perpendiculr to the sttic field. Becuse of the gyroscopic property of the electron spins the resultnt mgnetiztion M in the YIG crystl will precess round Ho; the precession increses in mplitude if the signl frequency coincides with the precession frequency, which is lso known s the ferrimgnetic resonnce frequency, nd is determined solely by the fundmentl constnts of the electron nd by the pplied mgnetic field Ho [21.As result of the precession n r.f. mgnetie-field component rises perpendiculr to the plne of Ho nd Hrf (fig. 1); this perpendiculr component cn be coupled out by mens of the second hlf-loop. It follows tht only signls t the precession frequency re coupled from the input loop to the output loop by the precessing mgnetiztion in the YIG sphere. Signls t other frequencies re unffected by the YIG sphere nd no r.f. power is trnsferred by the YIG filter becuse there is no coupling between the two orthogonl loops. Thus YIG filter will give single unmbiguous response, which cn be tuned over rnge of more thn ten to one in frequency simply by vrying the pplied sttic mgnetic field. The electricl behviour of YIG filters is in mny spects the sme s tht of conventionl microwve filters with trnsmission-line resontors or Ing. P. Roschmnn is with Philips Forschungslbortorium Hmburg GmbH, Hmburg, Germny. cvities, but YIG resontors do hve some unique fetures (including certin limittions) which will be described in the following section. Severl completely ssembled YIG devices re shown in fig. 2. Their size is minly determined by the electromgnet used for tuning. Resonnce; lower cut-off frequency In pplictions of single-crystl YIG smples s ferrimgnetic resontors for microwve filters the uniform-precession resonnce mode (UPR mode) is utilized. This is the fundmentl resonnce mode in which ll electron spins in the YIG smple precess with the sme mplitude nd phse ngle bout the sttic mgnetic field. Higher-order resonnce modes lso exist in which the mplitude nd phse of the precession re not the sme ll over the YIG smple (usully sphere) nd vry in regulr geometricl pttern. The Fig.t. Bnd-pss filter with YIG resontor. Input nd output re coupled to the YIG sphere YIG by two orthogonl hlf-loops. The sphere is mgnetized by sttic externl field Ho; if n r.f. mgnetic field Hr! is coupled in, the resulting mgnetiztion M precesses bout the direction of Ho becuse of the gyroscopic property of the electron spins in the mteril. The precession introduces mgnetie-field components tht cn be coupled out by the output semiloop. The precession ngulr frequency w increses linerly with the mgnetic field strength Ho, which is djusted to tune the filter to the frequency required. Other frequencies do not excite the precession nd re therefore not trnsmitted by the filter.
Philips tech. Rev. 32, No. 9/1 0/ 11/ 12 YIG FILTERS 323 Fig. 2. Severl tunble YIG devices. The electromgnets, whose connections cn be seen on the front of the housings, determine the size of the devices. resonnce modes of YIG smples sufficiently smll compred with the wvelength for the effects of wve propgtion through the smple to be neglected hve been clculted by L. R. Wlker [3]; these re clled mgnetosttic modes or Wlker modes. The resonnt freq uency of the U PR mode for xilly exceeded, for typicl YIG resontors with dimeter of 0.3 mm, mgnetized spheroids with circulr symmetry bout Ho t frequencies bove 30 GHz. is given by: The resonnt frequencies In of the higher-order mgnerosttie modes re locted in frequency bnd round the resonnt fre- (I) quency fo of the UPR mode: f = y {Ho + H + (Nt- Nz)Ms}, where y is the gyrorngnetic rtio, which is equl to 35.2 khz/(a/m) (2.8 MHz/Oe). In the reltion(i)ho is the externl sttic or qusisttie mgnetic field nd H is the crystl-nisotropy field, which my be regrded s n dditionl externl field whose mgnitude nd sign depend on the crystllogrphic orienttion of the YIG resontor with respect to Ho. The quntities N, nd Ne re the demgnetizing fctors for the YIG smple in the trnsverse nd xil directions respectively. Both vrywith its geometric shpe; for sphere V, is equl to Nz, which mens tht the lst term in (I) vnishes. Consequently the UPR resonnt frequency of sphere does not depend on the sturtion mgnetiztion Ms, which is constnt of the mteril nd hs vlue of 1.42 xl 0 5 A/m (1780 Oe) for YIG. In some pplictions the YIG resontor cnnot be mde very smll compred with the wvelength nd wve-propgtion effects hve to be tken into ccount. For sphere in which Ni is equl to N«, the resonnt frequency is given by (4): f 4n2 ( cl )2} = y { Ho + H.- -90 Ms(Er + 5);:.;-, (2) where Er is the reltive dielectric constnt (Er = 16 for YIG) cl the sphere dimeter nd A the free-spce wvelength t resonnce. Unlike tht of the UPR mode, the resonnt frequency is not independent ofthe dirnensions of the smple. The propgtion term remins smller thn 50 MHz if the rtio of the dimeter of the sphere to the wvelength is less thn I : 30. This rtio is fo - yntms < fn < fo + Y (0.5 - Nt)Ms. (3) Fortuntely only few of the higher-order modes re excited in homogeneous r.f. mgnetic field, nd only wekly. In multistge filters the level of interfering higher-order modes cn be suppressed further by using spheres with slightly different Ms. This will not chnge the resonnt frequency of the UPR mode but the higher-order modes will hve slightly different resonnt frequencies owing to their dependence on Ms. Thus the min response remins unchnged wheres the interstge coupling of the unwnted higher-order modes is considerbly reduced. Tt lso follows from eqs. (I) nd (2) tht there re no resonnces t higher hrmonics of the frequency jo; this mens tht YIG resontor gives only single response between d.c, nd millimetre wvelengths, which cn be tuned linerly through frequency bnd of more thn decde by n externl sttic or qusisttic mgnetic field. (l) See for exmple: G. L. Mtthei, L. Young nd E. M. T. Jones, Microwve filters, impednce-mtching networks, nd coupling structures, McGrw-Hill, New York 1964. [2) See lso: M. Lemke nd W. Schilz, Microwve integrted circuits on ferrite substrte; this issue, pge 315. (3] L. R. Wlker, Resonnt modes of ferromgnetic spheroids, J. pp!. Phys. 29, 318-323, 1958. [4] J. E. Mercereu, Ferromgnetic resonnce g fctor to order (kro)2, J. ppl. Phys. 30, 184S-185S, 1959.
324 P. RÖSCHMANN Philips tech. Rev. 32, No. 9/10/11/12 Single-crystl YIG hs the smllest known ferri-x mgnetic resonnce linewidth (of the order of 1 MHz [5]).Imperfections in the surfce nd impurities in the crystl give losses becuse of scttering of r.f. energy into the crystllttice; highly polished surfce nd high degree of purity nd homogeneity of the YIG crystl re therefore required to obtin the high Qo (qulity fctor) which is possible with YIG resontors. Curves showing the mesured Qo plotted ginst' frequency for YIG nd YGIG ( glliumsubstituted YIG) spheres nd for YIG disc re shown in jig. 3 r6]. The Qo decreses rpidly to zero t the lower frequencies. This occurs when the sttic mgnetic field Ho corresponding to low frequencies becomes so wek tht the YIG resontor is no longer mgneticlly 2'~--------~r---------~ M.=1.I.2xlOSp,lm 10 OOOI----------+---------..l(1780 Oe) s 2 I 1.42(1780)...,," " I././ 109JL.1----.t;\---,----L.,!:-L...l...J.,2!;-----iSl--:-!.10 -f GHz Fig. 3. Unloded Qo (qulity fctor) plotted ginst frequency J, mesured for YIG nd YGIG spheres (solid lines) nd YIG disc (dshed) [61. sturted nd the internl mgnetic field pproches zero, becuse the spins re then no longer ligned prllel nd r.f. energy couples from the UPR mode to the crystl lttice. The cut-off frequency I«of YIG resontor tht is obtined when the internl mgnetic field Hiz pproches zero cn be found from (1) when we neglect Hndput Hlz = Ho- NzMs = 0: I«=yNtMs. For spheres, with Nç = 1/3, the cut-offfrequency given by (4) is 1660 MHz; mesured vlues re somewht higher (round 1800 MHz) becuse not ll the electron spins re ligned s soon s Hi«becomes greter thn zero (this cn be seen from the rounded corners ofthe hysteresis loop). The cut-off frequency of ferrimgnetic resontor cn be lowered by using thin xilly mgnetized discs which hve n Ni dose to zero, or by reducing the sturtion mgnetiztion of the resontor mteril. The (4) sturtion mgnetiztion cn be reduced either by substituting gllium t iron sites in the YIG system (y3gxfe5-x012, with typicl x-vlues between 0.05 nd 0.9) or by heting the YIG resontor nd mking use of the nturl decrese of M; with incresing temperture. All these methods cn of course be combined to extend the ppliction of YIG resontors to lower frequencies; owing to poor Qo nd wek coupling, pplictions re not fesible below 200 or 100 MHz. The upper limit of the useful frequency rnge is only determined by the high tuning fields required; prcticl limit lies t bout 56 GHz, requiring field of 1.6 MA/m (20 koe). Temperture dependence YIG resontors cn be operted from liquid-helium tempertures up to little below the Curie temperture, which is t bout 280 oe. In the usul temperture rnge for pplictions, -40 C to +80 C, the effect of the temperture on Qo nd fo cn be entirely ccounted for by the temperture dependence of Ms nd H. It hs been found experimentlly tht t frequencies well bovejs the qulity fctor Qois pproximtely proportionl to Ms; the resulting vrition in Qo with temperture is not lrge, of the order of ± 10% between -40 C nd +80 C. The requirements for the temperture stbility of the resonnt frequency re quite strict since YIG filters re nrrow-bndwidth devices. Optimum performnce is obtined with sphericl resontors, becuse Nt is equl to Ne nd eqs. (1) or (2) show tht H is the chief temperture-sensitive prmeter. Depending on the crystllogrphic orienttion with respect to the tuning field, the temperture coefficient of the resonnt frequency my be djusted between positive or negtive vlue of bout 1 MHz;oC, nd very low vlue (20 khz;oq cn be obtined with crefully djusted sphere. In other shpes of resontor M; hs direct effect on the resonnt frequency. Thin discs, which re sometimes used becuse of their low [«nd high Qo, hve temperture coefficient of the order of 10 MHz;oC. Non-linerity; power limiting Depending on the pplied r.f. power level YIG resontors hve either liner or non-liner response. Mrked non-linerity ppers suddenly bove shrply defined r.f. power level which is different for different mterils nd for different signl frequencies. This power level is very low (bout 10 flw) if n r.f. signl t the UPR-mode frequency fo cn prmetriclly excite spin wves t frequency fo/2. This is possible in frequency bnd whose upper limit cn be shown to
Philips tech. Rev. 32, No. 9/10/11/12 YIG FILTERS 325 be 2)' NtMs [7]. This hppens to be twice the cut-off frequency fe, so tht these spin wves cn occur when the resonnt frequency of the filter lies betweenfe nd 2fe. Signls t frequencies bove 2fe minly couple to degenerte spin wves nd the threshold for nonlinerity is ofthe order of 10 m W to 100 mw. The nonlinerity cn be utilized for mking pssive r.f. power limiters, but it lso reduces the rnge of ppliction of liner YIG devices to systems operting t r.f. power levels below 100 mw. Coupling; prcticl exmples The r.f. mgnetic field, which couples the r.f. signl-s to YIG resontor, should be perpendiculr to the tuning field to chieve the mximum coupling. The coupling is proportionl to M'; nd the volume of the YIG resontor nd it lso depends on the dimensions nd impednce of the trnsmission line. Unlike trnsmission-line resontors YIG resontors will only give reltively wek coupling, which mens tht these resontors will not be hevily dmped by the trnsmission lines coupled to them. As consequence the bndwidth of YIG filter remins smll; the mximum chievble bndwidth (between the-3 db points) is of the order of I or 2 per cent of the resonnt freq uency. A coupling section tht is frequently used is the 01'- Fig. 4. ) Two-stge bnd-pss filter designed on the principle outlined in fig. 1. The upper hlf of the electromgnet hs been thogonl-semiloop rrngement shown in fig. 1, which tken off nd is shown on the left. This filter cn be tuned from will give single-stge bnd-pss filter. Multistge filters, 1 GHz to 20 G Hz, the 3 db bndwidth incresing from 20 MHz to 45 M Hz. b) The (wo YIG resontors with coupling loops. which re often required for incresed selectivity, re obtined by cscding such coupling sections. A twostge bnd-pss filter using this principle is shown in jig. 4; the upper hlf of the tuning mgnet hs been removed. This prticulr filter cn be continuously tuned 1 from 1 GHz to 20 GHz nd hs 3 db bndwidth vrying from 20 to 45 MHz nd pssbnd losses between 1.5 db nd 3 db. Fig. 5 shows typicl response for filter of this type tuned to 9 GHz; spurious response due to coupling of higher-order mgnetosttic modes cn lso be seen; t other freq uencies the rejection is more thn 50 db. Bnd-stop filters re obtined by inserting YIG resontors into trnsmission line t pproximtely qurter-wvelength spcing; symmetricl stripline is usully chosen, so tht the tuning mgnet cn be brought close to the stripline conductor without disturbing the r.f. field (jig. 6). This configurtion my be represented by n equivlent circuit with lumped elements. Let us first consider the cse in which there is only one YIG sphere. This my be represented by prllel-resonnt circuit coupled to coupling winding in the trnsmission line (fig. 6b). In the sme wy s the mgneticlly coupled prllel circuit t resonnce considerbly reinforces the mgnetic field inside the Fig. 5. Attenution of the filter shown in fig. 4 s function of frequency. The filter is tuned to 9 GHz. Aprt from spurious response due to higher-order mgnetosttic resonnce the rejection is greter thn 50 db outside the pss bnd. [5) Since the resonnce mesurements re usully performed t fixed frequency while subjecting the YIG smple to vrying mgnetic field, linewidths re generlly given in mgnetic units in the literture; 1 MHz corresponds to 28.4 A/m or 0.357 Oe. [6) The single crystls were grown from solution of YIG (or YGIG) in molten led oxide nd led fluoride, in process described in W. Tolksdorf, Growth of yttrium iron grnet single crystls, J. Crystl Growth 3/4, 463-466,1968. [7) H. Suhl, The nonliner behvior of ferrites t high microwve signlieveis, Proc. IRE 44, 1270-1284, 1956. -f b
326 P. RÖSCHMANN Philips tech. Rev. 32, No. 9/10/11/12 coupling winding, the precession field of the resonnt YIG sphere loclly reinforces the mgnetic field of the stripline. The resultnt effect is tht the line hs high impednce t the loction of the resontor. Owing to the distributed nture of the stripline second YIG sphere spced qurter-wvelength from the first presents low impednce t the reference plne of the first sphere; this my be represented in the equivlent circuit by series-resonnt circuit connected in prllel. If the coupled prllel-resonnt circuit of fig. 6b is replced by n equivlent prllel circuit cong ~ OdB 00 10 nected into the line, the equivlent circuit represented in fig. 6c is obtined for the two-stge bnd-stop filter of fig. 6. The corresponding bnd-stop-filter response is given in fig. 6d; this figure lso shows the voltge stnding-wve rtio S. The tuning rnge is limited to bout one or two octves becuse of the Aj4 seprtion of the resontors. A nonreciprocl-ttenution response is most effectively obtined by coupling the YIG resontor to circulrly polrized r.f. mgnetic fields. These re present in wveguide nd cn be set up in coxil or microstrip line by using specil techniques. Nonreciprocl YIG filters my be pplied s nrrow-bnd tunble isoltors, circultors or directionl filters. We should note here tht nonreciprocl phse shift is given by the orthogonl semiloops shown in fig. I, lthough the r.f. field is linerly polrized here. Since the precession of the mgnetiztion in the YIG resontor hs fixed sense of rottion the direction of wve propgtion determines whether the phse shift will be + 90 or -90. It hs been stted bove tht the size of YIG devices is minly given by the required tuning mgnet. Since the highest required tuning field is deterrnined by the highest frequency to be tuned, tuning power nd mgnet size cn only be kept smll by pying creful ttention to the height required for the ir gp when designing the r.f. section. Typicl ir-gp dimensions given by different designs re 1 mm to 2 mm for the orthogonl hlf-loop, 1.5 mm to 3 mm for symmetricl stripline nd 2 mm to 4 mm for wveguides. The dimeter of the pole fces should be t lest five times the height of the ir gp to provide homogeneous tuning field. Fixed-tuned YIG filters with permnent mgnets re much smller thn filters in wveguide or coxil line, 1 20 2 13 1.2 60 11 5 r çj_ 80 1.05 84 86GHz -f Fig.6. Two-stge YJG bnd-stop filter. ) Cross-section. Two YIG spheres (YIC) re ern bedded in the dielectric of symmetricl stripline (St strip conductor, CP ground plnes) t pproximtely qurter-wvelength spcing. The whole rrngement is plced between the poles of mgnet giving sttic mgnetic field Ho. b) A single YIG resontor behves like prllel-resonnt circuit coupled to the line (or ppropritely trnsformed nd inserted into the line). c) Equivlent circuit offilter contining two resontors t A/4 spcing. d) Attenution nd voltge stnding-wve rtio S in the frequency bnd including the resonnce. Fig. 7. Fixed-frequency two-stge YJG bnd-pss filter with permnent mgnets, to be inserted into microstrip line. From left to right: upper pole piece, coupling structure for YIG resontors with lower pole piece nd two permnent mgnets, microstrip substrte nd ssembled filter. The nrrow strip on the substrte is the microstrip line; the filter is connected to it by two contct pins. Foreground: two YIG resontors glued to tiny rods for mnipulting them nd mounting them in position.
Philips tech. Rev. 32, No. 9/10/11/12 YIG FILTERS 321 prticulrly for the lower microwve frequencies, where trnsmission-line resontors become incresingly lrge. YIG resontors re indeed smll enough to be rub'========~~======== 5------------~~------------ W------------~------------ 20------------~~---------- used in microstrip circuits s high-q resontors. An experimentl two-stge YIG bnd-pss filter with permnent tuning mgnet for microstrip ppliction is shown in jig. 7; it cn be fixed to the substrte of n integrted microstrip circuit by screws. Fig. 8 shows the performnce of this filter. Bnd-pss or bnd-stop filters of this kind re fesible for frequencies from bout 1 GHz to more thn 12 GHz. Mny other devices cn be mde with YIG resontors, e.g. fst switchble filters, tunble frequency discrimintors, frequency meters, mgnetie-field mesuring probes, tunble trnsistor nd Gunn oscilltors nd tunble hrmonic genertors with vrctor multipliers. m------~--------~------ 23 24 25 26 27GHz -----f Fig. 8. Mesured frequency response of the fixed-frequency YIG bnd-pss filter shown in fig. 7. Summry. Single crystls of the ferrite mteril yttrium iron grnet (YIG) give the smllest known ferrimgnetic-resonnce linewidth. Since microwve signls re efficiently coupled to the ferrimgnetic resonnce, single-crystl YIG smples cn be used s mgneticlly tunble microwve resontors with unloded Q-fctors up to 10000 nd liner tuning rnge ofmore thn ten times in frequency. YIG resontors re used in devices such s tunble bnd-pss or bnd-stop filters. The resontors cn be used for signl frequencies from bout 100 MHz up to 60 GHz, depending on mteril chrcteristics nd shpe. Spheres of YIG will give low temperture coefficient for the resonnt frequency (bout 20 khz/ C). The resonnce effect is non-liner bove n r.f. power level of between 10 nd 100 mw (bove 10 (JoWt the lowest frequencies); this is of use in power limiters.