dielectric resonator filters

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974 DIELECTRICRESONATORFILTERS
polarizationandincreasedbandwidthforcylindricaldielectric DIELECTRIC RESONATOR FILTERS
resonatorantenna,Electron.Lett.37:406–408(March2001).
21. K. P. Esselle, Circularly polarized higher-order rectangular
dielectric resonator antenna, Electron. Lett. 32:1742–1743
(Sept.1996). S.BILA
22. C. Y. Huang, J. Y. Wu, and K. L. Wong, Cross-slot-coupled D.BAILLARGEAT
microstrip antenna and dielectric resonator antenna for S.VERDEYME
polarization, IEEE Trans. Anten. Propag. AP-47:605–609
P.GUILLON
(1999).
IRCOM
23. M. T. Lee, K. M. Luk, E. K. N. Yung, and K. W. Leung, Limoges,France
Microstripline feed circularly polarized cylindrical dielectric
resonatorantenna,MicrowaveOpt.Technol.Lett.24:206–207
(March2000). Because microwave filtering is an important function re-
quired to keep a number of different systems in working
24. K. W. Leung and H. K. Ng, Theory and experiment of
circularlypolarizeddielectricresonatorantennawithapara- order, the specifications of a filter are varied. We can,
sitic patch, IEEE Trans. Anten. Propag. AP-51:405–412 however, try to classify some of them as presented in
(March2003). Table 1. The constrains are electrical, mechanical, ther-
25. R. K. Mongia, A. Ittipiboon, M. Cuhacim, and D. Rosecoe, mal,andcommercial.
Circularly polarized dielectric resonator antenna, Electron. Theobjectiveinthisarticleistoshowtheadvantagesof
Lett.30:1361–1362(Aug.1994). the dielectric resonator (DR) technique to satisfy some of
26. K. W. Leung, W. C. Wong, K. M. Luk, and E. K. N. Yung, these functions, along with its disadvantages, in compar-
Circular-polarised dielectric resonator antenna excited by isonwithsomeotherwell-knownsolutions.
dual conformal strips, Electron. Lett. 36:484–486 (March DRs are suitable for bandpass filtering. DR filters are
2000). classifiedasthree-dimensional(3D)devices,inopposition
27. A. Petosa, A. Ittipiboon, and M. Cuhaci, Array of circular- totwo-dimensional(2D)planarones.
polarisedcrossdielectric resonatorantennas, Electron. Lett. The main advantages of 2D solutions are their
32:1742–1743(Sept.1996).
relative bycompact dimensions, their easier integration
28. Z. Li, C. Wu, and J. Litva, Adjustable frequency dielectric in circuit or module environment, and their well-known
resonatorantenna,Electron.Lett.32:606–607(March1996).
designandmanufacturingprocedures.Theyare,however,
29. Z.N.Chen,K.W.Leung,K.M.Luk,andE.K.N.Yung,Effect limitedintheirapplicationstotheprocessingoflowpow-
of parasitic disk on a coaxial probe-fed dielectric resonator
er, sizable relative bandwidth signal, in relation to the
antenna, Microwave Opt. Technol. Lett. 15:166–168 (June
poor unloaded quality factor of localized microwave ele-
1997).
ments or planar resonators. Some solutions are proposed
30. H.K.NgandK.W.Leung,ExcitationofCPaperture-coupled
torestrictlosses,suchasapplyingsupraconductorsorac-
dielectric resonator antenna with a parasitic patch, IEEE
tive-element techniques, but they remain inadequate to
Antennas and Propagation Soc. Int. Symp. Digest, Boston,
replace 3D devices, in particular for high-power require-
July2001,Vol.4,pp.202–205.
ments.
31. K.W.Leung,W.C.Wong,andH.K.Ng,Circularlypolarized
In the class of 3D devices, designers have first chosen
slot-coupled dielectric resonator antenna with a parasitic
patch,IEEEAnten.WirelessPropag.Lett.1:57–59(2002). waveguidesormetallicemptycavitiestosatisfytheirvery
narrowbandwidthfilteringrequirements.However,since
32. K.W.LeungandH.K.Ng,Dielectricresonatorantennafed
byadisplacedconformalstrip,MicrowaveOpt.Technol.Lett. the mid-1980s, high-dielectric-constant materials,having
29:185–187(May2001). lowlosstangentandgoodthermalstability,havebecome
33. R. D. Nevels, The annular aperture antenna with a hemi- available.TheDRsolutionhasbeenpreferredforanum-
spherical center conductor extension, IEEE Trans. Anten. ber of applications, in particular spatial ones. This tech-
Propag.AP-35:41–45(Jan.1987). nique allows us to reduce significantly the cavities and
34. R. D. Nevels and J. E. Wheeler, Radiation from a dielectric waveguide device sizes, for equivalent electrical and in-
coatedhemisphericalconductorfedbyacoaxialtransmission creased thermal performances. Some average ratios can
line, IEEE Trans. Electromagn. Compat. 31:16–20 (Feb. be given for dual-mode resonators (DR compared with
1989). cavity):
35. K.W.Leung,K.M.Luk,K.Y.A.Lai,andD.Lin,Theoryand
experimentofcoaxialprobefeddielectricresonatorantenna, 1:4involume
IEEETrans.Anten.Propag.AP-41:1390–1398(1993).
1:2inmass
36. K.W.Leung,K.M.Luk,K.Y.A.Lai,andD.Lin,Theoryand
experiment of an aperture-coupled hemispherical dielectric
resonatorantenna,IEEETrans.Anten.Propag.AP-43:1192– Moreover, the DR shape and the mode in which it is
1198(1995). excited can be chosen to give a response to particular re-
37. K. W. Leung, Analysis of zonal and rectangular slot on a quirements,aswewillseelaterinthisarticle.Anumber
conducting spherical cavity, IEEE Trans. Anten. Propag. of DR shapes and filter topologies have, however, been
49:1739–1745(Dec.2001). proposed.Ourworkhereislimitedtothepresentationof
38. K. M. Luk and K. W. Leung, eds., Dielectric Resonator themostpopularones.
Antennas, Baldock, Hertfordshire, England; Philadelphia: In this article, we present some characteristic
ResearchStudiesPressLtd.,2003. parameters of DR filters, which are generally introduced
DIELECTRICRESONATORFILTERS 975
Table1. MicrowaveFilterSpecifications
Electrical Mechanical Thermal Commercial
Centralfrequency Massandvolume Temperaturerangeofuse Componentsandmaterialscosts
Passbandwidth Vibrationresistance Maximumdissipatedpower Machiningcost
Designcost
Passbandripple Machiningtolerances Sensitivityofelectrical Delayfordesignandrealizationoffilter
responsetotemperature
variations
Out-of-bandselectivityand Manufacturingdifficulties
rejection
Responseisolation
Insertionlosses
SWR
Groupdelay
Powercapabilities
during the synthesis procedure. These definitions are Approaches developed to design DR filters are dis-
helpful in explaining the choices of filter designers, in cussedinSection4.Afour-poleDRfiltersynthesisispro-
particular theDRshapes andarrangementsinmultipole posedasanexample.
devices.
In Section 1, the class of devices loaded by cylindrical 1. ELECTRICALCHARACTERISTICPARAMETERSOF
DRsisinvestigated.ThisisacommonshapefortheDR.It ADRFILTER
canbeexcitedonasymmetricmode(TE orTM )oron
0n 0m
afirst hybrid mode (HEM11).Different DR arrangements Applying conventional methods, the design of microwave
inthefilterarepresentedanddiscussed. filters starts with the selection of an ideal transfer func-
For particular applications in microwave filtering, tion that fulfills the electrical objectives of the specifica-
wecanfittheDR shapeortheDR mode.Forhigh-power tions.Thesynthesisofthisidealtransferfunctionleadsto
applications, it is important to put the high-dielectric- anequivalentlumped-elementcircuit.Thiscircuitischar-
constantmaterialincontactwithametallicenclosure,to acterized by a coupling matrix that depends on the
improve the thermal dissipation. DRs of a quarter-cut lumped-element values. A number of studies have been
cylinder,acylindricalrod,oradielectricplateshieldedin devoted to this task [1,2]. Different circuit topologies can
ametalliccavityareinvestigated.Solutionsarealsogiven be chosen. However, for the DR filters presented in this
to optimize the isolation of the filter response on the article,theequivalentcircuitisclosetotheonepresented
frequency axis, or to apply DR to the millimeter wave in Fig. 1 (canonical symmetric design). Nevertheless,
filtering. These particular applications are included in if another solution is chosen, the same characteristic
Section2. parametersmayhavetobecomputed.
1:n1 C R M1,2 C R C R
P1 1 L /2 L /3 2 L /3 . . . L /2 1
L /2 L /3 L /2
M1,n M2,n − 1 Mn/2,n/2 − 1
L /2 L /3 L /2
P2 n L/2 L /3 n − 1 L /3 . . . L /2 n/2 − 1
R
C R C R C
1:n2 Mn − 1,n
Figure1. Equivalentcircuitofasymmetricn-polefilter.
976 DIELECTRICRESONATORFILTERS
FromthecircuitpresentedFig.1,wedefinethefollowing: 3, we explain how the dimensions of the filter are com-
putedfromknowledgeoftheparametersf ,M ,andQ .
0 ij ei
* Thecentralfrequencyofthefilter:
1 2. FILTERSCOMPOSEDOFCYLINDRICALDRs
f ¼ p ð1Þ
0 ffiffiffiffiffiffiffi
2p LC
Cylindrical DRs are more often used to realize multipole
* Theunloadedqualityfactorofeachresonator: filters. We discuss this class of solutions here. The DR is
generally shielded in a metallic box, to avoid radiation
Lo losses. It can then be excited on transverse electric TE
Q ¼ 0; o ¼2pf ð2Þ 0n
0 R 0 0 modes, transverse magnetic TM0m modes, or hybrid
HEM modes. The natures of the transmission lines or
nm
* The input and output coupling coefficients. In the waveguidesusedtocouplethefilter,thenatureoftheDRs
electricalscheme,thecouplinglevelsbetweentheex- arrangement in the device, and the nature of the electri-
citationaccess(P1andP2)andthefirstandlastres- cal, mechanical, and thermal characteristics of the filter
onators (1 and n) are characterized, respectively, by depend on the choice of the DR mode. Table 2 compares
theratios1/n1and1/n2.Itishowevergenerallypre- the performance levels of the TE01, TM01, and HEM11
ferredtodefineexternalqualityfactorsQei[1]atport modes.Thedimensionsareoptimizedtoobtainaresonant
i,ði2f1;2gÞ,by frequencyequalto4GHz.WenoticethattheDRactingon
theTE modeisthelessbulkyone.Eveniftheelectrical
01
Q ¼2pLf0 with ð3Þ performancesarecomparable,theTM01modeismorera-
ei Rei diativeinthecavity,whichincreasesthemetalliclosseson
theenclosure.TheHEM modeisinfactveryinteresting
11
Rei¼R0n2i ð4Þ for reduction offilter size. The filter performance of each
particularTE,TM,orhybridmodeisdiscussedbelow.
astheexternalloadingresistanceatportP.Coupling
i
coefficientsa arealsodefinedatportiby
i 2.1. MonomodeFilter
Q The DRs are excited on the symmetric TM or TE
a ¼ 0 ð5Þ 01 01
i Q modes. An n-pole ‘‘monomode’’ filter is then composed of
ei
nDRs.ThedimensionsofeachDRandofthemetallicen-
* Thecouplingcoefficientbetweenresonators.Theres- closurearegenerallychosentooptimize,atthefiltercen-
onators are intercoupled, longitudinally and cross- ter frequency, the dielectric and metallic losses and the
wise, in the general case. We define a coupling devicesizes,aswellastoavoidspuriousresponsesaround
coefficientK betweenresonatorsiandjby thefilterbandpass.
ij
Different topologies of the TE mode, have been re-
01
K ¼Mij ð6Þ ported in the literature. The DRs can be placed side by
ij L side on the same plane. To obtain good isolation on this
mode, the ratio between diameter and height of each DR
Thecrosswisecouplingcoefficients(exceptKn=2;n=2(cid:1)1) is generally chosen to be 2. Then the radial radiation of
may cancel to obtain conventional Butterworth or each DR is small and the DRs can be coupled directly; a
Chebyshev responses. Some of them are different metallicirisdoesnothavetobeplacedsystematicallybe-
from zero and can be negative for elliptic bandpass tweentheDRstolimitthefiltersize.
functionrealizations,includingtransmissionzerosin Two examples of realization are presented in Figs. 2
theout-of-bandpartofthetransmissionresponse. and3.Differenttechniquescanbeemployedtocouplethe
filter.Propagativerectangularwaveguidescanbeconnect-
These parameters help thedesigner perform the third edtobothendsofawaveguidesectionabovecutoff,which
synthesisstep,thecomputationofthedevicedimensions. contains the DR. The TE mode of the DRs is excited if
01
The topology of the filter, in particular the DR arrange- their axis are positioned along the wide dimension of the
ment, is easily directly deduced from the equivalent-cir- monomodewaveguide(Fig.2).Thedistancesbetweenthe
cuitone,which,infact,justifiesthisapproach.InSection first(andrespectivelylast)DRandthejunctionsbetween
Table2. ComparisonbetweenTE ,TM ,HEM ,andDRaModePerformanceLevels
01 01 11
f (GHz) Q D (mm) H (mm) D (mm) H (mm)
0 0 RD RD C c
TE 4 8600 14 5.5 28 19.5
01
TM 4 7500 28 8.3 52 56
01
HEM 4 9600 19.3 6 40 20
11
aCylindricalDR(diameterDRD,heightHRD,permittivityer¼36,losstangent10(cid:1)4)enclosedinacylindricalmetalliccavity(diameterDC,heightHC,metallic
conductivity1.7(cid:7)107S/m).
DIELECTRICRESONATORFILTERS 977
Propagative waveguide
a
1 2 … n n b
y
X z Evanescent waveguide
Figure 2. DRs excited on a TE mode
01
(a) (b) throughrectangularwaveguides.
the waveguide sections enable us to tune the level of the obtain an elliptic response on these symmetric modes, in
input(respectivelyoutput)couplingcoefficient.Thistech- the same device we can combine axial and side-by-side
niqueissuitableforhigh-powerapplications. mountingconfigurations.Atwo-stagedeviceisconstruct-
To improve the integration of the filter in its environ- ed.ThetransversalcouplingM canthenbeachieved,as
ij
ment,wemustcouplethefirstandlastDRstomicrostrip it has been done for empty metallic cavities. A negative
lines (Fig. 3). Nevertheless, the metallic losses of such a couplingisobtainedbysettingsomeupperandlowercav-
structure increases, as the DR must be placed near the ity axis; the resulting transmission zeros placed around
metallic strip and ground plane to obtain the required thepassbandresponseincreasethefilterselectivity[8].
couplinglevels.Theevolutionofthecouplingcoefficientas Differenttechniques,includingthosementionedprevi-
afunctionofthedistancebetweenthelineandtheDRis ously, have been developed for the mounting of DRs in
giveninRef.3. their enclosure; for instance, the DRs can be glued on a
Dielectricresonatorsmightalsobecoupledthroughco- dielectric support. This technique may, however, be
axial probes [4] or loops [5]. Particular attention to the critical because of the generation of parasitic gaps
positioning of the excitation systems around the DR en- between the glued materials and the poor glue loss tan-
ableustoobtainagoodisolationofthebandpassresponse gent. A mounting based on a differential dilatation
onthefrequencyaxis. phenomenon between each DR and it environment is
From the devices shown in Figs. 2a and 2b [4–6], we more suitable for obtaining high electrical performance.
obtain narrow-bandpass Chebyshev or Butterworth re- The capability of the filter to withstand vibration is
sponses.Stopbandfilterscanalsoberealizedeasilyusing fundamental for space applications. Some test measure-
theseDRcouplingtechniques,couplingtheDRtoaprop- mentsaregiven,forexample,inRef.9.
agativewaveguideoratransmissionline[7].
Coupling the DRs side by side enables us to maintain
them easily, such as on a dielectric substrate, whose ma- 2.2. Dual-ModeFilters
terialischosentoimprovethetemperaturestabilityofthe
Dual-mode filters [10] are now widely used because they
filter. Moreover, some tuning elements can be integrated
offerequivalentelectricalperformancelevels,smallersize,
around the DRs; some metallic or dielectric screws are
and less mass than do classical fundamental TE or TM-
generallyplacedalongtheDRsaxistotunethefilterres-
mode filters. A metallic screw, or another perturbation is
onantfrequency,aswellasbetweentheDRstoadjustthe
placed around the DR to break the rotational symmetry.
couplingcoefficients.
Then, on the first or second hybrid mode, the two polar-
On the TE , TM , and TM modes, DRs have also
01 01 02 izationssectionsareimposed,andtheirfrequenciesdiffer
been mounted axially on a cylindrical dielectric rod. To
in relation to the perturbation dimension. Figure 4 pre-
sents a two-pole dual-mode filter, composed of only one
DR. Two monomode DRs would be coupled to obtain
Metallic cavity the same electrical response. The DR is excited through
coaxial probes. Two tuning screws are generally added
in the excitation probe axis to tune the central resonant
frequency.
Thecouplingscrewisplacedatanangleof451fromthe
excitationaxis.Inthiscase,thesymmetryofthestructure
suffices to fix the direction of the two polarizations. The
RD2 RD1 RD3 electromagnetic environment of each mode differs; thus
theresonantfrequenciesf andf ofthetwopolarizations
1 2
differ.Thepowercombiningisconstructivebetweenf and
1
f at the output access, which explains the bandpass re-
2
sponseobtainedfromthisdevice.Sometransmissionzeros
Microstrip line arealsoobserved,duetothecombinationofoppositephases
Figure 3. DR lines excited on a TE mode throughmicrostrip betweenthetwopolarizations,andbetweenthesephases
01
lines. andahigher-ordermodeoftheDR[11].
978 DIELECTRICRESONATORFILTERS
rectangularirises,forpowerapplications.Theseirisesare
thengenerallyplacedinaplaneperpendiculartotheDR
Metallic axis.
screw
AdjacentDRscanalsobecoupleddirectly,ratherthan-
iriscoupled[13].Thenrealizationsofsmallcouplinglevels
may require large separation between adjacent DRs, and
may consequently require significant sizes. However, the
introduction of evanescent waveguide sections between
DRs enable us to reduce the device dimensions [14]. The
Coaxial drawbacks of this method are the filter spurious charac-
probe 1 D teristics and the dependent coupling level between the
modesetsofadjacentDRs.Inthesamewayasmonomode
Metallic
realizations, dual–mode DRs can be mounted in a planar
enclosure
relationshiptooneanother.EachDRisagainenclosedina
metallic cavity. The DR intercouplings are controlled in-
dependently by a metallic iris that contains two rectan-
Coaxial
gular noncrossing apertures placed in an appropriate
probe 2
manner[15].Thissolutionisinterestingforitsflexibility
Figure4. Dual-modeDRexcitedbytwocoaxialprobes. inthearrangementoftheDRcavities.
More than two modes have also been coupled in the
sameDRcavity,toconserveweightandsizeincomparison
For n-pole elliptic realization, with n42 and n as an
with the previous solutions. The two polarizations of the
oddnumber,weneedtocoupleparallelmodesinadjacent
HEM modes and the TM mode have been simulta-
DRs (longitudinal coupling) and to avoid extra coupling 11 01
neously excited in a planar DR-mounted cavity. Two of
betweenorthogonalmodesofdifferentDRs.Threescrews
these three-pole modules have been coupled through an
are placed around each DR as shown in Fig. 4, and adja-
iriscomposedoftwoseparateT-shapedapertures[16].
centDRsaregenerally iris-coupled.Twoorthogonalrect-
angularaperturesmachinedinametallicplateenableus
toimposetherequiredcouplinglevelbetweeneachsetof
parallel polarizations. To obtain a negative sign on some 3. PARTICULARAPPLICATIONSOFDRSIN
crosswisecouplingcoefficients,thedifferentscrewsarenot MICROWAVEFILTERING
positioned at the same angle with the excitations in the
differentcavities.Thistechniqueiswellknownformetal- 3.1. DRforHigh-PowerApplications
lic cavity realizations [12].An example offour-pole topol-
The dual-mode devices we have presented above are in-
ogy is presented in Fig. 5, where the DRs are coupled to
teresting for their high electrical performance levels and
input–outputcoaxialprobes.
limited sizes. But even if the filter dissipated power is
The excitation can also take the form of rectangular
small, the resulting thermal dissipation remains critical
waveguides,coupledtotheinput–outputcavitiesthrough
for certain applications, such as space applications, be-
causethethermalconductivityofmostdielectricmaterial
ispoor.
Asolutionconsistsofpositioningthehighpermittivity
resonators in contact with the metallic enclosure, to im-
prove the thermal dissipation efficiency, and then to im-
provethepower-handlingcapabilityofthefilter.
Coaxial
D Wecanfirsttakeadvantageoftheelectromagneticfield
probe
symmetryofacylindricalDR.Itcanbedividedintotwoor
Coupling
moreparts,withoutmodifyingtheresonantfrequencyand
screw
field repartition of some modes, if the physical metallic
walls are placed in planes in which electrical wall condi-
Crossing
iris tionsarenaturallyverified[17,18].Inthiswayacylindri-
cal DR excited on a TE mode can be split, for example,
01
intofourparts.Ifeachofthecutplanesareincontactwith
a metallic wall(Fig. 6), all quarter-cut DRs will resonate
atthesamefrequency.
The improvement of the power-handling capability is
Tuning notthesolepurposeofthistechnique.Anumberofcylin-
screw dricalDRmodesdonotsatisfytheelectricalwallcondition
in the planes where they are imposed on the quarter-cut
DR. They are then suppressed in the ‘‘image’’ DR. Hence
the out-of-band rejection performances of the filter is
Figure5. Exampleoffour-poledual-modeDRfilter. improved,suppressingspuriousresponses.
DIELECTRICRESONATORFILTERS 979
Slot machined to couple
Metallic the DR two polarizations
enclosure
DR Metallic
enclosure
DR
Figure8. TMdual-moderesonator.
quality factor Q of the DR. We can note, however,
0
that the image resonator might be preferred to coaxial
dielectricfieldresonators,consideringthesizesandlosses
at the same frequency. Figure 7 presents a possible
(a)
arrangement of the DRs to realize an elliptic five-pole
function[17].
Different techniques have been proposed to increase
Metallic theunloadedqualityfactorofthesplitDR.TMdual-mode
enclosure DRshavebeendevelopedforuseintheLandCfrequency
bands for mobile communication applications. A cross is
formed as shown in Fig. 8, by two parallelepipedic DRs
excitedonaTM mode[19].Thetuningelementrequired
01
to couple the two degenerated modes is not a metallic
screw,butaperturbationdirectlymachinednearthecen-
terofthe cross.Anunloaded qualityfactorequalto9000
Quarter
hasbeenobtainedat1.9GHz,foradielectriclosstangent
cut DR
(b) equalto5(cid:7)10(cid:1)5[20].Ahigh-permittivitydielectricplate
has also been placed in a metallic enclosure to provide a
Figure 6. Equivalent cylindrical (a) and quarter-cut (b) DRs
goodcompromisebetweentheunloadedqualityfactorlev-
excitedonaTE mode(——electricfieldlines).
01
elandthethermaldissipationcapability[21].Thecorners
of a thin parallelepipedic plate have been cut to provide
This technique also provides very compact structures, a good contact between the resonator and a cylindrical
reducingthesizenotonlyoftheDRbutalsoofthemetallic metalliccavity(Fig.9).
enclosure. This is an important advantage, particularly Thedimensionsareoptimizedtolimitthemetallicand
for 900-MHz–3-GHz applications. Nevertheless, the dielectriclossesonthefirstTEmodethathasdegenerat-
metallic losses on the metallic plane in contact with the ed. It has been shown that the electrical performance
DR increase dramatically, resulting in a poor unloaded of this resonator is not far from that of the cylindrical
Half cylindrical DRs Transversal probe coupling
5 3 1
4 2
Iris coupling between DRs
Figure 7. Five-pole elliptic filter using the
Waveguide output split-DRtechnique.
980 DIELECTRICRESONATORFILTERS
3.2. FilterConfigurationsforOptimizationof
Out-of-BandRejection
Conventional DR filters have relative poor stopband re-
jectionperformance,duetotheexcitationofhigher-order
moderesonances.Alowpassfilter,placedattheoutputof
thebandpassDRfilter,mightsolvethisproblem,butthe
M
bulkand theelectricalperformance ofthecascadedfilter
suffer from this solution. Different filter configurations
have,however,beenproposedtoincreasetheout-of-band
rejection.
H E
We have already underlined that the quarter-cut DR,
or the TM DR, which are of interest for power applica-
01
tions,arealsoefficienttechniquesforeliminationofsome
ofthespuriousresponses.
Coupling structures have been designed to suppress
the excitation of some modes. A single-mode TE filter
01
realization is, for example, presented in Ref. 23. The
diameter: height ratio of the DR is generally chosen to
optimizethemodeisolation.Aholecanbemachinedinthe
cylindrical DR, along its axis [24,25], and the DR shape
can be matched [26] to increase this isolation. A more
sophisticated solution consists of mixing DRs excited on
D
differentmodesinasamefilter.Toobtainpartofthering
Figure9. High-permittivitydielectricplateresonatortechnique. DR isolation, and part of the compactness of dual-mode
devices,TE ringDRsandaHEM dual-modeDRhave
01 11
been coupled to realize six-pole elliptic filters, combining
dual-mode one, and this solution is more suitable for fourDRs.DRscanbemountedaxially[27]orsidebyside
power applications. Metallic screws are generally [28]intheirmetallicenclosures.Asanexample,thecenter
placed around the dielectric plate to couple the first frequency of the realized filter is equal to 1.23GHz; its
TE polarizations. Slots are then machined in the plate, passband is20MHz, and the out-of-bandrejection is bet-
both to couple these polarizations and to optimize the terthan (cid:1)40dBinthe1–1.9GHzfrequencyband[27].
out-of-band rejection of the filter. Superimposed cavities
are coupled through metallic cross irises.The topology of
3.3. DRforHigh-FrequencyApplications
aneight-poleautocorrectedquasiellipticfilterispresented
in Fig. 10. The transmission and reflection responses, Whenthefrequencyincreases,thedimensionsofcylindri-
along with the group delay of the filter, are presented in calDRsexcitedonthefirstTE ,TM ,andHEM modes
01 01 11
Fig.11. become too small. The limit of conventional DR applica-
Some other studies have been performed to optimize tionscanbesetaround20GHz.Tosolvethemanufactur-
theDRshapetoincreasetheunloadedqualityfactorofthe ing problem, spherical DRs have been proposed. But the
resonators, in particular by choosing adequate forms of criticalmechanicalstabilityofthedevices,alongwiththe
the DR dielectric support in contact with the metallic spurious modes around the bandpass limits their appli-
enclosure[22]. cations.
Regulating screw
Cross screw
Coaxial bore
Figure10. Dielectricplateeight-poleconnect- Cross iris
edellipticfilter.
DIELECTRICRESONATORFILTERS 981
CH2 S21/M log MAG 10 dB/ Ref −.92 dB 2: −21.215 dB CH2 S22 log MAG 5 dB/ Ref 0 dB 3: 5.9921 dB
−35.000 000 MHz 25.000 000 MHz
∆ Ref = 1 ∆ Ref = 1
Marker 2-1 Marker 3-1
−35 MHz 1∆ 25 MHz
3
2
2
3
1∆
C2
x2 x2
Center 3 930,000 000 MHz Span 20,000 000 MHz Center 3 930,000 000 MHz Span 80,000 000 MHz
(a) (b)
CH S log MAG 5 dB/ Ref 0 dB 3: 5.9921 dB
2 22
25.000 000 MHz
∆ Ref = 1
Marker 3-1
25 MHz
3
2
1∆
C2
x2
Center 3 930,000 000 MHz Span 80,000 000 MHz
(c)
Figure11. (a,b)Transmissionandreflectioncoefficientvariationsasafunctionofthefrequency;
(c)groupdelayvariationinfilterpassband.
We can, however, use cylindrical DRs on whispering physicalcharacteristics,andparticularattentionmustbe
gallery modes [29]. For important azimuthal variation paidtotheirdesign.
number, the DR can beused easily up to 100GHz. More- Thepurposeofthetheoreticaldesigncanbenotonlyto
over,thefieldisveryeffectivelystoredinwiththeDR,and optimizethefilterperformancesbutalsotoreducethecost
the unloaded quality factor, which thus depends only on of the product. If the design is not efficient, the time re-
themateriallosstangent,isimportant.Examplesoffilter quired for the tuning can be important; different devices
realizationsaregiveninRef.30. are manufactured, and even in the phase when the di-
mensions are known, an experimenter must spend time
andefforttotuneeachfilter.
4. THEORETICALDESIGNOFMICROWAVEDRFILTERS
However, DR structures are difficult to analyze, be-
cause their geometries are very complex. We have seen
4.1. Introduction
thatthefiltertopologiesarediverse;DRscanbeintercou-
DRsareusedfortherealizationofnarrowbandfiltersup pled or coupled through a metallic iris; they may be ex-
to 0.01% relative bandwidth. The electrical responses of cited by coaxial probes, metallic waveguides, and
suchdevicesarethenverysensitivetotheirgeometricand microstrip lines; their shapes are not systematically
982 DIELECTRICRESONATORFILTERS
cylindrical; and they can be maintained in their metallic applyingthefinite-elementmethod[39,40].Now,withthe
enclosures through a wide variety of systems. Moreover, evolution of computer capabilities, a number of research
thestructuresareverycompact,andifwecandefinedif- teams are interested in the electromagnetic optimization
ferent segments in its composition, strong couplings are ofDRdevicesapplyingnumericalsimulation.Anumberof
generated between the DRs through high-order modes. articles dealwith the rigorous design of multipole filters.
Thus the classical approach that is applied in the circuit Inthissectionwewilldescribeasolutionfortherigorous
software, namely, the segmentation method, is not effi- design of a multipole DR filter using the finite-element
cienthere;wecannotcharacterizeeachsegmentindepen- method[40].
dently from the others, and we cannot connect the
differentcontributionstoobtainthedeviceresponse.
4.2. MethodforOptimizedDesignofaDRFilter
Analytical-approachmodelswereinitiallydevelopedto
assist designers. These methods are described in Ref. 31. Theproceduregenerallyappliedtodeterminethegeomet-
Since the late 1980s, rigorous analyses have been per- ric dimensions of a multipole filter is deduced from the
formed, first on some parts of the DR filter. Examples lumped-element synthesis presented in Section 1. To ex-
include application of modal methods [32,33], the finite- plainthisapproach,wehavechosenheretodesignadual-
element method [34], or the method of lines [35] to char- mode four-pole DR filter because this design groups to-
acterize axisymmetric dielectric-loaded metallic cavities, gethersomeproblemsfoundinalargevarietyofDRfilter
computingtheresonantfrequenciesofthesedevices.Some topologies. In the dual-mode DR presented in Section 1,
other studies have been performed on the design of the metallic screws are replaced by slots directly ma-
three-dimensional resonator, which is nonsymmetrical in chined in the DR. The four-pole filter, shown in Fig. 12,
structure. The resonant frequency of a DR shielded in a consists of a metallic cavity, two input/output coaxial
parallelepipedic enclosure has been computed applying probes, and two slotted DRs coupled through metallic
the modal method [36] and the finite-element method cross irises. Because the experimental filter will not be
[37,38]. From these computations we can easily deduce tuned,thesynthesisprocedurehastobeperformedrigor-
the coupling coefficient between two DRs for symmetric ously.Tocomputethefilterdimensionsthatsatisfygiven
structures. The coupling coefficient between a DR and a electrical characteristics, we develop the approach pre-
waveguide or a transmission line has been computed by sentedinFig.13.
Dielectric
support Notch 1-2
Notch R1
Crossed
iris Iris 2-3
Iris 1-4
Slotted
resonator
Notch 3-4
Notch R2
z
x
y
Metallic cavities : Dielectric resonators : Crossed iris :
H = 14.1 mm H = 3.4 mm L = 5.20 mm
C DR 14
RC = 15.5 mm RDR = 7.6 mm L23 = 7.70 mm
(cid:1)DR = 37 w = 1.00 mm
t = 1.00 mm
Tuning notches : Coupling notches : Notch-DR distances :
D = 0.62 mm D = 0.93 mm d = 1.10 mm
DR1 12 DR1
D = 0.62 mm D = 0.93 mm d = 1.10 mm
DR2 34 DR2
Figure12. Four-poleslottedDRfilter. w=1.00mm w=1.00mm
DIELECTRICRESONATORFILTERS 983
Inthethirdstage,anelectromagneticoptimizationloop
Ideal transfer function
isperformedapplyingthefollowingprocedure:
Lumped element 1. The3Dfinite-elementmethodisappliedinorderto
synthesis computethe scatteringparameters between theac-
cessportsofthewholestructure.
Electromagnetic
Ideal coupling matrix 2. The scattering parameters are approximated as ra-
synthesis
tionalfunctionsinthefrequencydomain.
3. Fromtheapproximatedrationalfunctions,anequiv-
Couplings
Geometrical dimensions Ok alentcircuit,namely,acouplingmatrix,ofthesim-
comparison
ulatedfilterissynthesized.
Electromagnetic 4. Bycomparingtheextractedcouplingmatrixandthe
Equivalent coupling matrix
analysis idealone,thefilterdimensionsarecorrectedaccord-
ing to the dimension sensitivities from the electro-
Lumped element magneticsynthesis.
Scattering parameters
synthesis
Theloopisperformedaslongastheelectricalobjective
Rational isnotattained.
Characteristic polynomials
approximation ThisprocedureisdetailedinRefs.40and41.Theideal
transferfunctionandtheelectromagneticresponseatthe
Figure13. Designmethodofmultipolefilter.
|S | (dB)
11
Inthefirststage,anequivalentlumped-elementcircuit
0
is synthesized from the ideal transfer function. The syn-
thesis leads to a coupling matrix that characterizes the
−10
ideal equivalent circuit. This objective coupling matrix
gives all the information about the ideal electrical char-
acteristicparametersofthefilter. −20
Applying the 3D finite-element method [40], we can
thencomputetheinitialdimensionsofthestructurewith −30
respect to the previous electrical parameters. An electro-
magneticsynthesisallowsustodeterminethefollowing: −40
1. The DR and metallic cavity dimensions required to −50
satisfythecenterfrequencyfvalue.
2. Theprobedepthpenetration,computedtoobtainthe −60 Ideal TF
requiredinput/outputcouplingcoefficientlevels.
FEM
3. Thedimensionofthecrossiristoobtaintherequired
5.46 5.48 5.5 5.52 5.54 5.56 5.58 5.6
coupling coefficient between the parallel polariza-
tions of the two DRs. The theoretical synthesis f (GHz)
method is generally interrupted here for classical |S | (dB)
12
applications.Screwsarethenplacedaroundthefil-
0
tertocouplethepolarizationsandtoaccountforthe
resonantfrequenciesofthefilter.Thenasetofirises
−10
are manufactured, and each experimental device
has to be tuned. Choosing the slotted DR solution,
−20
wecancontinuewiththesynthesiscomputations.
4. The coupling notch dimensions, which impose the
−30
couplingcoefficientbetweenthetwopolarizationsof
eachDR.
−40
5. The dimensions of a second notch, which are intro-
ducedtocompensate fortheinfluenceoftheprobes −50
andtheirisontheresonantfrequencyoftheexcited
polarization. −60 Ideal TF
Then,allthedimensionsofthedevicepresentedinFig.12 FEM
are known, but only approximately because of the seg-
5.46 5.48 5.5 5.52 5.54 5.56 5.58 5.6
mentation approach applied in these initial steps, which
f (GHz)
doesnotaccountfortheindirectdependencebetweenthe
differentelements. Figure14. Comparisonofidealandelectromagneticresults.