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A waveguide is a microwave trans-mission line that uses only a singleconductor. It has low attenuation andexcellent power-handling capability.It is usable to frequencies in excess of100 GHz and can provide precisionthat is not ordinarily available incoaxial lines or strip transmission

lines. A waveguide also has inherenthighpass filter characteristics suchas cutoff frequency and dispersivetransmission characteristics.

This article is primarily concernedwith waveguides that are in theshape of non-square rectangulartubes. These tubes are wider than

Richard M. Kurzrok Professional Engineer RMK Consultants, 82-34 210th St.,Queens Village, NY 11427-1310;(718)-776-6343, FAX: (718) 776-6087, e-mail:rmkconsulting@aol.com.

Design WaveguideBandpass Filters Despite more recent technologies, waveguide

bandpass filters that operate above 8 GHzare still used for precision designs and highpower levels.

DESIGN FEATURE

Bandpass Filters

WAVEGUIDE bandpass filters are frequency-selective circuits ordevices that perform valuable functions in microwave equipmentused in communications, electronic warfare (EW), radar, andautomatic test equipment (ATE). They are most compatible with

waveguide antenna feeds. They are required for high-power applications,and are preferred for precision performance. At low signal levels, they areprimarily used at frequencies from 8 to more than 100 GHz. The main func-tion of a waveguide filter is to provide adequate stopband selectivity with-out introducing unacceptable passband insertion losses and distortions.For example, in microwave receivers, waveguide bandpass filters rejectunwanted out-of-band interference and establish sensitivity by defining thefront-end noise bandwidth. In microwave transmitters, they reduceunwanted frequencies (spurii) and suppress transmitter noise at receivefrequencies. Waveguide bandpass filters are also used in variousmicrowave multiplexers. This article presents a discussion of key featuresin waveguide bandpass filter design, development, and construction.

1. Analysis of filter specifications (electrical, mechanical, environmental, and cost)2. Determination of a compliant filter-response shape3. Selection of an appropriate filter structure4. Computation of filter-coupling parameters and resonator lengths5. Computation and/or development of filter couplings6. Determination of applicable filter fabrication methods7. Preparation of filter-shop drawings through manual or AutoCAD8. Fabrication of prototype filter in model shop or by external vendor9. Assembly, alignment, and test of prototype filter

10. Record data and modify/recycle (if necessary)

Table 1: Waveguide bandpass-filter typicaldesign and development cycle

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they are high, which means that theyhave an aspect ratio of greater than1:1. These waveguides propagate inthe dominant TE10 mode, and theiruseful frequency range is limited toapproximately 40 percent of centerfrequency. For waveguides with a 2:1aspect ratio (two units wide for everyone unit high), the dominant-modepropagation is unique up to two timesthe dominant-mode cutoff frequency.

FILTER-DESIGN TECHNIQUESWaveguide bandpass filters origi-

nated in Bell Telephone Laboratoriesand the MIT Radiation Laboratory ofWorld War II. Early waveguidebandpass filters used quarter-wavecoupled resonators.1 In 1957, a mile-stone paper2 introduced direct-cou-pled waveguide bandpass filters thatquickly evolved into a preferred con-figuration. Much of the prior art andnew original work on waveguidebandpass filters can be found in a1964 classic reference3 among thoselisted at the end of this article.

The design equations for direct-coupled waveguide bandpass filters2

start with the normalized circuit g’sof a lowpass prototype. For Tcheby-chev (equal-passband-ripple) re-sponses normalized to the ripplebandwidth, normalized susceptancesfor the shunt-inductive couplings andfilter-corrected resonant lengths canbe readily computed. Normalizationto the 3-dB bandwidth or differentfilter response shapes can also beused.4,5 Some of the design equationscan be rewritten in terms of alternateparameters such as normalizedsingly loaded q’s and coefficients ofcoupling.6

The total Q of a bandpass filter isdefined by equation 1:

QT=F/BW (1)

where:QT = the total Q,F = the center frequency, andBW= the normalizing bandwidth.For nominal half-wavelength

waveguide resonators, the effectivetotal Q, taking into account disper-sion, is:

Q=2QT[p (lG0/l0)2] (2)

where:lG 0 = the guide wavelength at fil-

ter’s center frequency,l 0 = Free-space wavelength at fil-

ter’s center frequency, andp = the transcendental number pi

(approximately 3.14).Normalized values of singly loaded

q’s (for input and output couplings)and coefficients of coupling (for inter-stage couplings) are attainable frompublished equations and handbooktables.5

Letting: q1 = the normalized input singly

loaded q,qn = the normalized output singly

loaded q, andkij = the normalized coefficient of

coupling between the ith and jth resonators.

Bandpass Filters

DESIGN FEATURE

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then:

Q1=Qq1=absolute inputsingly loaded Q (3)

Qn=Qqn=absolute outputsingly loaded Q (4)

Kij=kij/Q=absolute coefficientof coupling between ith and

jth resonators (5)

now:

X0=SQR[(1/Q1)/(1-1/Q1)]=1/B0 (6)

Xn=SQR[(1/Qn)/(1-1/Qn)]=1/Bn (7)

Xij=Kij/(1-Kij2)=1/Bij (8)

where:X0 = the normalized input coupling

reactance, Xn = the normalized output cou-

pling reactance, andXij = the normalized interstage

coupling reactance for resonators iand j.

These normalized inductive cou-pling reactances can be used in thedesign equations of reference 2 todetermine the lengths of the waveg-uide bandpass filter resonators.now:

B0 = the normalized input couplingsusceptance,

Bn = the normalized output cou-pling susceptance, and

Bij = the normalized interstagecoupling susceptance for resonators iand j.

Beyond calculating a ballpark 10-percent bandwidth in guide wave-length, the approximate design equa-tions must be reformulated to takeinto account the frequency sensitivi-ty of distributed (transmission-line)circuits. A viable method for devel-oping broader-bandwidth filtersentails use of prototypes for multi-quarter-wave transformers7 andother techniques.8

Using electromagnetic (EM)-fieldtheory, designers can improve filteraccuracy and eliminate the additionalcomplexity and cost of using filter-tuning screws. But despite this newdesign technique, approximatedesign and development methods2

have proven adequate for mostwaveguide bandpass-filter design.Use of tuning screws, with or withoutcoupling screws, has continued to beacceptable.

Table 1 shows a typical design anddevelopment cycle. Computer-aidedanalysis and design and fabricationliaison are important in achievingtechnical success within schedule andbudget. Table 2 shows samples ofpreliminary design computations.

TUNABILITY Direct-coupled waveguide band-

pass filters are usually tuned withcapacitive screws centrally locatedon the waveguide broad wall(s) andat the high-impedance planes of the

waveguide resonators. These screwscompensate for design inaccuraciesand fabrication tolerances. Manyrectangular-waveguide filters can betuned over a 10-percent frequencyrange. Filter couplings are frequencysensitive, and designers can expectto encounter variations in bandwidthand response shape over the tuningrange.

Increased tuning-screw penetra-tion depth degrades resonatorunloaded Q’s and causes increased fil-ter passband insertion losses. Tun-ing-screw penetration also degradesa filter’s peak power-handling capac-ity. A design decision not to use tun-ing screws must consider filter trans-mission and reflection specifications,

Bandpass Filters

DESIGN FEATURE

Waveguide size

WR-229WR-137WR-112WR-90WR-75WR-62WR-51WR-42WR-28

English tuning screws

12-2810-328-326-324-402-562-561-720-80

Metric tuning screws

6.0 3 15.0 3 0.84.0 3 0.73.5 3 0.63.0 3 0.52.0 3 0.42.0 3 0.41.6 3 3.51.6 3 1.5

Table 3: Typical tuning screw sizes forvarious waveguide bands

Design parameter

Waveguide sizeCenter frequency3-dB bandwidthQT

Number of polesPassband rippleNormalizationFilter symmetryNormalized q1

Normalized k12

Normalized k23

(lG0/l0)2

QInput normalized susceptance B0

Interstage normalized susceptance B12

Interstage normalized susceptance B23

First resonator lengthSecond resonator length

Value

WR-7513.25 GHz40 MHz331.2540.001 dB3-dB bandwidthSymmetrical0.91140.77650.54121.546136.4111.06175.7252.00.537 in. (1.36 cm)0.552 in. (1.40 cm)

Table 2: Sample preliminary design computations

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DESIGN FEATURE

Bandpass Filters

fabrication tolerances, filter inputand output interfaces, as well as pro-duction volume. As with other typesof filters, tunability becomes less of anecessity as the percent bandwidth isincreased. Table 3 shows typical tun-ing-screw sizes for some popularrectangular-waveguide sizes. Brassscrews are preferable to stainless-steel screws.

Environmental changes can havediscernible effects on the tuning ofwaveguide bandpass filters.9 Ther-mal expansion in a waveguide’s metalwalls and the presence of humiditycan detune a waveguide bandpass fil-ter. This can become an acute prob-lem when the filter bandwidth is verynarrow. Altitude and corrosion alsocan affect performance.

COUPLINGThe design must also account for

normalized susceptances of the fil-ter’s couplings. There are several dif-ferent types of inductive-couplingstructures that can be used in waveg-uide bandpass filters.10 The desirednormalized susceptances can beobtained from handbook data11 or byusing developmental procedures.11,13 Alternatively, singly loaded Q’sand coefficients of coupling can beobtained developmentally.12,13

When the waveguide bandpass fil-ter must compensate for mismatchesat source and load interfaces,adjustable input and output cou-plings are desirable. When filterbandwidth must be adjustable over aspecified tuning range, adjustableinterstage couplings are also desir-able. Adjustable couplings also per-mit precision design and alignment to

meet stringent performance specifi-cations. Table 4 shows typical cou-pling-post diameters. Coupling iris-es, apertures, and vanes usethin-precision shim stock. A 0.031-in.(0.07874-cm)-thick stock is used inWR-112 and WR-90, while 0.020-in.(0.0508-cm)-thick stock is used inWR-75, WR-51, WR-42, and WR-28.Some waveguide bandpass filters useboth posts and irises.

Waveguide bandpass filtersdesigned in WR-430 waveguide weretunable over the 1.7-to-2.3-GHz fre-quency range, using three differentmodels, all with adjustable filter cou-plings. These filters were five-pole,0.001-dB ripple units designed for anominal 60-MHz, 3-dB bandwidth.Over the central 20 MHz of the pass-band, the filters had return losses inexcess of 30 dB. This was necessaryto meet echo-distortion specificationsin a high-capacity, multihop, terres-trial-communications system.Mechanical parts for these filters aresummarized in Table 5.

INSERTION LOSSWaveguide bandpass-filter inser-

tion losses are quite important inmicrowave front-end applications.Lossy filters can dissipate preciouspower in transmitters, and degradenoise figures in receivers. For awaveguide bandpass filter with aspecified center frequency, band-width, and responses shape, the pass-band insertion loss is primarilydetermined by the unloaded Q of thefilter resonators.14 Practical unload-ed Q data are available for real-worldwaveguide bandpass filters.15 Thefollowing five factors affect the res-

Waveguide size

WR-229WR-137WR-112WR-90WR-75WR-62WR-51WR-42WR-28

Post diameter-in.

0.3120.1870.1560.1250.0930.0620.0460.0310.031

Post diameter-mm

8.05.04.03.02.01.51.00.750.75

Table 4: Typical coupling post diametersfor various waveguide bands

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DESIGN FEATURE

Bandpass Filters

onator unloaded Q’s:16

1 . S i z e and c r oss - sect i ona l geometry

2. Mode of wave propagation3. Interior materials of construc-

tion4. Interior surface finish5. Interior surface contaminationSpurious couplings into unwanted

modes can result in dissipation thatfurther degrades resonator unloadedq’s. Some filter-response shapes canbe helpful to reduce dissipative loss-es.17 Elliptic-function filters oftenexhibit lower dissipation losses at theexpense of complexity and unit cost.

FABRICATION TECHNIQUESWaveguide bandpass filters usual-

ly use extruded copper (Cu) or Cualloy tubing with typical surface fin-ishes of approximately 16 min. Tub-ing radii have a very small effect onactual waveguide cutoff frequency.Good metallic conductivity should bemaintained to at least three skindepths. Waveguide flanges are oftensilver (Ag) soldered to the waveg-uide housing. Other parts such astuning bushings, coupling screws,coupling irises, and posts can be softsoldered to the housing. Cu conduc-tors must be protected against corro-sion. Gold (Au) plating and varnishwork best.18 The best surface finish,8 min. or less, is attainable throughthe electroforming process usingstainless-steel mandrels. Cu andnickel (Ni) can be electroformed.

Invar waveguide is needed forvery-narrow bandwidth filters whenenvironmental detuning cannot betolerated. Pressurization is used tocombat the effects of humidity. Fortunable filters, sealing and evacua-tion of the filter would require filtertuning through bellows. This isavoided with a dynamic dehydratorsystem maintaining an ongoing pres-

sure of approximately 2 psi. For pres-surized filters, pressure fittings andwaveguide windows are required.

A waveguide has two differentpower-handling capabilities—aver-age power and peak power. Averagepower handling is defined as anacceptable temperature rise due toincidental dissipation, while peakpower handling is defined as a powerlevel where voltage breakdownoccurs. Average power handling isenhanced by heat-flow techniques,such as air and liquid cooling, radiat-ing fins, and heat pipes. Peak powerhandling is enhanced by evacuation,sealing, and use of gases such as sul-phur hexafluoride. High-powerwaveguide bandpass filters aredesigned with rounded corners andno sharp discontinuities. Tuning andcoupling mechanisms must bedesigned for high-power operation.

Waveguide bandpass filters can bedesigned for coaxial interfaces usingadjustable input and output probecouplings.19 Power handling is oftenlimited by the choice of coaxial connectors.

ALTERNATE STRUCTURESWaveguide cross-sections other

than non-square rectangular shouldalso be considered. Oversize waveg-uides can have higher unloaded Q’sthan standard rectangular waveg-uides. Cylindrical3 and square20

waveguides can support dual-modeoperation, which is useful for cross-polarized antenna feeds. The TE01circular electric mode in cylindricalwaveguides3 has the highest unload-ed Q but is not the dominant mode.Ridged waveguides21 have degradedunloaded-Q and power-handlingcapabilities but are capable of single-mode operation well beyond anoctave in frequency. Filter miniatur-ization can be achieved using evanes-

Waveguide bandpass filter’s part

Resonator tuning screwsCoupling screwsInput/output coupling double postsInterstage coupling double posts

Physical realization

5/8-243/8-240.375 diameter0.625 diameter

Table 5: 2-GHz waveguide (WR-430)bandpass-filter mechanical parts

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DESIGN FEATURE

Bandpass Filters

cent-mode resonators22 or dielectricresonators.23 In waveguides, higher-order modes can propagate abovereadily determinable cutoff frequen-cies. For design purposes, modecharts3,9 are useful to determinewaveguide cross-section. EM-fieldconfigurations9,11 are effective indetermining methods of excitationand coupling.

Conventional waveguide bandpassfilters have frequency-sensitive cou-plings, resulting in substantial varia-tions in filter bandwidth over a tun-ing range. A different waveguidebandpass-filter structure has circum-vented this difficulty. The filter usesfixed resonator lengths, and each res-onator is tuned by varying thewaveguide width.24 Input, output,and interstage couplings use trans-verse coupling apertures located forminimum frequency sensitivity of fil-ter bandwidth over a tuning range.

In conventional waveguide band-pass filters, non-adjacent resonatorsare not coupled. These filters are con-sidered minimum phase-shift net-works. Adding one or more bridgecouplings between non-adjacent res-onators converts a general filter25-29

to a non-minimum phase-shift net-work. This class of waveguide band-pass filters can realize elliptic-func-tion responses or provide enhanceddifferential group delay within thefilter passband. Some of these filtersemploy dual-mode resonators,26,27

which result in appreciable savings infilter size, weight, and cost.

Corrugated waveguide bandpassfilters and waffle-iron filters use low-pass structures in waveguides to pro-vide high-frequency selectivity.Low-frequency selectivity is provid-ed by waveguide cutoff. Both of thesefilters were created by Dr. S.B. Cohnand are described in reference 2.

Waveguide bandpass filters arealso used in microwave multiplexersthat include directional filters. 3 Thefilters use inductive-coupling iriseswith adjustable input- and output-coupling screws. Further discussionof microwave multiplexers is beyondthe scope of this article. Three surveyarticles on microwave filters are list-ed in references 30, 31, and 32.

Waveguides continue to thrive as

new applications open up in the mil-limeter range of frequencies. Re-searchers continue to investigatewaveguide theory and develop newand improved structures and materi-als to reduce bandpass-filter costsand ease alignment.

AcknowledgmentThis paper has been provided with only a limited bibliog-

raphy. Many other engineers and scientists have made sig-nificant contributions to the design and development ofwaveguide bandpass filters. Use of adjustable couplingscrews in waveguide bandpass filters was suggested byE.M. Bradburd.

References1. W.W. Mumford, “Maximally Flat Filters in Waveg-

uide,” Bell Sys. Tech. Journal, Vol. 27, pp. 684-713, October1948.

2. S.B. Cohn, “Direct-Coupled Resonator Band-Pass Fil-ters,” Proc. IRE, Vol. 45, pp. 187-195, February 1957.

3. Matthaei, Young, and Jones, Microwave Filters,Impedance Matching Networks, and Coupling Structures,McGraw-Hill, 1964.

4. M. Dishal, “Design of Dissipative Bandpass FiltersProducing Exact Amplitude-Frequency Characteristics,”Proc. IRE, September 1949.

5. A.I. Zverev, Handbook of Filter Synthesis, John Wiley& Sons, New York, 1967.

6. R.M. Kurzrok, “Interchangeability Of Coupling Param-eters In Waveguide Bandpass Filters,” Frequency Tech-nology, Vol. 8, pp. 12-13, July 1970.

7. L. Young, “The Quarter-Wave Transformer PrototypeCircuit,” IRE Trans MTT, Vol. MTT-8, pp. 483-489,September 1960.

8. T.R. Cuthbert Jr., “Wideband Direct-Coupled FilterHaving Exact Response Shapes,” IEEE MTT-S Newslet-ter, pp. 27-38, Spring 1996.

9. “Reference Data for Engineers, Radio, Electronics,Computer, And Communications,” SAMS, Eighth Edition,Prentice Hall Computer, Carmel, IN, Ch. 30, 1995.

10. R.M. Kurzrok, “Inductive Couplings—The BestChoice for Waveguide Filters,” EDN, pp. 46-49,143-144,November 8, 1967.

11. Microwave Engineers’ Handbook, Vol. 1, ArtechHouse, Dedham, MA, pp. 19-92, 1971.

12. M. Dishal, “Alignment and Adjustment of Syn-chronously Tuned Multiple-Resonator Circuit Filters,”Proc. IRE, Vol. 39, pp. 1448-1455, November 1951.

13. R.M. Kurzrok, “Nodal Voltages Offer Key to FilterDesign,” Microwaves & RF, Part 1, pp. 72, 75-76, 79-80,82,84, April 1999 and Part 2, pp. 67-69, May 1999.

14. S.B. Cohn, “Dissipation Loss in Multiple-CoupledResonator Filters,” Proc. IRE, Vol. 47, pp. 1342-1348,August 1959.

15. C.M. Kudsia and V. O’Donovan, Microwave Filters forCommunications Systems, Artech House, Dedham, MA,pp. 129-130, 1974.

16. R.M. Cox and W.E. Rupp, “Fight Waveguide Losses5 Ways,” Microwaves, Vol. 5, pp. 32-40, August 1966.

17. J.J. Taub, “Minimum Loss Band Pass Filters,”Microwave Journal, pp. 67-76, November 1963.

18. W.F. Smith, “How to Combat Waveguide Corrosion-Gold Plating and Varnish Work Best,” Microwaves, pp. 34-38, August 1965.

19. R.M. Kurzrok, “Waveguide Bandpass Filters withCoaxial Interfaces Reduce Equipment Costs,” AppliedMicrowave & Wireless, pp. 100 and 102, June 1999.

20. N.A. Spencer, “Crossed-Mode Tunable Selector forMicrowaves,” IRE Convention Record, Part 5, pp. 129-132,1956.

21. S.B. Cohn, “Properties of Ridge Waveguide,” Proc.IRE, Vol. 35, pp. 783-788, 1947.

22. G.F. Craven and C.K. Mok, “The Design of Evanes-cent Mode Waveguide Bandpass Filters for a PrescribedInsertion Loss Characteristic,” IEEE Trans MTT, Vol.MTT-19, pp. 295-308, March 1971.

23. D. Kajfez and P. Guillon, Dielectric Resonators, Vec-tor Field, Oxford, MS, 1990.

24. R.L. Sleven, “Design of a Tunable Multi-CavityWaveguide Bandpass Filter,” IRE Convention Record,Part 3, pp. 91-112, 1959.

25. R.M. Kurzrok, “General Three Resonator Filters inWaveguide,” IEEE Trans MTT, Vol. MTT-14, p. 46, Jan-uary 1966.

26. A.E. Williams, “A Four Cavity Elliptic WaveguideFilter,” IEEE Trans MTT, Vol. MTT-18, pp. 1109-1114,December 1970.

27. A.E. Atia and A.E. Williams, “Non-Minimum PhaseOptimum Amplitude Bandpass Waveguide Filters,” IEEETrans MTT, Vol. MTT-22, pp. 425-431, April 1974.

28. D.A. Taggert and R.D. Wanselow, “Mixed Mode Fil-ters,” IEEE Trans MTT, Vol. MTT-22, pp. 898-902, Octo-ber 1974.

29. R. Levy, “Filters with Single Transmission Zeros atReal or Imaginary Frequencies,” IEEE Trans MTT, Vol.MTT-24, pp. 172-182, April 1976.

30. E.N. Torgow, “Microwave Filters,” Electro-Technol-ogy, Vol. 67, pp. 90-96, April 1961.

31. J.D. Rhodes, “Microwave Filters,” IEEE Circuitsand Systems, Vol. 7, pp. 2-8, August 1975.

32. R. Levy and S.B. Cohn, “A Brief History ofMicrowave Filter Research, Design, and Development,”IEEE Trans MTT, Vol. MTT-32, pp. 1055-1067, September1984.