IEEE TRANSACTIONS ON MiCROWAVE THEORY AND TECHNIQUES VOL. MTT-13, NO. 5

IV[icrowave Filtem-1965LEO YOUNG, SENIOR MEMBER, IEEE

A&sfractA review of recent and current work on microwavefilters is presented, and an extensive bibliography of recent articles isappended. The review is largely qualitative and pictorial, rather thanmathematical Among the microwave filter topics discussed are band-pass filters with cascaded lifes or cavities; band-pass and band-stopfilters with stubs and parallel-line coupling; low-pass and high-passfilters; the connection between dissipation loss, group delay, andpower-handling capacity; delay equalizers; diplexers; directionalfilters; tunable filters, especially magnetically tunable filters; dielec-tric-resonator titers; filter techniques applied to semiconductor de-vices; the connection between tilters and directional couplers; filterswith open walls; and filters for millimeter waves and higher fre-quencies.

1. INTRODUCTION

T

HE PRESENT PAPER is a review paper withemphasis on developments o,f the past threeyears. (Although most of the referenced papers

have been published since September 1962, the bibliog-raphy is classified and sufficiently extensive so that thereader should have little difficulty in ~inding earlier pub-lications of interest to him.)

Filters are at the heart of many design problems.They are used to separate or combine different fre-quencies, as in frequency converters or multipliers, orin multiplex communications. The electromagneticspectrum is limited and has to be shared; filters are usedto confine the radiation from high-power transmitterswithin assigned spectral limits; conversely, other filtersare used to protect receivers from interference outsidetheir operating bands. Filter-like networks occur in im-pedance matching, as between two transmission lines ofdifferent characteristic impedances; or between a re-sistive generator and a reactive load, such as a diodein a parametric amplifier. Sometimes it is necessary toobtain certain phase (or time delay) characteristics, asfor pulse stretching; or to compensate for the distortionproduced by another filter or dispersive structure (likea length of waveguide). There is need for filters at allfrequencies, from very low through microwave to op-tical frequencies and beyond.

One may approach the subject of microwave filtersfrom the point of view of waves in a transmission lineor waveguide (this might be called the physicists pointof view), or one may extrapolate from lumped-constantfilters (this view is adopted by perhaps most electricalengineers). The latter point of view has proved the moreuseful for the systematic design of microwave filters.For this reason, we shall start by referring the reader

Manuscript received June 1, 1965.The author is with the Sta nforrl R esea,rch Institute Menlo Park,

Calif.

to a few relevantconstant networks.

SEPTEMBEN, 1965

publications [1 ] [12 ] on lunlped-References [11 ~51 are textbooks.

References [4], [6 ] [9 ], together \vith Chapter 4 ofReference [13 ], contain numerical tables for lurrlped-constant filters useful as prototypes for the design ofmany microwave filters.

Figure 1 shows typical response curves for four itypesof lumped-constant low-pass filters, all of which may beused as prototypes for lumped-constant high-pass (Fig.2), band-stop (Fig. 3), and band-pass filters (Fig. 4), aswell as for microwave filters. Numerical tables forfilters having the type of response shown in Figs. 1(a)and (b) will be found in Chapter 4 of Reference [13];similarly, Fig. 1 (c) goes with References [7] and [9],and Fig. 1(d) goes with Reference [6]. The changesnecessary to convert from the low-pass prototype to theother lumped-constant types is indicated in Fig. 5. Themost common low-pass prototype, corresponding toFigs. 1 (a) and (b), is shown in Fig. 6.

II. MICROWAVE FILTERS [13]-- [18]

The electromagnetic radiation fields from a shortwire carrying RF current exceed the magnetic indu~:tionfield and the electric transition field at distances greaterthan one-radian wavelength (about one-sixth of awavelength) from the wire. Thus, radiation can nolonger be neglected, as it conventionally is neglected forlumped-constant circuits, when the physical dimensionsof the network approach one wavelength. Nevertheless,it is possible to design a resonant cavity or shieldedresonator as if it were a resonant LC circuit over asmall bandwidth since both have certain fundamentalproperties in common. (They both store energy whichcontinually oscillates between electric and magneticform, and they both couple to one or more outside re-sistive circuits; in other words, they both behave likea damped simple harmonic oscillator.)

An exact method of designing microwave filters isbased on Richards transformation [18], which holdsonly for microwave circuits with commensurable linelengths. This transformation maps the entire rea,l-fre-quency axis of the lumped-constant prototype ontofinite portions of the real-frequency axis of the trans-mission-line circuit, and then the respons{e pattern isrepeated periodically. (See Sections III and V.) ~Ehys -ically, this repetition corresponds to repeated incre-ments of one-half wavelength in the electrical linelengths of the transmission-line circuit, as the frequ encyincreases. These repetitions in the behavior of the cir-cuit as the frequency increases are usually undesirableand are then referred to as spurious responses. In taddi -

489

490 IEEE TRANSACTiONS ON MICROWAVE THEORY AND TECHNIQUES SEPTEMBER

tion, spurious responses will arise in microwave filtersat high enough frequencies because of the occurrence ofhigher-order modes.

A flow chart showing many kinds of filter using com-mensurable line lengths, and other filters derivablefrom them, is presented in Fig. 7. This chart will be-come clearer after reading the following sections.

Microwave filters may be classified by function(band-pass, band-stop, etc.), by mode of operation (re-

(a)

(b)

(c)

(d)

Fig. 1. Lumped-constant low-pass filter characteristics; (a) maxi-mally flat, (b) Chebyshev, (c) Chebyshev transformer, and (d)elliptic-function.

FREQUENCY+

Fig. 3. Lumped-constant band-stop filter characteristics; (a) maxi-mally flat, (b) Chebyshev, (c) Chebyshev transformer, and (d)elliptic-function.

LOW-PASS

TO

-m+=:+C.

BAND-STOP 1

-1-1 (B, C= CONST, )

-&, 1

I W-PASI ~ ==--@- =,+: ITO

BAND-PASS 1

-I- 0

(D, E = CONSTJ

Fig. 5. Element substitutions corresponding to frequency trans-formations to turn a low-pass filter into a high-pass, band-stop,or band-pass filter.

fleeting, absorbing, etc.), by physical structure (co-axial line, rectangular waveguide, etc.), by application(tunable or fixed-tuned), by loading (singly terminated,doubly terminated, etc.), by energy manifestation(electromagnetic, spin-wave, acoustic, etc.), and so on.Most of these types will now be described, but it mustbe remembered that the groupings are somewhat arbi-trary and there is bound to be considerable overlapunder any classification scheme.

(a)

(b)

Fig. 2. Lumped-constant high-pass filter characteristics; (a) maxi-mally flat, (b) Chebyshev, (c) Chebyshev transformer, and (d)elliptic-f unction.

a)!U I!L&lc)gb)u u d)

FREQUENCY+

Fig. 4. Lumped-constant band-pass filter characteristics; (a) maxi-mally flat, (b) Chebyshev, (c) Chebyshev transformer, and (d)elliptic-function.

.-

w nC;=.gn %+[9+1.n=odd

L; =g, L;=g3

~Ezzl~

n = even

(b)Fig. 6. The four lumped-constant low-pass filter prototype circuits.

iq=gn

-------1or

--l %=9,,.- . ~,j,j

1965 YOUNG: 1965 FILTERS 49T

inn-w -[+3:\ JNL L. P. = LO W- PAS!3H. P = HIGH-PASS) B, P. = BAND-PASSR S. = BAND-STOPQ EXACT THEORY AND (Q EXACT THEORY] AVAILABLE o c1 lMFEDANCE --NUMERICAL TABLES DERIVED DESIGNAVAILABLE AdmittanceDUALS- EXACT DERIVATION

< APPROXIMATE DE RI VATI13N

Fig. 7 Flow chart showing derivationof filters with commensurable (ornearly commensurable) line le1lgths

492 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUESSEPTEMBER

Fig. 8. An L-band seven-section quarter-wave transformerin waveguide [150].

Fig. 9. A C-band six-resonator direct-coupled-cavity filterin waveguide [57].

III. FILTERS WITH CASCADED LINESOR CAVITIES [19] [25]

A periodic structure, such as a waveguide or coaxialline loaded periodically with posts or irises, has filterproperties. However, the pass bands and stop bands areclearly defined only for an infinite length of line,whereas in practice the input and output lines mustusually be in uniform waveguide or transmission line.In a sense, the problem is not how to design the filter(the periodic structure) but how to match between un-loaded and loaded lines. For an optimum match, agradual loading is required, starting with light loadingat the ends and increasing to the greatest loading at thecenter. The structure is now only approximatelyperiodicit is a filter.

We have just described the wave (or physicists) viewof a direct-coupled-resonator filter, consisting of end-

(b)Fig. 10. Direct-coupled-resonator filters in coaxial and strip lines.

(a)

1-

0 fo 2 f. 3ftJ

o fo 2fo

FREQUENCY

Fig. 11. The periodic nature of the frequency response of transmis-sion-line filters; (a) quarter-wave transformer, and (b) half-wavefilter [20].

coupled transmission-line resonators or cavities. Thenetwork engineer would start with a lumped-constantfilter and approximately transform the LC resonatorsinto transmission-line form. Cohns paper [19 ] is themost useful on this subject, having served as the basisfor much subsequent work. It generally applies tomicrowave filters with fractional bandwidths up toaround 30 percent, provided that the pass-band VSWRis not too low.

Returning to the idea of the periodically loaded line,we should like to know if at least one type of periodicloading can be designed exactly, so that others may bedesigned from it by suitable approximations. Thequarter-wave transformer, for which a complete syn-thesis procedure was first given by Riblet [19a], is such

1965 YOUNG, 1965 FILTERS 493

a prototype [20], the periodic loading being obtainedby impedance steps. The impedance ratios at the stepsin a typical quarter-wave transformer are on the orderof 20 percent from unity, and are seldom greater than?-to- 1, as can be seen from Fig. S. The correspondingimpedance ratios at the steps of the quarter-wave trans-former prototype are frequently on the order of 10O-to-1, and may be as high as 10,000 -to-l or even higher.Clearly, such a transformer is not practical, but themathematical theory is the same for any impedanceratio, and exact solutions are possible for the idealtransformer [13 ], [20 ] [22 ]. The impedance steps arethen replaced by other more realizable discontinuities,such as shunt inductances (irises, posts) or series ca-pacitances, each having a discontinuity lJSWR equalto the corresponding step impedance ratio [23]. Twofilters of this type are shown in Figs. 9 and 10, and alsoin circles (Q), (R), and (.S) in Fig. 7.

The lumped-constant loy-pass prototype [19] iseasier to use, but the quarter-wave transformer proto-type [20 ] enables one to predict the filter performancemore accurately, especially when the bandwidth islarge or the pass-band t7SWR is particularly low, orboth.

The step-tw-ist filter of DeLoach [25] has equal linelengths between junctions, and is a good example of afilter that could more efficiently be designed from astepped-impedance prototype [20], [22 ].

The frequency response of a quarter-wave trans-former (Fig. 8) or a direct-coupled-resonator filter(Figs. 9 and 10) is periodic, or approximately periodic,in frequency. (For waveguides, substitute reciprocalguide wavelength in place of frequency. ) This periodic-ity is indicated in Fig. 11 for an ideal quarter-wavetransformer and an ideal half-wave filter [20], [22].The response of actual filters [23], [24] will be modifiedby the frequency sensitivity of the couplings and even-tually by the generation of higher-order modes.

I [:. TEM-Mo~E BAND-PASS FILTERS WITH PAR~LLEL-LINE COUPLING [26]- [34]

Consider the filter shown in Fig. 10. To obtain largebandwidths, adjacent resonators have to be coupledtightly, which requires large series capacitances at thegaps and therefore small, critical gaps. If the resonatorscould be coupled on their sides instei~d of at their ends,then wider, less critical gaps would be possible. Suchan arrangement is indicated in circle (L) of Fig. 7,showing a parallel-coupled resonator filter [26 ]. Sincethe facing areas are larger, the gaps are also wider andless critical. However, the coupling is no longer purelycapacitive (with equi-phase surfaces), since the over-lapping lengths are one-quarter-wave long at bandcenter and the phase varies along them. The design ofthese filters [26], [27 ] is based on other concepts [13],[26], developed by Jones and Bolljahn, which we shallnot discuss here.

The interdigital-line filter [28 ] [33 ] was first built

by Bolljahn and Matthaei. Filters using circular rodshave been constructed by Cristal [30] (Fig. 12). Eachresonator is one-quarter-wave long at bmd center,when the ends of the rods are open-circuited. As in theparallel-coupled filter, the resonator spacings are notvery critical. In addition, the resonator commenis it-self for many applications by its compact form, Anexact design theory for interdigi tal filters and relatedstructures is given by Wenzel in this issue [33]. l[~rac -tional pass-band band~vidths in excess of one octavehave been obtained.

The digital resonators of the interdigital filter canbe made shorter than one-quarter wavelength at bandcenter, and the filter becomes even moire compact bycapacitively loading the ends of the rods [32!], as sholvnin Robinsons filter (Fig. 13). Also, the first spuriouspass band is thereby moved further awav from the de-sign center frequency.

Another very compact structure is the coml~linefilter developed by Matthaei [34] (Fig. 14), which issimilar in many ways to the capacitively loaded inter-digital-line filter. In the comb-line filter the ca paci-tances are all on the same side. They are necessary tothe functioning of the filter, since there is no couplingbetween quarter-wave digital resonators when theyare all grounded on one side, and all open-circuited onthe other. The rods are typically one-eighth of a \rave-Iength long at midband. The first spurious pass lband.then does not occur till past the fourth harmonic fre-quency. The comb-line filter is more compact than an(unloaded) interdigital line filter. Current design pro-cedures are suitable only for up to relatively narrowbandwidths, on the order of 10 per cent. The comb~linefilter is likely to find most application at VHF, UHF,and the lower microwave frequencies.

The parallel-coupled, interdigital, and, comb-linefilters are indicated in circles (L), (M) and (Y) in Fig. 7.

V. BAND-STOP FILTERS [35]- [45]

Various band-stop filters have been developed atStanford Research Institute [35 ] [40]. Many of them[35], [36], [39] consist of a length of transmission, lineand either series, short-circuited stubsor shunt, (open-circuited stubsor both, as indicated in circles (1?) and(C) in Fig. 7. They are a good illustration of the ap-plication of Richards transformation [18] to the low-pass prototype. Richards transformation is illustratedin Fig. 15, showing how the transformation (A) into(B) is accomplished in Fig. 7. Note the periodic natureof the band-stop filter response. To realize the requiredcluster of stubs on a single junction is usually notmechanically convenient; in coaxial line it could be con-structed as shown in Fig. 16. It is often more convenientto separate the stubs, one to a junction, and this can beaccomplished by means of the Kuroda identities (a)or (b) in Fig. 17. Kurodas identity makes it possibleto spread out the stubs; moreover, each stub is of the

494 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES SEPTEMBER

Fig. 13. An L-band capacitively loaded interdigital filter [32].

Fig. 14. An L-band comb-line filter [34].

Z=LS

AND

c

m

t

Y=cs

WHERE, FOR REAL FREQUENCIES,

~.jw

THEN :

HZo e+

z = Zos

Y = Yos

S=jtan~= j tan (const. x o)

8DEGREES

Fig. 15. Element substitutions (corresponding to Richards trans-formation) to t+rn a lumped-constant low-pass filter into acommensurable-hne-length band-stop filter. The periodic natureof the new frequency response is also indicated.

-d

(a)

(b)

Fig. 16. Physical realization of several stubsatone junction in coaxial line.

(!!)II

1965 YOUNG: 1965 FILTERS

KU RODAS ID I: NT ITIES

a)w=bdlI 1 I I

I 1 L

1 I

Zoz;=n

ZozlZo+z,

~h=~n

Yo Y,

yo+yl

z~ = nzo

Y; = nY~

Z.Z\. T

z;

z, +z~

Z;=z, +zo

Y; = y, +Y~

n and m

Z(3n .[+

z,

z,~=[+_

Zo

Yon .l+ Y,

Y,~.l+_

Yo

Zon .l+

z,

Y~n .I+y

495

CHECK

z;yl=~z~= ~j m

Y; z, =. .=

Yb ZO m

z; z,Zb Z(3

Y; Y,

Y; Yo

Fig. 17. Kurodas identities [46]. (Heavy lines represent transmission lines, or unit elernellts, all of the same Iength e.)

Fig. 18. An L-band band-stop filter with stubs [36].

same type. For instance, the stubs in Fig. 18 are allshunt, open-circuited. The four band-stop filters [35 ],[38 ], [40] in Figs. 19 through 22 are more suitable fornarrower stop bands. The spur-linle filter may be con-sidered to be obtainable from the stub filter (Fig. 18)by laying the stubs parallel to the main line; the parallel-

line coupling opposes the junction coupling, weak eningit and making the filter more suitable for narrower stopbands. These band-stop filters are indicated in circles(B) through (F) in Fig. 7.

A more general kind of band-stop filter [37] can bedesigned which has three separate, but symmetricallyplaced, poles of attenuation. This filter is based on thelow-pass prototypes of Saal and Ulbrich [61], as in. circle(G) of Fig. 7. It uses one double stub, as in circle (1?) ofFig. 7; it has not been possible so far to accommodatemore than one double stub, when all the stubs are sep-arated (no more than one to a junction), becauseKurodas identity does not apply to a double stub.(However, concerning a generalization of Kulrodasidentity, see the end of Section VI. )

VI. FILTERS WITH STUBS: GENERAI. THEORY [46]- [.53]

We shall begin with some general remarks aboutKurodas identities: The two Kuroda identities of thefirst kind in Fig. 17 are the same, except that both boxeshave been turned around. In each identity a series,short-circuited stub is exchanged for a shunt, open-cir-cuited stub. (Note that no impedance transformer isrequired. ) Also, each circuit transmits at dc.

The two Kuroda identities of the second kind inter-change two like stubs; furthermore, an impedance

496 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES SEPTEMBER

BRASS

\

Fig. 19. An L-band parallel-coupled-line band-stop filter [35].

Fig. 20. An L-band spur-line band-stop filter [35].

E

LOCKS

Fig. 21. A C-band narrow-band band-stop filter [40].

transformer is required. Each circuit is totally reflectingat dc. It is not possible to separate the stubs in Fig.16(b) and obtain stubs all of one kind, as can be donefor the stubs in Fig. 16(a) to obtain a filter like thatshown in Fig. 18. The reason is that the two Kurodaidentities of the second kind do not change the stubtype. Thus, it is not possible in Fig. 7 to make an exacttransformation from (1) to (~), as was possible from(B) to (C). The appearance of a transformer in the lasttwo identities is a further complication, which howeverdisappears for symrnetr~cal filters, since then the trans-formers can be passed through the circuit, changing theimpedance levels of the elements passed over and,finally, the symmetrical series of transformers from eachhalf of the filter combine at the center into two trans-formers that cancel. For unsymmetrical band-passfilters, application of a Kuroda identity of the secondkind leaves a transformer in the circuit.

A filter [13] which could be (but was not) designedby making use of a succession of Kuroda identities ofthe second kind is shown in Fig. 23, and schematicallyin circle (1) of Fig. 7. The filter is highly redundantsince the thirteen stubs have only a single pole ofattenuation at zero frequency. Thus, the same per-formance could be obtained (in principle) by a filterwith twelve line sections in cascade and but a singlestub. Of course, the impedance of the single stub mightturn out to be so low as to make it impractical torealize. One could use any number of stubs between oneand thirteen (preferably an odd number to avoid a

Fig. 22. An X-band narrow-band band-stop filter in waveguide [40].

transformer), compromising between the impedancelevel and the number of the stubs. Filters of this typeare also the subject of a recent paper by Riblet [52].

To avoid redundancy, or in other words, to obtainoptimum filters (filters having the fewest number ofelements to meet a specified frequency characteristic),one cannot use only shunt, short-circuited stubs, as inFig. 23, or only series, open-circuited stubs, since theycould all be reduced to a single stub. One must alternatebetween the two stub types, as indicated in circle (N)of Fig. 7. Filters of this general design have recentlybeen treated by Horton and Wenzel [49], and byCarlin and Kohler [51]. They make use of the connect-ing lines between stubs, as well as the stubs themselves,to contribute to the filter performance. In contrast,designs based on the low-pass prototype [circle (A) inFig. 7], after separation of one or more stubs by one ofKurodas identities, do not give optimum filters; theconnecting lines between stubs are redundant sincethey do not contribute to the filter performance (butonly toward a simpler mechanical design).

An important practical consideration is the value ofthe impedances of the stubs and connecting lines. Thespread between realizable impedance values is limitedin practice; for instance, in coaxial line, between 15ohms and 150 ohms is usually considered reasonable. A5-ohm stub would have an inconveniently low im-pedance. This situation can always be remedied by in-

1965 YOUNG: 1965 FILTERS 497

troducing redundancy. For instance, a 5-ohm shuntstub could be replaced by three 15-ohm shunt stubs inparallel, then separated by Kurodas identity. How-ever, the filter is then no longer toptimlum according toour definition. (It would be useful to have some kind ofnew ~optimum synthesis procedure, in which upperand lower bounds for the impedances are specified as anadd;t;onal constraint to the problem. )

For illustration of this point, consider four numericalexamples, including two of the examples given byHorton and Wenzel [49]. They all have a 3-to-1 passband with a ripple of 0.1 dB. Let m be the minimumnumber of stubs (either shunt, short-circuited, or series,open-circuited), and n the minimurn~ number of con-necting lines between stubs. One would expect m to con-tribute much more to the stop-band attenuation than n.This is borne out on comparing, say, the (m= 5, n =2)filter with the (m= 1, n =8) filter. The latter corre-sponds to the type of filter shown in Fig. 23 (with allbut one stub redundant). Two additional curves areplotted in Fig. 24, both for filters with n== O and derivedfrom the low-pass prototype circuit, Fig. 6 or circle (A)in Fig. 7. one filter is (m = 5, n = O), and is inferior tothe (m=5, n=2) filter; the other is (m=7, n= O), andis the best of the four filters considered. This, of course,was to be expected since a nonredundant stub wouldcontribute more to the stop-band attenuation than aconnecting line. However, it was not possible to predicthow the impedances would turn out. It was found thatthe (WZ= 5, n =2) filter was realized with two redundantstubs so as to make all impedances nearly equal [49],and thus it ended up with seven rather than five stubs.The (m= 7, n = O) filter could not be realized as suchbecause seven stubs could not be crowded at one j unc-tion; however, it could be realized with two redundantconnecting lines introduced by Kurodas identity fromoutside the filter. Thus the final Practical structures forthe (m= 7, n = O) filter would be very similar to thosefor the (WZ= 5, n =2) filter, and both would contain thesame number of elements of each kind.

Band-pass filters with stubs that create poles of at-tenuation close to the pass band have been describedby Matthaei [13], pp. 605614. They use stubs thatare one-half wavelength long at band center, as in-dicated in circle (K) of Fig. 7.

Recently, Kurodas identity has been extended byLevy [47 ]. In particular, this generalization can be ap-plied to removal of the limitation on transmission-lineelliptic-function [6] filters, mentioned in Section V. Itshould be possible to design such lilters with severaldouble stubs, requiring no more than one stub per junc-tion, spread out along the main line.

VII. LOW-PASS AND HIGH-PASS FILrEIW [54]-- [60]The low-pass prototype filter of Fig. 6, or circle (A)

in Fig. 7, can be turned into a transmission-line filter byreplacing each series inductance by a short high-im-pedance line, and each shunt capacitance by a low-

\

\

m = MINIMUM NUMBER

CONNECTING LINES

o 0.5 1.0 I .5

NORMALIZE FREQUENCY

o

Fig. 24. Attenuation characteristics of optimum band-pass filterswith stubs, showing the effect of the number of stubs an (d thenumber of internal connecting lines (taken partly from lSLefer-euce [49]).

impedance line, as indicated in circle (X) of Fig. 7. Acoaxial line filter of this type [13] is shown in Fig. 25.In waveguide, it can lead to the waffle-iron filter [54]-[56] developed by Cohn and others at Stanford Re-search Institute. The waffle-iron filter can be desi;gnedto have a wide pass band (on the order of al waveguideband) [55 ], [56], as well as a very wide stc~p band (al-most three octaves for the composite filter shown inFig. 26). It will handle moderately high power levels,and makes a very compact unit.

Low-impedance, high-impedance short-line low-passfilters can also be designed from a stepped-irnpeclanceprototype [20 ], [22]. The effect of the cclrner sl-~unt-capacitances at the steps must be allowed for in anypractical filter.

High-pass filters in coaxial or strip line may take theform shown in Fig. 10 [57]. Waveguide is a naturalhigh-pass filter. As is apparent from Fig. 27, the prob-lem reduces to the design of a good inhomogeneoustransformer [13 ], [60] that is, a transformer in whichthe guide wavelength changes along the transformer. I t

498 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUESSEPTEM8ER

Fig. 25. A coaxial low-pass filter [13].

Fig. 26. An L-band waffle-iron filter with stopband up to 13,7 Gc [56].

is usually necessary to obtain a good match relativelyclose to the cutoff frequency, where the impedance ofthe near-cutoff waveguide is still high and changingfast. (Another application of inhomogeneous trans-formers has nothing directly to do with filtering, butconcerns making a transition piece between two dif-ferent waveguide sizes, as in Riblets paper [60] in thisissue. )

VIII. DISSIPATION Loss, GROUP DFiLAY, AND POWER-HANDLING CAPACITY [61 ]- [69]

Filters are usually designed by first neglecting dis-sipation loss, and then allowing for the dissipation losson the assumption that it is small. A remarkably ac.curate formula for the midband dissipation loss ofband-pass filters has been given by Cohn [61] for well-matched filters that are designed from a low-pass pro-totype. The formula can readily be modified [68] forfilters that are appreciable y mismatched, and then con-tinues to hold quite accurately for filters with up toseveral decibels of reflection loss. It can also be ex-tended to band-stop filters [40]. The mid band dissipa-

Fig. 27. A high-pass filter in waveguide using twoinhomogeneous quarter-wave transformers.

tion loss of a stepped-impedance filter can also be cal-culated quite accurately [62 ]. Taub [63 ] [65 ] hasgiven numerical curves for the insertion loss of lossyequal-element filters as a function of frequency, bothfor band-pass and band-stop filters.

The dissipation loss is closely related to the groupdelay [13 ], [68] and is nearly proportional to it overmost of the pass band. This is intuitively acceptable,since the longer the energy remains inside the filter, thegreater should be the amount of its dissipation in thefilter.

Figure 28 shows some typical curves. Curve (a) is thegeneral shape of either the dissipation loss vs. frequency,or the group delay vs. frequency characteristic. Noticethe two sharp peaks which usually occur just outsidethe pass band. The effect of the dissipation loss on theoverall insertion loss is to produce

1965

DISSIPATIONLOSS

(a)

I II I

ill

I I FREQUENCY --+1 I

YOUNG: 1965 FILTERS

REFLECTIONPLUS

DISSIPATIONLOSS

(b)

499

I II I

\i i/

1 ~FREQUEIYCY _

Fig, 28. Dissipation loss characteristic and effect on overall insertion 10.s for typical band-pass filters [13].

FREQUENCY+

Fi~. 29. Equivalent po~verratios imthesix cavities ofadirect-coupled-resollatorfilterof 10-percent bandwidth [13].

TAP EREO

(VARIABLE cuTo FF)

\ WA VEGU IDE

Fig. 30. Delay equalizer using acirmdatorandatapered waveguide [71].

X. DIPLEX~RS AND NIULTIrLEXERS [76] -[S1]Adiplexer separates power entering a common input

into two frequency bands; or conversely, it combinestwo frequency bands arriving separately into acommonoutput. A multiplexer extends this principle from twoto many channels. Frequently, a multiplexer is madeup of a cascade of diplexers because of the mechanicalproblems that arise in connecting many filters close toa single junction.

Diplexers in which there are adequate guard bandsbetween channels may be designed by suitably con-necting two separate, doubly terminated filters onto aT-j unction. The design procedure is not so simple whenthe bands are contiguous [7679], that is, when theycross over at the 3-dB points (and thus have no guardbands to separate them). This case is illustrated in Fig.31 for the case of a band-pass and a band-stop filter.It is possible to maintain perfect match at the common

port, provided that the two filters are designedl assingly terminated, maximally flat filters [1], [76].

Two filters having contiguous pass bands are shownin Figs. 32 and 33. The filter in Fig. 32 was built byMatthaei and Cristal [79], and it has a relatively nar-row pass band of about 5 per cent at L-band. The filterin Fig. 33 was built by Matthaei and Schi Ffman, andit has a relatively wide pass band of one octave (4 to8 Gc) .

XI. DrRE~TIONAL FILTERS [82 ]-8,4]Directional filters [13 ] can be constructed in wave-

guide and in strip line, as indicated in Fig. 34. Craven,Stopp, and Thomas [82] and Williams [82a] describefilters such as that shown in Fig. 34(a). Standley [33],[84] reports on filters such as that shown in Fig. 34(d);he analyzes discontinuity effects, which often set a prac-tical limit on the performance of such filters.

Directional filters can also be realized in a straight-forward manner by joining two quadrature hybrick incascade through a pair of identical filters. For example,in the polarization filter of Fig. 34(a), the two hybridsare the two junctions at top and bottom, and the singlecircular tube represents two waveguides b:y vitrue ofthe two independent circularly polarized waves thatpropagate in it.

Directional filters can be used as channel-droppingfilters, or as matched diplexers with contiguous channels(compare Fig. 31). However, the isolation in one chan-nel w-ill generally not be very good in practice becauseof the small (but not negligible) reflection in the passband of the filter pair.

XII. TUNABLE FILTERS [85 ]- [94]Filters can be tuned mechanically [S5 ] [87 ] or elec-

tronically. They have been tuned electronically by amagnetic field [88 ] [92], by a varactor [93], and bymeans of a plasma [94].

500 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES SEPTEMBER

vfBAND-PASS FILTER RESPONSEBAND-STOP FILTER RESPONSE

\

T

Fig.

. % WI bFREQUENCY

Fig. 31. Characteristics of complementary band-passand band-stop filters.

32. An ~-band diplexer composed of an interdigital filtera parallel-coupled-line band-stop filter [79].

-

Q)

Fig. 33. A wideband diplexer (pass band of interdigital filter= stopband of band-stop filter =4 to 8 Gc).

and

Magnetically tunable filters using single-crystalferromagnetic resonators of yttrium iron garnet (YIG)have proved very successful at microwave frequencies.They attain high unloaded Q, and it is therefore possibleto build band-pass filters with relatively low insertionloss (typically 12 dB per resonator), and band-stopfilters with relatively high attenuation [88 ]. The filteris tuned by adjusting the applied (static) magneticfield; the resonant frequency in megacycles is approxi-mately equal to 2.8 times the applied magnetic field inoersteds. The lowest frequency at which a ferromag-netic resonator can be operated depends on the sampleshape and material. For example, a pure YIG spherecan be resonated down to about 2 Gc, but it rapidlyloses unloaded Q as this frequency is approached. Apure YI G disk can be tuned to much lower frequenciesfor example, down to about 500 Mc for a diameter-to-thickness ratio of 10-to-1. (An infinitely thin disktheoretically has no lower-frequency limit.) A disk alsotends to have fewer spurious-mode resonances than asphere. On the debit side, disks are difficult to machine,expensive, fragile, and more temperature-sensitive thanspheres. For this reason, where a pure YIG sphere willnot do (below about 2 C,c), it is generally preferred to

(a)

,, ky- -D--v +VHALF HALF ONEWAVELENGTH WAVELENGTH WAVELENGTHSTRIPS STRIP STRIP+V +V12 l~z

Az

(b) (c)

(d)Fig. 34. Some directional filters; (a) in waveguide,

and (b) in strip line [13].

dope the YI&for instance, by gallium substititution.Doping reduces the saturation magnetization and thusthe internal demagnetizing field, and it permits filteroperation down to a few hundred megacycles. Dopinghas several undesirable effects. It reduces the unlo~dedQ (increases filter losses), and Imakes it more difficultto couple to the doped YIG resonator. In addition, sinceit is difficult to control the uniformity of the doping,there will be appreciable inhomogeneities within onecrystal, and there is likely to be a relatively large spreadin resonant frequencies between doped resonators.

The first single-resonator YIG filter was reported byDeGrasse, and the first multiresonator filter was re-ported by Carter [13]. Two magnetically tunable

1965 YOUNG: 1965 FILTERS 501

Fig. 35.YIGfrom

Magnetically tunable band-pass filter, using two gallium-spheres and low-pass matching transformers [7], tunable1.3 to 2.7 Gc.

Fig, 36. Magnetically tunable band-stop filter, using two YIGspheres (one has been removed), tunable from 2.2 to 6 Gc [88].

filters built recently by Matthaei [88] are shown inFigs. 35 and 36. They use YIG spheres as the resonators.One sphere mounted at the end of a dielectric rod canbe seen in each photograph.

Blau [92a] has lowered the saturation magnetizationof a gallium YI G resonator by heating it, and hasoperated it down to 50 Mc. However, heating alsolowers the unloaded Q of the resonator, thus increasingfilter insertion loss.

Each ferromagnetic sphere may be treated as a res-onator from the circuit point of view, and one has todevise means for coupling into and out of it. Thecoupling is through the RF magnetic field, whichshould therefore be made as strong as possible over awide frequency band (the tuning range of the filter).This result implies that the ferromagnetic resonatorshould be placed at a low impedance point, which canbe accomplished either by dielectric loading or by animpedance transformer.

@l@mlL METAL-wALLED WAVEGUIOE

/

oI

Fig. 37. Dielect

mit-resonator filters using TiOZ disks [96].

YIG resonators saturate at relatively low powerlevels (typically below one milliwatt), and they aretherefore also used as limiters [91].

XII I. DIELECTRIC-RESONATOR AND DIELECTRIC-LOADED FILTERS [95 ]-[100]

Okaya and Barash [95] showed that high unloadedQ (on the order of 104) can be obtained with materialshaving high dielectric constant (on the order of 80).This phenomenon makes it possible to use small volumesof such materials as dielectric resonators [96 ] [99a ].Theoretically, no metal walls would be required, but it isnecessary in practice to provide shielding. Filters canthen be constructed from these resonators, and can bemade very compact. Such a filter is sketched in Fig. 37,adapted from Cohn [96 ]. The filters can be tuned, forinstance, by adjusting the spacing between resonators.If the material is ferroelectric, the possibility exists oftuning the resonance electrically, by the application ofa high electric field.

The chief drawback of high-dielectric-constant reso-nators is the excessive dependence of the resonant fre-quence on temperature, at least with present-day ma-terials.

XIV. FILTER TECHNIQUES APPLIED TO SEMICONDUCTORDEVICES [101] -[109]

Rapid strides in the semiconductor art and the prog-ress toward ever-higher frequencies have led to theapplication of microwave filter techniques to varioussemiconductor devices. They include frequency multi-pliers [101 ], [102], frequency converters [103], andamplifiers [104 ] [106a], as well as diode phase shifters[107] and switches [108]. Circuits have become moreintegrated [109 ], and this trend is likely to continue.

XV. STEPPED-IMPEDANCE FILTERS AS DIRECTIONALCOUPLERS [110-12o]

From the design point of view, there is a strong re-semblance between filters and certain types of direc-tional coupler. Nowhere is this more apparent, perhaps,than with the TEM-mode coupled-transmission-linedirectional coupler, pioneered by Jones, Bolljahn, andShimizu [13]. (There are at least two papers on this

502 IEEE TRANSACTiONS ON MICROWAVE THEORY AND TECHNIQUES

subject in this filter issue [117], [118 ].) The corre-spondence reduces to the stepped-impedance filterprototype shown in Fig. 38. The design of the TEM-mode backward-wave coupler reduces to the design of astepped-impedance filter, with the reflected wave be-coming the coupled component. The input and outputimpedances of the prototype must be the same (ZO inFig. 38). The design problem is to maintain nearlyconstant (equal-ripple) reflection over a specified stopband.

Two kinds of coupler are of practical importance, theasymmetrical coupler [1 IO] [1 14] of Fig. 38(a) andthe symmetrical coupler [115 ] [120] of Fig. 38(b). Theformer requires fewer sections, while only the lattermaintains phase quadrature between the two outputs,which is usually of importance for 3-d B couplers. Anasymmetrical coupler realization in strip transmissionline is sketched in Fig. 39.

We make a final comment on the asymmetricalcoupler prototype [Fig. 38(a) ], illustrating its resem-blance to and difference from a band-pass filter. Theproblem of constant coupling reduces to one of con-stant reflection coefficient magnitude for the prototype.Now the junction of two lines of different characteristicimpedances gives a perfectly constant reflection co-efficient. It may therefore be expected that the couplerof Fig. 38(a) should be designed as a quarter-wavetransformer from 20 to some impedance 2.; the ratio2./20 would then be nearly constant and would de-termine the coupling. This approach is indicated on aSmith chart in Fig. 40(a). The difference between thecoupler and the transformer is that it is only the varia-tion in the magnitude of the reflection coefficient thatinterests us in the coupler, whereas the transformer ap-proach has minimized the variation in the vectorialchange of the reflection coefficient. Thus, an optimumdesign allows the tip of the reflection coefficient vectorto lie anywhere inside the annul us shown in Fig. 40(b),the radial width of which can be made appreciably lessthan the diameter of the circle in Fig. 40(a), for a givennumber of sections. The author has analyzed the per-formance of couplers based on quarter-wave trans-formers [20 ], and that of couplers based on Levystables [111 ], and has found the latter to give ap-preciably better performance,

XVI. COUPLERS FROM FILTERS AND FILTERS FROMCOUPLERS [121]- [125]

The connection between couplers and filters is furtherexemplified by the branch guide coupler [121 ] shownin Fig. 41, which can be designed to a close approxima-tion from a quarter-wave-transformer prototype.

Directional couplers can also serve as filters [123].This principle depends on the fact that complete trans-fer of power can occur only between two transmissionlines having the same phase velocity [124]. If one lineis made dispersive with respect to the other, 100-per-cent coupling occurs over only a narrow frequencyband, where the two phase velocity curves cross.

Z. 20

(a)

II 1

I

Z. Z.

(b)Fig. 38. Stepped-impedance filters that serve as prototypes for

TEM-mode backward-wave directional couplers; (a) asymmetri-cal, and (b) symmetrical.

MAIN OUTPUT

Fig. 39. Typical TEM-mode backward-wave directionalcoupler in strip line.

(a)

(b)Fig. 40. Diagram showing why the optimum prototype in Fig.

38(a) is not based on a quarter-wave transformer.

1965 YOUNG: 1965 FILTERS 503

Fig. 44. An S-band diplexer in rectangular waveguideusing open-wall construction [131].

Fig. 41. An S-band branch-guide directional coupler [121].

Fig. 45. A low-pass leaky-waveguide filter usingopen-wall construction [133].

XVII. FILTERS WITH OPEN WALLS [126]- [133]Fig. 42. An L-band circular-waveguide TEO,-mode

high-power tunable filter [13].

Fig. 43. An X-band circular-waveguide TEO1-mode trapped-mode filter using open-wall construction [129].

Microwave filters that are to operate at high poweror with very low insertion loss are usually constructedin waveguide, and sometimes in overmoded guide, suchas the circular TEO1-mode. Figure 42 shows a three-cavity tunable filter constructed by Jones [13]. Wave-guide filters, especially when in overmoded guide, sufferfrom spurious frequency responses; that is, in the stopband there will be occasional resonances and the at-tenuat ion drops sharply over a very narrow band. Todamp out these spurious resonances, a number of filtershave necently been tested at Stanford Research Insti-tute, using an open-wall construction, reminiscent ofleaky-wave filters [126] [128]. However, in this case, afilter is first designed as a band-pass filter and then se-lected walls are removed. An open-wall TEO1-modefilter [129] is shown in Fig. 43, and an open-wall rec-tangular waveguide filter is described in another paper[130] in this issue. An open-wall waveguide diplexer[131] is shown in Fig. 44, and an open-wall low-passfilter [133 ] is shown in Fig. 4.5.

504 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES SEPTEMBER

XVIII. FILTERS FOR MILLIMETER WAVES AND HIGHERFREQUENCIES [134]- [143]

Filters at millimeter wavelengths have been built inTEO ~circular waveguides [134][137 ]. The Fabry-Perotresonator [137 ] [139] and other filter types and di-rectional couplers [140 ] [142] have been adapted fromoptics. There are many points of similarity betweenmicrowave and optical filters [141 ].

A stack of separated dielectric plates makes a goodreflector when the thicknesses of the plates and theseparations between them are equal to or close to one-quarter wavelength. Two such stacks, spaced an in-tegral number of half-wavelengths apart, as indicatedin Fig. 46, form a Fabry-Perot resonator.

When the diameter of this system does not equalmany wavelengths, there is appreciable outward radia-

tion, causing a drop in the unloaded Q. Such a drop canbe remedied to a large extent by placing spherical mir-rors at or near confocal spacing. If coupling losses areto be kept low, some sophistication is necessary in

QUARTER-WAVEDIELECTRIC SHEETS

/%

coupling to the con focal resonator. A system devised bythe author and B. M. Schiffman is shown in Fig. 47.The thin dielectric sheets determine the maximumpossible coupling; the coupling and bandwidth are thencontrolled by moving the mirrors C and D in unison.

There has recently been renewed interest in millimeterand submillimeter waves [137]. The main problemtoday is still a lack of reliable inexpensive powersources, especially above 150 Gc. New types of trans-mission line are also being developed. With sufficientprogress in these developments, we may expect to seemore activity in the area of submillimeter wave filters.

XIX. MISCELLANEOUS FILTERS [144]- [153]

A few filters have escaped classification. Torgow andLubell [1.44] have described a combination of band-pass and band-stop filter to obtain steep skirt selec-tivity. They make the interesting observation that,with prc)perly spaced filters, very sharp spuriousresonances (the two stop bands almost canceling oneanother) are prevented by the damping due to thesmall amount of dissipation.

Log-periodic structures [146 ]- [148], described byDuHamel and others, offer the possibility of compo-nents with very wide bandwidths.

An interesting type of band-pass filter [13] is shownin Fig. 48 and in circle (W) of Fig. 7. Resonators are ca-pacitively coupled in such a way to suppress the firstspurious resonance so that the filter has a wide stop band.

A differential phase shifter is not a filter, but theSchiffman phase shifter [152] of Fig. 49 has been widely

Fig. 46. Millimeter-wave Fabry-Perot interferometerusing dielectric stacks.

Fig. 48. A band-pass filter with wide stop band [13].

Fig. 47. A band-pass confocal resonator filtershowing low-loss coupling mechanism.

STRIP LINE ABOVEGROUNO PLANE 5

J

r

I

1,

IT--

-- ,+

I__ u [lL (-E- lr

Fig. 49. A wideband 90-degree differential phase shifter [152].

1965 YOUNG: 1965 FILTERS 505

used and depends on the theory of parallel-coupledlines, as do certain types of filter (Section IV).

We have not discussed experimental procedures in thealignment of filters. For this material we direct thereaders attention to References [13] and [153].

XX. CONCLUSION

We are at the end of our journey. We have attemptedto conduct the reader past the principal types of filtersof interest today. We have relied on photographs anddiagrams, rather than on mathematics, to convey animpression of the needs felt and the ideas generated.The reader will find a fuller description of many of thefilters in Reference [13], which reports developmentsup to early 1963, whereas the present paper covers thework undertaken since late 1962.

The presentation has been colored by the authorsparticular interests, and some omissions were inevi-table. No attempt was made to scan every relevantjournal.1 We apologize in advance to any author whosework may not have been given proper credit, whetherthrough ignorance or oversight.

ACKNOWLEDGMENT

The author wishes to acknowledge his indebtednessto the many workers whose ideas have touched him,and have often become part of him. In particular, theauthor has benefited from many discussions with hiscolleagues at Stanford Research Institute, especiallyB. M. Schiffman, Dr. E. G. Cristal, and Dr. G. L.Matthaei (now at the University of California). Mr.Schiff man supplied the basic idea fc,r Fig. 7, checkedFig. 17, and computed the two (n= O) curves in Fig. 24.

The author also wishes to thank Nathan Lipetz,John Agrios, and William Dattilo of the U. S. ArmyElectronics Laboratory, Fort Monmouth, N. J., fortheir continued support of most of the microwavefilter work performed at SRI.

Finally, the author is grateful to Miss Mary LouBaker for overseeing the typing of the manuscript onvery short notice.

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Lam@d- Constant Filters and P~ototype.s

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McGraw-Hill, 1962.[5] H. W. Bode, Network Analysis and Feedback Am@i$er Design.

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>.

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G. L. Matthaei, Leo Young, and E. M. T. Jones, Micrc,waueFilte~s, Iw+edunce Matching Networks, and CouplingSkc-tares. New York: McGraw-Hill, 1964.L. Young, Progress in circuit theory19601963: Microwavefilters, IEEE Trans. on Circuit Theory, vol. CT-11, pp.10-12, March 1964.E. N. Torgow, Microwave filters, Elect~o- Technolo~y,, vol.67, pp. 90-96, April 1961.R. E. Wells, Microwave bandpass filter design, Mzcrozvuve1., vol. 5, pp. 9298, November 1962; pp. 8288, December1962.R. M. Kurzrok, Couplings in direct-coupled waveguide hand-pass filter s, IEEE Trans. on Microwave Thewy and Tech-niques (Correspondence), vol. MTT- 10, pp. 389390, Sep-tember 1962.P. 1. Richards, Resistor-transmission-line circuits, .Proc.IRE, vol. 36, pp. 217220, February 1948.

Filters with Cascaded Lines or Cavities

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[19a] H. J, Rlblet, General synthesis of quarter-wave impedancetransformers, IRE Trans. on Microwave Theory and Tech-niques, vol. MTT-5, pp. 3643, January 1957.

[20] L. Young, Stepped impedance transformers and filter proto-types, IRE Trans. on Microwave Theory and Tech% @es,vol. MTT-10, pp. 339359, September 1962.

[21] H. J. Carlin,, Cascaded transmission line synthesis, Poly-tech nic Institute of Brooklyn, Brooklyn, N. Y., Rept.PIBMRI 889-61. Am-ii 1961.

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R. Levy, Tables o] element values for the distributed low-pass prototype filter, this issue, page 514.L. Young, Direct-coupled cavity filters for wide and narrowbandwidths, IRE Trans. on Micyowave Theory and Tech-niques, vol. MTT-11, pp. 162178, May 1963.K. Whiting, The effect of increased design bandwidth upondirect-coupled-resonator filters, IEEE T?ans. on MicwwaveTheory and Techniques, vol. MTT- 11, pp. 5.57-560, November1963.B. C. DeLoach, Direct- and quarter-wave-coupled micro-wave band-pass filters with adjustable transmission charac-teristics and fixed center frequencies. IEEE Trans. nw. ,.Microwave Tkervy and Te.hniq~es, vol. MTT-12, pp. 73-77,January 1964.

TEM-Mode Filte~s with Parallel-Line Coupling[26] S. B. Cohn, Parallel-coupled transmission-ii me-resonator iil-

ters, IRE Trans. on Microwane Theory and Techniques, vol.MTT-6~ pp. 223-231, April 1958.

[27] H. Sm,th, (Computer-generated tables for filter design, Electronic Design, vol. 11., pp. 54-57, lblav 10, 1963.

[28] G. 1.. Matthaei, (Interdlgltal band-pass filters, IRE Trans.on Mzcrowave Theory and Techniques, vol. M TT- 1(O, PP.479-491, November 1962.

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506 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES SEPTEMBER

Band-Stop Filters

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B. M. Schiffman and G. L. Matthaei, Exact design of band.stop microwave filter s, IEEE Trans. on Microwave Theoryand Techniques, vol. MTT-12, pp. 615, January 1964.B, M. Schiffman, A harmomc rejection filter designed by anexact method, IEEE Trans. on Mic~owave Theory andTechniques, vol. MTT-12, pp. 5860, January 1964.B. M. Schiffman, A multiharmonic rejection filter designedby an exact method, IEEE Trans. on Microwave Theory andTechniques, vol. MTT-12, pp. .512516, September 1964.B. M. Schiffman, Capacitively-coupled stub filter, IEEETrans. on Microwave Theory and Techniques (Co~respondence),vol. MTT-13, pp. 253254, March 1964.E. G. Cristal, Addendum to an exact method for synthesis ofmicrowave band-stop filters, IEEE Trans. on M.icyowaveTheory and Techniques, vol. MTT-12, pp. 369-382, May 1964.L. Young, G. L. Matthaei, and E. M. T. Jones, Microwaveband-stop filters with narrow stop bands, IRE Trans. onMicrowave Theory and Techniques, vol. MTT-10, pp. 416-427,November 1962.P. D. Lube]], A simple relation between cavity Q and maxi-mum rejection for narrow-band microwave band-stop fil-ters, IEEE Trans. on Micvowave Theory and Techniques(Correspondence), vol. MTT-12, p. 145, January 1964.R. D. Standley and A. C. Todd, A note on strip-line band-stop filters with narrow stop bands,> IEEE Trans. on M~cro.waue Theory and Techniques (CowesPondence), vol. MTT-1 1,pp. 548549, iVovember 1963.W. T. Flannery, A. Fox, L. N. Engel, and F. J. Morris,Microwave rejection networks, IEEE Trans. on Electyo-nzagnetic Coszpatibilityl vol. EM C-7, pp. 2530, March 1965.B. C. DeLoach. Radial-line coaxial filters in the microwaveregion, IEEE rTrans. on Mic~owave Theory and Techniques,vol. MTT-11, pp. 5055, January 1963.

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Filters with Stubs (General)[46] N. Ozaki and J. Ishii, Synthesis of a class of strip-line

filters, IRE Trans. on Circuit Theory, vol. CT-.5, pp. 104109,June 1958.

[47] R. Levy, A general equivalent circuit transformation fordistributed networks, IEEE Trans. on Circuit Theory (Cor-respondence), vol. CT-12, pp. 457458, September 1965.

[48] R., J. Wenzel, (Exa~t design of TEM microwave networksusing quarter-wave hnes, IEEE Tran~. on Microwave Theoryand Techniques, vol. MTT-12, pp. 941 11, January 1964.

[49] M. C. Horton and R. J. Wenzel, General theory and designOf Optilmum quarter-wave TEM filters,> IEEE TYans. onllic~owave Theom and Tecknigues, vol. MTT-13, ~~. 3 16327, May 1965. -

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H. J. Carjin and W. Kohler, Direct synthesis of band-passtransmission line structures, IEEE Trans. on MicrowaveTheory and Techniques, vol. MTT-13, pp. 283-297, May 1965.H. J. Riblet, The application of a new class of equal-ripplefunctions to some familiar transmission-line problems, IEEE T~ans. on Microwave Theo~y and Techniques, vol.MTT-12, pp. 415421, July 1964.W. W. Mumford, An exact design technique for a type ofmaximally flat quarter-wave-coupled band-pass filter, 1963PTGMTT Symposiz~m Digert, pp. 57-61.

Low-Pass and High-Pass Filters

[54] E. Sharp, A high-power wide-band waffle-iron filter, IEEETrans. on Microwave Theo~y and Techniques, VOI. MTT-I 1.pp. 111116, March 1963.

-.

[55] L. Young and B. M. Schiffman, [New and improved types ofwaffle-iron filters,~ Proc. IEE (London), vol. 110, pp. 1191-1198, July 1963.

[561 L. Young, Postscript to two papers on waffle-iron filters, IEEE Trans. on Microwave Theory and Techniqt~es, vol.MTT-11, pp. 555557, November 1963.

[57] L. Young and B. M. Schiffman, A useful high-pass filterdesign, Microwave J., vol. 6, pp. 7880, February 1963.

[58] G. Oltman, Sharp cutoff microwave filters, IRE T~ans. onMicrowave T?zeory and Techniques, vol. MTT-11, pp. 3035,January 1963.

[59] C. C. H. Tang, Nonuniform waveguide high-pass filters withextremely steep cutoff, IEEE Trans. on Microwave Theoryand Teclwvigzces, vol. M TT- 1?, pp. 300309, May 1964.

[60] H. J. Riblet, A xeneral design procedure for auarter-wave-Iength inhomoge;eous impedance transformers having ap-proximately equa]-ripple performance, this issue, page 622.

Dissipation Loss, Group Delay, and Powe~-HandlingCapacity

[61] S. B. Cohn, Dissipation loss in multiple-coupled-resonatorfilters, Proc. IRE, vol. 47, pp. 13421348, August 1959.

[62] L. Young, Prediction of absorption loss in multilayer inter-ference filters, J. @t. SOC. Am., VO]. 52, pp. 753761, July1962.

[63] J. J. Taub, Design of minimum loss band-pass filters, Microwave J., vol. 6, pp. 6776, November 1963.

[64] J. J. Taub and H. J. Hindin, Minimum insertion 10SS micro-wave filters, MicYowave J., vol. 7: pp. 41-45, August 1964.

[651 J. J. Taub and R. L. Sleven! Design of band-stop filters in thepresence of dlssipation~ this issue, page 589.

[66] L. Young, Some considerations in the design of narrow-bandwavegukIe filters, IEEE Trans. on Microwave Theory andTechniques, vol. MTT-1 l? pp. 522527, November 1963.

[67] H. J. Riblet, (The couphng coefficients of an unsymmetricalhigh-Q 10SSY waveguide resonator, IEEE Tyans. on &fSCYo-wave Theory and Techniques, vol. MTT-11, pp. 7883,January 1963.

[68] L. Young, Group delay and dissipation loss in transmission-Iine filters, IEEE Trans. on Microwave Theory and Te~h-niques (Correspondence), vol. MTT- 11, pp. 2 152 17, MayIwiz-----

[69] H. H. Schreiber, Phase and time delay of Butterworth and~~6\byshev filters, Microwaves, vol. 4, pp. 1421, March

Delay Equalization

[70] C. H. Tang, Delay equalization by tapered cutoff wave-guides, IEEE Trans. on Microwave Theory and Teclmiques,vol. MTT-12, pp. 608615, November 1964.

[71] E. N. Torgow, Equalization of waveguide delay distortion, 1965 G-MTT Symposium Digest, pp. 3943.

[72] D. Merle, Development of group-delay equalizers for 4~9\$; PYOC. IEE (London), VO1. 112, pp. 289295, February

[73~ K. Woo, An adjustable microwave delay equalizer, IEEETram-. on Microwave Theory and Techniques, vol. MTT-13,pp. 22&232, March 1965.

[74] J. P. Bobis, Symmetrical-antimetrical filters with maximally~~4group delay, h!Ficrowaves, vol. 3, pp. 2027, February

[751 W. J. D. Steenart, The synthesis of coupled transmissionline all-pass networks in cascades of 1 to n, IEEE Trans. onMicrowave Theory and Techniques, vol. MTT-11, pp. 2329.January 1963.

Diplexers and Jlulkiplexers

[76] E. G. Cristal and G. L. Matthaei, A technique for the designof multiplexer having contiguous channels, ~ IEEE T7an~.on Microwave Theory and Techniques, vol. MTT-12, pp. 8393,January 1964.

[77] R. G, Veltrop and R. B. Wilds, Modified tables for the designof optimum diplexers, LIzcrowave J., Vo], 7 pp. 76_80June 1964.

[78] R. J. Wenzel, Application of exact synthesis methods ofmultichannel filter design, IEEE Trans. on MicrowaveTheory and Techniques, vol. MTT-13, pp. 5-15, January 1965.

[79] G. L. Matthaei and E. G. Cristal, Multiplexer channel-

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separating units using interdigital and parallel-coupled fil-ters, IEEE Trans. on Micyowave Theory and Techniques,vol. MTT-13, pp. 328334, May 1965.L. v. d. Kint and E. Schanda, A microwave quadruplexer, IEEE Tram-. on Microwave Theo~y and Techniques (Cor-respondence), vol. MTT-11, pp. 9092, January 1963.G. L. Matthaei and E. G. Cristal, Theory and design of di.plexers and multiplexer in A dnances % Mic~owaves. L.Young, Ed., New York: Academic Press, to be published.

Directional Filters

[82] G. Craven, D. W. Stopp, and R. R. Thomas, Resonant-slothybrid junctions and channel-dropping filters, PYOC. IEE(London), vol. 112, pp. 669-680, April 1965.

[82a] R. L. Williams, A thr:e-cavity circularly polarized wave-guide directional filter yielding a maximally flat response, IRE Tvans. on Microwave Theory and Techniques, vol. MTT-10,PP. 32328, September 1962.

[831 R. D. ~tandley, (Frequency response of strip-line travelingwave dmect]onal filters, 7~IEEE Trans. on Microwave Theoryand Techniques, vol. MTT- 11, pp. 264265, July 1963.

[84] R. D. Standley and A. C. Todd, Discontinuity effects insingle traveling wave filters, IEEE Trans. on MicyowaveTheory and Techniques (Correspondence), vol. MTT-11, pp.551-552, November 1963.

1965 YOUNG: 1965 FILTERS 507

Tunable Filters

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H. L. Schumacher, Direct coupled ganged tuned bandpassfilters! Microwave Y., vol. 7, pp. 48-52, J uly 1964.R. Wdds, G. Wheeler, and E. Cota, Compact tunable filters, Mic~ozvrrue ~., vol. 7, pp 6065, May 196$.M. H. N. Potok, Capacitive-iris-type mechanically tu nablewaveguide filters for the X-band, Proc. IEE (London), vol.109, pp. 505510, November 1962.G. L. Matthaei, Magnetically tunablle band-stop filters, IEEE Trans. on Microwave Theory and Techniques, vol.MTT-13, pp. 203-212, March 1965.G. H. Thiess, Theorv and design of tunable YIG filters, Microwaves, vol. 3, pp: 1431, Se~tember 1964.F. Reggia, Magnetically tunable microwave bandpass filter, Microwave J., vol. 6, pp. 72-84, January 1963.R. C. Cumming and D. W. Howell, YIG filters as envelopelimiters, this issue, page 616.R. L. Comstock, Synthesis of filter-limiters using ferro-magnetic resonators, IEEE T~ans. on Microwave Theo~y andTechniques, vol. MTT-12, pp. 599-607, November 1964.R. Blau, YIG filters in the 50500 Mc range, PYOC. IEEE,vol. 52, pp. 10741075, September 1964.P. S. Carter, Side-wall, coupled, strip-transmission-linemagnetically tunable filters employing terrimaguetic YI Gresonators, IEEE Trans. on Microwave Tkeory and Tech-niques, vol. MTT-13, pp. 306-315, May 1965.A. P. Benguerel and N. S. Nahman~ A varactor tuned UHFcoaxial filter, IEEE T~ans. on Jfwrowave Theory and Tech-~~6&es (Cowespotcdence), vol. MTT- 12, pp. 468469, July

I. Kaufman and W. H. Steier, A plasma-column band-passmicrowave filter, IEEE Trans. on Micyowave Theory andTechniques, vol. MTT-10, pp. 431439, November 1962.

Dielectric-Resonato~ and Dielectric-Loaded Filters

[95] A. Okaya and L. F. Barash, The dielectric microwaveresonator, Proc. IRE, vol. 50, pp. 20812092! October 1962.

[96] S. B. Cohn, Microwave filters containing high-Q dielectricresonators, 1965 G-MTT Symposium Digest, pp. 49-53.

[97] H. J. Shawl A. Karp, and D. K. Winslc,w, Circuit propertiesof dielectric resonators, Stanford University, Stanford,Calif., Microwave Lab. Rept. (in preparation).

[98] H. Y. Lee, Natural resonant frequencies of microwave di-electric resonators, IEEE Trans. on Microwave Theo~y andTechniques (Correspondence), vol. MTT- 13, p. 256, March 1965.

[99] R. V. DAiello and A. J. Prager, Dielectric resonators formicrowave applications, IEEE Trans. on Microwave Theoryand Techniques, vol. MTT-12, pp. 549550, September 1964.

[99a] D. L. Rebsch, D. C. Webb, R. A. Moore, and J. D. Cowli-shavi, A mode chart for accurate design of cylindrical dielec.tric resonators, IEEE Tvans. on Micyowave Theo~y andTechniques, vol. MTT-13, pp. 468-469, July 1965.

[100] E. O. Ammann and R. J. Morris, Tunable! dielectric-loadedmicrowave cavities capable of high Q amd high filling factor, IEEE Trans. on Microwave Theory and Techniques, vol.MTT-11, pp. 528-542, November 1963.

Filter Techniques Applied to Semiconductor Devices

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C. L. Cuccia, Broad-band multiplier chains with interdigitalfilters, Microwaves: vol. 3, pp. 22-25, June 1964.R. J. Wenzel, Wldeband varactor harmonic multipliers, 1965 G-MTT Symposium Digest, pp. 61-65,F. S. Coale and P. M. LaTourrette, Filter-diode integration, 1965 G-MTT Symposium Digest, pp. 67-71.B. L. Humphreys, Characteristics of broadband parametricamplifiers using filter networks, -Prc,c. IEE (London), vol.111, pp. 264274, February 1964.W. J. Getsinger and G. L. Matthaei, Some aspects of thedesign of wide-band up-converters and nondegenerate par-ametric amplifiers, IEEE Trans. on Microwave Theory andTechniques,. vol. MTT-12, pp. 7787, January 1964.W. J. Getsmger Prototypes for use in broadbanding reflec-tion amplifiers, IEEE Trans. on Microwave Theory andTechniques, vol. MTT- 11, pp. 486-49:7, November 1963.J H. Lepoff and G. J. Wheeler, Octave bandwidth tunnel-diode amplifier, IEEE Trans. on Microwave Theory andTechniques, vol. MTT-12, pp. 21-26, January 1964.J. F. White, High power, p-i-n diode controlled, microwavetransmission phase shifters, IEEE Trans. on MicrowaveTheory and Techniques, vol. MTT-1.3, pp. 233242, March1965.H. J. Peppiatt, A. V. McDaniel, Jr., and J. B. Linker, Jr.,A 7-Gc/s narrow-band waveguide switch using p-i-n junctiondiodes, IEEE Trans. on Microwave Theory and Techniques,vol. MTT-13,+pp. 4447, January 1965.A. Uhlir, Microwave application of integrated-circuit tech-niques, Proc. IEEE, vol. 52, pp. 1617-1623, December 1964.

Stepped-Impedance Filters as Di~ectional Coupleys

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[11 1]

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R. Levy, General synthesis of asymmetric rnulti-elerneutcoupled-transmission-line directional couplers, lEEE T~ans.on ilficrowave Theory and Techniques, vol. MTT- 11, pp.226-237, lUIV 1963.R. Levi,- Tables for asymmetric multi-element coupled-transmission-line directional couplers, IEEE Trans. onMicrowave Theory and Techniques, vol. MTT- 12, pp. 275-279, May 1964.R. 1. Mohr and 1. E. h!fcFarland. Exact a nalvsis of asvm-me~ric couplers,Microwaves, VO1.2, pp. 9093, March 1563.L. Sweet, A method of improving the response of waveguidedirectional couplers, IEEE Tvans. on Microwave Theo~y andTechniques (Cowespondence), vol. MTT-11, p. 554, November196.3.R. Levy, Transmission-line directional couplers for verybroadband operation, Proc. IEE (London), vol. 112, pp.469-476, April 1965.L. Young, The analytical equivalence of TEhI.mode di-rectional couplers and transmission-line stepped-impeclauce~~;~, Proc, IEE (London), vol. 110, pp. 275-281, February., -.

H. Seidel and J. Rosen, Multiplicity in cascade transmimion-line synthesis-Parts I and II , IEEE Trans. on MicrowaveTheorv and Techniques. vol. lWTT-13, pp. 257-283, May 1965;

f optimum symmetricalpp. 3~8407, July 196S. -- -E. G. Cristal and L. Young, Tables ofTEM-mode coupled-transmission-line d-irectionaj couplers, this issue, page 544.

.

P. P. Toulios and A. C. Todd. Svnthesis of svmmetric TEM-mode directional couplers,! IEEE T~ans; on Micr~,waveTheory and Techniques, this msue, page 586.S. B. Cohn, The re-entrant cross section and wide-band3-db hybrid couplers, IEEE T~ans. on Micrownve Theory andTechniques, vol. MTT-11, pp. 254258, July 1963.J. P. Shelton, J. Wolfe, and R. C. Van Wagoner, Tandemcouplers and phase shifters for multi-octave bandwidth,Microwaves, vol. 4, pp. 1419, April 1965. (Further detadswill be found in the P~oceedings of the Foun!eenth A mcaalSymOosium, USAF Antenna Research and DeveloDmenl~ Pro-g;arn, spolisored by the Air Force Avionics ~.abora tory,Wright-Patterson AFB, Ohio; ilIonticello, Ill., october,1964.)

Couplers from Filters and Filtevs from Coupleys

[1 21] L, Young, Synchronous branch guide directional couplersfor low and high power applications, IRE Trans. on Micro-wave Theory and Techniques, vol. MTT-10, pp. 45%475,November 1962.

[122] H. Smith, Tables for the design of aperture type waveguidecouplers, Microwuve J., vol. 6, pp. 919+, June 1963.

[123] L. R. Whicker and A. K. Kamal, Designing coupled-wave~~on#lective filters, Microwaves, vol. 4, pp. 3440, Jalnuary-----

[124] J. S. Cook, A. G. Fox and W. H. Louisell, Broadband direc-tional couplers employing non-constant propagation in cou-pling coefficients, Bell Monograph 2460f 1955. Also BellSys. Tech. J., vol. 34, pp. 807-870, July 1955.

[125] R. Levy, Directional couplers, m Advances in Microwaves.L. Young, Ed. New York: Academic Press, tc, be published.

Filte~s with Open Walls

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E. G. Cristal, A l.; inch coaxial leaky-wave filter for thesuppression of spurious energy, Microwave J., vol. (5, pp.72-76, September 1963.E. G. Cristal, Analytical solution to a waveguide leaky-wavestructure, IEEE Trans. on Microwave Theory and Tech-niques, vol. MTT-11, pp. 182190, May 1963.E. Wantuch and R. Maines, A novel high-power harmonicsuppressor, IEEE Tvans. on Microwave Theory and Tech-niques, vol. MTT-10, pp. 428431, November 1962.G. L. Matthaei and D. B. Weller, Circular TEoll-mode,trapped-mode bandpass filters, this issue, page 581.B. M. Schiffman, L. Young, and G. Matthaei, A rectangularwaveguide filter using trapped-mode resonator s, this issue,page 575.E. G. Cristal, A method for the design of non-reflecting high-power microwave band-pass filters, Microwave J., vol. 8,to be published.C. K. Birdsall and R. M. Whit:, Experiments with tlhe for-bidden regions of open period]c structures: Application toabsorptive filters, IEEE Trans. on Microwccve Thecwy andTechnique:, vol. MTT-12, pp. 197202, March 1964.B. M. Schdlman, L. Young, and G. L. Mat,thaei, A new. typeof low-pass filter that attenuates by dksipati on, this Issue,page 699.

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES

Filters for Millimeter Waves and Higher Frequencies[134] E. A. illarcatili, A circular-electric hybrid junction and some

channel-dropping filters, Bell Sys. Tech. J., vol. 40, pp. 185-196, January 1961.

[1351 E. A. Marcatili and D. A. Bisbee. Band-snlittin~ filter. Bell. .

Sys. Tech. J., vol. 40, pp. 197-213, Janua~y 196~. [136] E. A. Marcatili, hlode-conversion filters, Bell Sys. Tech. J.,

vol. 40~ pp. 149184, January 1961.[137] The Mdlimeter and Submillimeter Conference Papers, IEEE

Trans. on Mwrozvave Theorv and Techwiaues. vol. MTT-11.September 1963.

>,

[138] R. W. Zimmerer, M. V. Anderson, G. L. Strine, and Y. Beers,{Millimeter wavelength resonant structures, IEEE Tvan.s. onMicrowave Theory and Techniques, vol. MTT-11, pp. 142149,March 1963.

[139] P. D. Clark, A self-consistent field analysis of spherical mirrorFabry-Perot resonators, Proc. IEEE, vol. 53, pp. 36-41,January 1965.

[140] J. J. Taub, H. J. Hindin, and G. P. Kurpis, Quasi-opticalwaveguide filters, IEEE T~ans. on Microwave Theory andTechniques (Co~respondence),November 1964.

VO1. MTT-12, pp. 618619,

(1411 L. Yourw and P. W. Baumeister. Microwave and oDtical in-. .

terferenc-e filters: Some similarities and differences, NEREMRecord, vol. 5, pp. 8-9, November 1963.

[142] L. Young and E. G. Cristal, Stacked dielectric low-pass andhigh-pass filters, Stanford Research Institute, Menlo Park,Calif.. Sec. IX. Final Re~t., SRI Proiect 4657. ContractAF 30(602)-3174, Septemb& 1964.

[143] W. L. Wolfe and S. S. Ballard, Optical materials, films, andfilters for infrared instrumentation, PYOC. IRE, vol. 47, pp.15401546, September 1959.

VOL. MTT-13, NO. 5 SEPTEMBER, 1965

Ifiscellaneous

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[149]

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[153]

E. N. Torgow and P. D. Lubell, [Band-pass filters with steepskirt selectivity, IEEE T~avcs. on Microwave Theory undTechniques (Cowespondence), vol. MTT- 13, pp. 124126, Jan-uary 1965.J. F. Lally and R. R. Ciehoski, A wide stop band UHFcoaxial band-pass filter, IEEE T~ans. on Microwave Theoryand Techniques (Correspondence), vol. M TT- 11, p. 452,September 1963.R. H. Duhamel and M. E. Armstrong, Characteristics of log-periodic transmission line circuits, 1964 G-MTT SymposiumDigest, pp. 9-20.J. W. Duncan, [Characteristic impedances of multiconductorstrip transmission lines, IEEE Tram-. on Mtcrowaue Theoryand Techniques, vol. MTT-13, pp. 1071 18, January 1965.R. M. Bevensee, Nonuniform TEIM transmission line. Part1: Lossless and log-periodic properties, Proc. IEE (London),vol. 112, pp. 644654, April 1965.M. McDermott and R. Levy, Very broadband coaxial dcreturns derived by microwave filter synthesis, Mic~ozvave J.,vol. 8, pp. 3336, February 1965.L. Young, Practical design of a wide-band quarter-wavetransformer in waveguide, Mic~owave J,, vol. 6, pp. 76-79,October 1963L. Young, Waveguide O-db and 3-db directional couplers asharmonic pads, llic~owave J., vol. 7, pp. 7987, March 1964.B. M. Schiffma+ A new class of broad-band microwave 90-degree phase shifters, IRE T~ans. on Microwave Theory andTechniques, vol. MTT-6, pp. 232-237, Auril 1958.E. L. G~nzton, Microwave ~?easurement.r. ~ew York: McGraw-Hill, 1957, pp. 417-424.

Band~Stop Filters for High~Power Applications

E. N. TORGOW, SENIOR MEMBER, IEEE, AND G. E. COLLINS

AbstractThere are several advantages to the use of band-stopfilters, rather than band-pass filters, in many systems. This is shownto be particularly true when signals at high-power levels must betransmitted or rejected,

A formula has been derived which expresses the external Q ofeach resonator in a band-stop filter in terms of the element valuesof the normalized low-pass prototype and the parameters of the fre-quency transformation. The peak power capacity of iris-coupledwaveguide cavity filters and TEM falters using capacitively coupledinductive stubs is then determined in terms of the external Q of thefirst resonator and the dimensions of the resonator. Experimentalresults given for a waveguide band-stop filter show good agreementwith theory.

1. INTRODUCTION

I

N THE recent literature a number of articles haveappeared expounding the virtues of band-stopfilters in lieu of band-pass filters for many applica-

tions [1], [Z]. In cases where a high rejection loss isrequired over a relatively narrow frequency band, andwhere low insertion loss is needed at a frequency closeto this rejection band, the band-stop filter is the more

Manuscript received June 1, 1965.The authors are with the Rantec Corporation, Calabasas, Calif.

efficient device. The band-stop filter can also be moreeasily aligned to exhibit its prescribed response. Eachresonator can be independently adjusted so that thecoupling from the main transmission line to that reso-nator yields the specified external Q. This is accom-plished by detuning all other resonators. When all of thecouplings are properly set, the band-stop filter is thenaligned by adjusting the individual cavity resonators inturn until peak rejection is obtained. In practice, verylittle additional trimming is required beyond this point.In Section II of this paper, a simple expression is de-rived which enables the design engineer to determinethe external Q of each resonator directly in terms of therequired performance and the element values of a nor-malized low-pass prototype filter [3].

The band-stop filter offers advantages when con-sidered as part of a diplexer or multiplexer. A combina-tion of band-pass and band-stop filters can be designedto approximate a true complementary pair, presentinga matched input over a very wide band of frequencies[4]. Band-stop filters can also be used in cascade con-nection with other filters to provide more complex re-jection characteristics [5]. This is a particular advan -

508