IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 11, NOVEMBER 2006 3923

Compact Partial H-Plane FiltersDong-Won Kim, Dong-Jin Kim, and Jeong-Hae Lee, Member, IEEE

Abstract—In this paper, three types of partial -plane filters,having advantages of compact, low cost, and mass-producibleproperties, are presented as compact waveguide filters, which areimplemented by partial -plane waveguide. Two types of partial

-plane filters have the same frequency responses as those ofconventional - and -plane filters, respectively, while their crosssections are one-quarter. To further reduce the length, the last typeof partial -plane filters is designed by using quarter-wavelengthresonators. The length of this filter is shorter by 29.2% than thatof the conventional -plane filter. In addition, it has a superiorspurious frequency response.

Index Terms—Partial -plane waveguide, partial -planefilter, spurious suppression.

I. INTRODUCTION

THE FAST development of RF/microwave technologygreatly stimulates the compact, low-cost, and mass-pro-

ducible properties for components. One of the most challengingcomponents is the filter, and its electrical performance is crucialfor overall system design. The -plane filter [1], [2], -planefilter [3], [4], and fin-line filter [5] are commonly used filtersmade by a rectangular waveguide since they have low lossand are easy to fabricate. Moreover, the -plane filter alsohas low-cost and mass-producible properties. However, despitetheir favorable characteristics, they have the disadvantages ofbulky volume at low frequency and spurious response below

(twice of the passband frequency). This paper, therefore,proposes three types of partial -plane filters (types 1–3)implemented by a partial -plane waveguide [6] as a new classof compact, low-cost, and mass-producible filter.

The partial -plane waveguide is a transversely folded rect-angular waveguide, which has the same dispersion character-istics for the first two dominant modes as those of the con-ventional rectangular waveguide, while its cross section is one-quarter [6]. By using the partial -plane waveguide, it is pos-sible to miniaturize the components made by rectangular wave-guide [7]. The partial -plane filters of types 1 [7] and 2 canbe compared with the conventional - and -plane filters, re-spectively, since they have the same mechanisms to implementthe evanescent waveguide and use inductive coupling. It will be

Manuscript received March 29, 2006; revised July 22, 2006. This work wassupported by the Ministry of Information and Communication, Korea, underthe Information Technology Research Center Support Program supervised bythe Institute of Information Technology Assessment (IITA-2005-C1090-0502-0029).

D.-W. Kim was with the Department of Radio Science and CommunicationEngineering, Hongik University, 121-791 Seoul, Korea. He is now with theMobile Communication Department, LG Electronics Institute of Technology,153-803 Seoul, Korea (e-mail: kdw3529@lge.com).

D.-J. Kim and J.-H. Lee are with the Department of Radio Science and Com-munication Engineering, Hongik University, 121-791 Seoul, Korea (e-mail:jeonglee@hongik.ac.kr).

Digital Object Identifier 10.1109/TMTT.2006.883652

Fig. 1. Schematic diagram of partial H-plane waveguide.

Fig. 2. E-field distributions of partialH-plane waveguide. (a) Dominant modeTE . (b) Second mode TE .

Fig. 3. Dispersion characteristics of partial H-plane waveguide (a: 23.8 mm,b: 12 mm, d: 20.2 mm, and metal vane thickness: 0.1 mm) and rectangular wave-guide (width: 47.55 mm and height: 22.15 mm) in the H-band.

shown that types 1 and 2 have the same frequency responsesand transversely reduced dimensions of one-quarter as those ofthe - and -plane filters, respectively. The partial -planefilter of type 3 is designed by modifying the type 1 filter anduses two different structures of evanescent waveguides. Its res-onators have a quarter-wavelength so that its length is shorterby 28.7% than that of the type 1 filter. Subsequently, the type3 filter has the reduced dimension toward not only transversedirection, but also longitudinal direction. In addition, the type3 filter has the sharp skirt characteristic and improved spuriousresponses compared with the other filters.

0018-9480/$20.00 © 2006 IEEE

3924 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 11, NOVEMBER 2006

Fig. 4. Structures of two types of partial H-plane filters. K : impedanceinverter values between ith resonator and i+ 1th resonator (i = 0; 1; . . . ; n).w : length of jth evanescent waveguide section (j = 1; 2; . . . ; n; n + 1).r : length of kth resonator (k = 1; 2; . . . ; n). s : the length of inserted jthH-plane metal insert in type 2. (a) Partial H-plane filter (type 1). (b) PartialH-plane filter (type 2).

Fig. 5. Impedance inverter (K-inverter) for evanescent waveguide.

To design three types of partial -plane filters, a numeri-cally efficient simulation-based filter design technique is devel-oped. This design technique is based on typical direct-coupledresonator filter design theory [8], [9] and it uses thoroughlyfrequency-dependant inverter theory. The proposed filters havebeen fabricated with coaxial to partial -plane waveguide tran-sition in the -band. Good agreement between measured andcomputed results will be presented.

Fig. 6. Unit cells of the partial H-plane filter type 1 (top) and 2 (bottom).

Fig. 7. Frequency responses of partial H-plane filter type 1 compared withE-plane filter. (a) Passband responses. (b) Spurious responses.

II. PARTIAL -PLANE WAVEGUIDE

The partial -plane waveguide has the shape of a partiallyinterleaved -plane metal vane within a rectangular waveguideand its cross section consists of three regions, as shown in Fig. 1.The thickness of the -plane metal vane is assumed to be verythin. The partial -plane waveguide has a mode andits dominant and second modes are shown in Fig. 2, which are

KIM et al.: COMPACT PARTIAL -PLANE FILTERS 3925

TABLE IDESIGNED FILTER SIZES OF TYPE 1 AND E-PLANE FILTER (UNIT: MILLIMETERS)

the and modes, respectively. The -compo-nent of the -field and the -component of the -field for the

mode, respectively, are derived as [6]

(region 1)

(region 2) (1)

(region 1)

(region 2)

(2)

is omitted. Free-space wavenumber is given by

(3)

Since and are continuous at , the characteristicequation for the mode is derived as

(4)

where is obtained from (3) and (4). The propagation con-stant and cutoff frequency are given by

(5)

(6)

where is the velocity of light. The dispersion characteristicscompared with the rectangular waveguide in the -band areshown in Fig. 3. Dispersion characteristics of the first twodominant modes are the same as those of the conventionalrectangular waveguide. Note that the cross section of thepartial -plane waveguide is one-quarter of the rectangularwaveguide. The detailed analytical expression and the modedefinition are described in [6].

III. PARTIAL -PLANE FILTERS—TYPES 1 AND 2

A. Structures

Structures of partial -plane filters of types 1 and 2 made by apartial -plane waveguide are illustrated in Fig. 4. They consistof resonators alternating with evanescent waveguide sections. Itis easily found out that they have the same structures as those

Fig. 8. Frequency responses of partial H-plane filter type 2 compared withH-plane filter. (a) Passband responses. (b) Spurious responses.

of the conventional - and -plane filters, respectively, if theyare unfolded along the -direction. Two partial -plane filtershave one-quarter cross sections as those of the conventional -and -plane filters, respectively.

An evanescent waveguide section of type 1 is implemented byinserting the -plane septa between the positions of and inthe plane of Fig. 1, while that of type 2 is implementedby inserting a rectangular metal insert in the -plane of Fig. 1.The principles for designing an evanescent waveguide of twopartial -plane filters are structurally the same as those of the

- and -plane filters, respectively.

B. Design Method

Two partial -plane filters are direct-coupled resonator fil-ters. They consist of half-wavelength resonators, which are ter-

3926 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 11, NOVEMBER 2006

TABLE IIDESIGNED FILTER SIZES OF TYPE 2 AND H-PLANE FILTER (UNIT: MILLIMETERS)

minated with shorted end. Thus, the evanescent waveguide canbe represented with an impedance inverter ( -inverter) circuit,as shown in Fig. 5. The reactance values of and are func-tions of sizes ( or in Fig. 4) for an evanescent waveguide.Normalized inverter value and negative electrical length aregiven by [9]

(7)

(8)

where is a wave impedance of a partial -plane waveguide.The normalized inverter values for an equal-ripple bandpassfilter are [8]

(9)

where are element values for an equal-ripplelow-pass prototype and is a normalized cutoff frequency.

, , and are guide wavelengths at center frequency andat lower and upper passband edge frequencies. is a relativebandwidth for a guide wavelength.

To determine sizes of filters, the partial filter design method,using a commercial electromagnetic (EM) simulator, is used inthis paper. Filter design based on numerical simulation is car-ried out via four steps. First we determine a unit cell to extract

-parameters, as shown in Fig. 6. The unit cell consists of partial-plane waveguides on both sides and an evanescent waveguide

in the center of unit cell. The evanescent waveguide section isthen directly involved in the T-equivalent circuit of Fig. 5. Usingcommercial EM simulators HFSS and/or CST MWS, we simu-late the unit cells for the arbitrarily length of or and extractthe -parameters for the center frequency of the filters. It is as-sumed that only the dominant mode propagates in the unit cells.

The second step is to convert extracted -parameters into anmatrix. Since the unit cells are symmetrical and re-

ciprocal structures, extracted -parameters must follow

(c)

Fig. 9. Two fabricated partialH-plane filters. (a) Type 1. (b) Type 2. (c) Coaxto partial H-plane waveguide transition (type 1).

and . The convertedmatrix is given by

(10)

KIM et al.: COMPACT PARTIAL -PLANE FILTERS 3927

Fig. 10. Measured and simulated responses of the two partial H-plane filterswith coax transition. (a) Type 1. (b) Type 2.

where the is an matrix of the entire unit cell andmust follow and .

In the third step, we obtain the matrix of the evanes-cent waveguide using

(11)

where and are matrices of the partial -planewaveguide and evanescent waveguide, respectively. Subse-quently, gives the exact reactance values for the arbitrarilylength of or using

(12)

By repeating the above three steps while varying the length ofor , we can obtain the exact reactance values for the length

of the evanescent waveguide.In the last step, the sizes for evanescent waveguide sections

of the filter ( or ) are obtained using (7) and (9) and the

Fig. 11. Structures of type 3 filter. w : length of jth evanescent waveguidesection (j = 1–6). r : length of kth resonator (k = 1–5). s : the length ofH-plane rectangular intaglio of the first, third, and fifth evanescent waveguidesections.

Fig. 12. Equivalent circuit of type 3 filter with quarter-wavelength resonators.

Fig. 13. Admittance inverter (J-inverter) for H-plane intaglio.

Fig. 14. Fabricated partial H-plane filter type 3.

calculated reactance values for evanescent waveguide. The neg-ative electrical lengths against each or are defined as(8) and resonator lengths are given by

(13)

3928 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 11, NOVEMBER 2006

TABLE IIIDESIGNED FILTER SIZES OF TYPES 1 AND 3 (UNIT: MILLIMETERS)

C. Design of Filters

Using the previously described method, we have designedtwo partial -plane filters together with - and -plane filtersin the -band. Their specifications are: 1) 5-GHz center fre-quency; 2) 0.01-dB passband ripple; 3) five poles; and 4) 5% rel-ative bandwidth. Inserted metal vane thickness of the designedfilters is 0.1 mm. The frequency responses of the type 1 and

-plane filter are compared in Fig. 7 and their designed sizesare listed in Table I. Type 1 has the same frequency responsesand one-quarter dimension as those of the -plane filter, respec-tively. Fig. 8 shows the frequency responses of the type 2 and

-plane filter, and their designed sizes are listed in Table II.Type 2 has the same frequency characteristics as that of the

-plane filter, while its dimension is one-quarter that of the-plane filter. To compare the insertion loss due to conduction

loss, the conductivity of 5.8 10 is assumed. The insertionlosses of the two partial -plane filters are larger than thoseof those of the - and -plane filters because of their compact-ness. In detail, the calculated insertion losses of types 1 and 2 are0.06 and 0.11 dB, respectively, and those of the - and -planefilters are 0.032 and 0.028 dB, respectively.

To verify our approach, the partial -plane filter has beendesigned along with coaxial to partial -plane waveguidetransition. The photographs of fabricated partial -plane filterswith transition are shown in Fig. 9. As shown in Fig. 1(b),the -field of the dominant mode focuses on the end of the

-plane metal vane. Thus, we introduce a coaxial transitionstructure. A coaxial probe from the narrow sidewall is insertedat the rectangular intaglio in the -plane metal vane. It islocated at a quarter-wavelength-long distance from the endmetal wall of the filter. A coaxial to partial -plane waveguidetransition is made of a commercially available subminiatureA (SMA) connector. The detailed photograph of the coax topartial -plane waveguide transition is shown in Fig. 9(c).The coaxial transition structure has been optimized usingcommercial EM simulators (CST MWS) by varying depth ofintaglio (de) and width of intaglio (wi) in Fig. 9(c). Note thatthe diameter of the coaxial probe is 4.1 mm. The resultingvalues of “de” and “wi” are 6.78 and 5.7 mm, respectively.Frequency responses obtained by simulation and measurementof the partial -plane filter are shown in Fig. 10, showing agood agreement.

IV. PARTIAL -PLANE FILTER—TYPE 3

To overcome disadvantages for the - and -plane filters,the compact type of them, called the partial -plane filter oftypes 1 and 2, are presented in Section III. Even though partial

-plane filters of types 1 and 2 have the same frequency char-acteristics and transversely reduced dimension as one-quarter ofthose of the - and -plane filters, they still have problems in

Fig. 15. Measured and simulated responses of partialH-plane filter of type 3.

that they have longitudinally long length and spurious frequencyresponse below (twice the passband frequency), as shownin Figs. 7 and 8.

Therefore, here, we propose the partial -plane filter of type3. The partial -plane filter of type 3 is designed by modifyingthe type 1 filter. The type 3 filter utilizes two different struc-tures of evanescent waveguides. One is the -plane septum,which acts as a short end (low impedance), and the other is the

-plane intaglio, which acts as an open end (high impedance),as shown in Fig. 11. Thus, the evanescent waveguides of the

-plane septum and -plane intaglio can be represented bythe - and -inverter circuits, respectively. The length of theresonator between the short and open ends should also be aquarter-wavelength. The half-wavelength resonator filter liketypes 1 and 2 is coupled - or -inverters on both ends, whilethe quarter-wavelength resonator filter like type 3 is coupled al-ternately by - and -inverters. Fig. 12 shows the equivalentcircuit of a partial -plane filter of type 3. The - and -in-verter circuits are shown in Figs. 5 and 13, respectively.

The normalized inverter values for an equal-ripple bandpassfilter of type 3 and resonator lengths are given by [10]

or

(14)

(15)

KIM et al.: COMPACT PARTIAL -PLANE FILTERS 3929

Fig. 16. Broadband responses of partialH-plane filter type 3 compared to theones of types 1 and 2. (a) Simulation. (b) Measurement.

Using the same design method as those of types 1 and 2, wehave designed a partial -plane filter of type 3. Their specifi-cations are: 1) 5-GHz center frequency; 2) 0.01-dB passbandripple; 3) five poles; and 4) 5% relative bandwidth. Insertedmetal vane thickness of designed filters was fabricated to be0.5 mm. Type 3 has been fabricated as shown in Fig. 14 and theirdesigned sizes are listed in Table III. The designed results indi-cate that type 3 has the reduced length by 28.7% resonatorsevanescent waveguides over that of the type 1 filter. The mea-sured and simulated responses of type 3 with designed sizes,describing a good agreement, are shown in Fig. 15. The fre-quency responses of the types 1–3 filter are compared in Fig. 16.The quarter-wavelength resonator filters have a second pass-band center at instead of , as is the case of half-wave-length resonator filters [10]. In detail, types 1 and 2 consistedof a half-wavelength resonator having the first spurious modeat 8.1 GHz, while that of type 3 with a quarter-wavelength res-onator occurs at 11 GHz. As a result, type 3 has the sharp skirtcharacteristic and superior spurious response compared to theother filters, as shown in Fig. 16.

V. CONCLUSION

Three types of compact waveguide filters, called the partial-plane filters, have been presented. They have the advantages

of compact, low-cost, and mass-producible properties. The par-tial -plane filters of types 1 and 2 have the same frequencyresponses even though their cross sections are one-quarter ofthose of the conventional - and -plane filters, respectively.The partial -plane filter of type 3, using two different typesof coupling sections, is designed based on quarter-wavelengthresonators. It has reduced dimension not only in the transversaldirection, but also in the longitudinal direction. It also has the su-perior skirt characteristic and harmonic responses to other par-tial -plane filters. To verify, we have designed three types ofpartial -plane filters in the -band. The measured data are ingood agreement with the computed results.

REFERENCES

[1] Y. C. Shih, “Design of waveguide E-plane filters with all-metal in-serts,” IEEE Trans. Microw. Theory Tech., vol. MTT-32, no. 7, pp.695–704, Jul. 1984.

[2] V. Postoyalko and D. S. Budimir, “Design of waveguide E-plane fil-ters with all-metal inserts by equal ripple optimization,” IEEE Trans.Microw. Theory Tech., vol. 42, no. 2, pp. 217–222, Feb. 1994.

[3] J. M. Cid and J. Zapata, “CAD of rectangular waveguide H-plane cir-cuits by segmentation, finite elements and artificial neural networks,”Electron. Lett., vol. 37, no. 2, pp. 98–99, 2001.

[4] P. Kozakowski and M. Mrozowski, “Gradient-based optimization offilters using FDTD software,” IEEE Trans. Microw. Wireless Compon.Lett., vol. 12, no. 10, pp. 389–391, Oct. 2002.

[5] F. Arndt, J. Bornemann, D. Grauerholz, and R. Vahldieck, “Theoryand design of low-insertion loss fin-line filters,” IEEE Trans. Microw.Theory Tech., vol. MTT-30, no. 2, pp. 155–163, Feb. 1982.

[6] D. W. Kim and J. H. Lee, “A partialH-plane waveguide as a new typeof compact waveguide,” Microw. Opt. Technol. Lett., vol. 43, no. 5, pp.426–428, May 2004.

[7] ——, “Partial H-plane filters with partial inserted H-plane metalvane,” IEEE Trans. Microw. Wireless Compon. Lett., vol. 15, no. 5,pp. 351–353, May 2005.

[8] R. Levy, “Theory of direct-coupled-cavity filters,” IEEE Trans. Mi-crow. Theory Tech., vol. MTT-15, no. 6, pp. 340–348, Jun. 1967.

[9] G. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters,Impedance-Matching Networks, and Coupling Structures. Boston,MA: Artech House, 1980.

[10] G. Matthaei, “Direct-coupled, bandpass filters with � =4 resonators,”in IRE Nat. Conv. Rec., 1958, pp. 98–111, pt. 1.

Dong-Won Kim was born in Seoul, Korea, in1977. He received the B.S. degree from MyoungjiUniversity, Yongin, Korea, in 2003, and the M.S.degree from Hongik University, Seoul, Korea, in2005, both in electronic and electrical engineering.

Since 2005, he has been with the Mobile Com-munication Department, LG Electronics Institute ofTechnology, Seoul, Korea. His current research inter-ests include microwave/millimeter-wave circuits.

3930 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 11, NOVEMBER 2006

Dong-Jin Kim was born in Daegu, Korea, in 1981.He received the B.S. degree in electronic and electricengineering from Hongik University, Seoul, Korea,in 2005, and is currently working toward the M.S. de-gree at Hongik University.

His current research interests include microwave/millimeter-wave circuits.

Jeong-Hae Lee (M’98) received the B.S. and M.S.degrees in electrical engineering from Seoul NationalUniversity, Seoul, Korea, in 1985 and 1988, respec-tively, and the Ph.D. degree in electrical engineeringfrom the University of California at Los Angeles, in1996.

From 1993 to 1996, he was a Visiting Scientistwith General Atomics, San Diego, CA, where hismajor research concerned the development of amillimeter-wave diagnostic system. Since 1996, hehas been with Hongik University, Seoul, Korea,

where he is currently an Associate Professor with the Department of RadioScience and Communication Engineering. His current research interestsinclude microwave/millimeter-wave circuits and millimeter-wave diagnostics.