диафрагмированные волноводные фильтры / 0bc38e83-09e3-4da4-93a7-dbd9bcfb36fc

I. INTRODUCTION

THE FAST development of RF/microwave technology greatly stimulates the compact, low-cost, and mass-pro- ducible properties for components. One of the most challenging components is the filter, and its electrical performance is crucial for overall system design. The -plane filter [1], [2], -plane filter [3], [4], and fin-line filter [5] are commonly used filters made by a rectangular waveguide since they have low loss and are easy to fabricate. Moreover, the -plane filter also has low-cost and mass-producible properties. However, despite their favorable characteristics, they have the disadvantages of bulky 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 class

of compact, low-cost, and mass-producible filter.

The partial -plane waveguide is a transversely folded rectangular waveguide, which has the same dispersion characteristics for the first two dominant modes as those of the conventional rectangular waveguide, while its cross section is onequarter [6]. By using the partial -plane waveguide, it is possible to miniaturize the components made by rectangular waveguide [7]. The partial -plane filters of types 1 [7] and 2 can be compared with the conventional - and -plane filters, respectively, since they have the same mechanisms to implement the evanescent waveguide and use inductive coupling. It will be

Fig. 2. E-field distributions of partial H-plane waveguide. (a) Dominant mode TE . (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 waveguide (width: 47.55 mm and height: 22.15 mm) in the H-band.

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

D.-W. Kim was with the Department of Radio Science and Communication Engineering, Hongik University, 121-791 Seoul, Korea. He is now with the Mobile 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 Communication Engineering, Hongik University, 121-791 Seoul, Korea (e-mail: jeonglee@hongik.ac.kr).

Digital Object Identifier 10.1109/TMTT.2006.883652

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

Fig. 4. Structures of two types of partial H-plane filters. K : impedance inverter 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 jth

H-plane metal insert in type 2. (a) Partial H-plane filter (type 1). (b) Partial

H-plane filter (type 2).

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

To design three types of partial -plane filters, a numerically efficient simulation-based filter design technique is developed. This design technique is based on typical direct-coupled resonator filter design theory [8], [9] and it uses thoroughly frequency-dependant inverter theory. The proposed filters have been fabricated with coaxial to partial -plane waveguide transition in the -band. Good agreement between measured and computed results will be presented.

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

II. PARTIAL -PLANE WAVEGUIDE

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

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

(region 2)

(2)

is omitted. Free-space wavenumber is given by

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

(5)

(6)

where is the velocity of light. The dispersion characteristics compared with the rectangular waveguide in the -band are shown in Fig. 3. Dispersion characteristics of the first two dominant modes are the same as those of the conventional rectangular waveguide. Note that the cross section of the partial -plane waveguide is one-quarter of the rectangular waveguide. The detailed analytical expression and the mode definition 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 a partial -plane waveguide are illustrated in Fig. 4. They consist of resonators alternating with evanescent waveguide sections. It is easily found out that they have the same structures as those

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

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

An evanescent waveguide section of type 1 is implemented by inserting the -plane septa between the positions of and in the plane of Fig. 1, while that of type 2 is implemented by inserting a rectangular metal insert in the -plane of Fig. 1. The principles for designing an evanescent waveguide of two partial -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 filters. They consist of half-wavelength resonators, which are ter-

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

(7)

(8)

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

(9)

where are element values for an equal-ripple low-pass prototype and is a normalized cutoff frequency. , , and are guide wavelengths at center frequency and at lower and upper passband edge frequencies. is a relative bandwidth for a guide wavelength.

To determine sizes of filters, the partial filter design method, using a commercial electromagnetic (EM) simulator, is used in this paper. Filter design based on numerical simulation is carried 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 is then directly involved in the T-equivalent circuit of Fig. 5. Using commercial EM simulators HFSS and/or CST MWS, we simulate the unit cells for the arbitrarily length of or and extract the -parameters for the center frequency of the filters. It is assumed that only the dominant mode propagates in the unit cells.

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

ciprocal structures, extracted -parameters must follow

(c)

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

and . The converted matrix is given by

(10)

(12)

By repeating the above three steps while varying the length of

or , 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

calculated reactance values for evanescent waveguide. The negative electrical lengths against each or are defined as

(8) and resonator lengths are given by

(13)

C. Design of Filters

Using the previously described method, we have designed two partial -plane filters together with - and -plane filters in the -band. Their specifications are: 1) 5-GHz center frequency; 2) 0.01-dB passband ripple; 3) five poles; and 4) 5% relative bandwidth. Inserted metal vane thickness of the designed filters is 0.1 mm. The frequency responses of the type 1 and -plane filter are compared in Fig. 7 and their designed sizes are listed in Table I. Type 1 has the same frequency responses and one-quarter dimension as those of the -plane filter, respectively. 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 insertion losses of the two partial -plane filters are larger than those of those of the - and -plane filters because of their compactness. In detail, the calculated insertion losses of types 1 and 2 are 0.06 and 0.11 dB, respectively, and those of the - and -plane filters are 0.032 and 0.028 dB, respectively.

To verify our approach, the partial -plane filter has been designed along with coaxial to partial -plane waveguide transition. The photographs of fabricated partial -plane filters with 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 transition structure. A coaxial probe from the narrow sidewall is inserted at the rectangular intaglio in the -plane metal vane. It is located at a quarter-wavelength-long distance from the end metal wall of the filter. A coaxial to partial -plane waveguide transition is made of a commercially available subminiature A (SMA) connector. The detailed photograph of the coax to partial -plane waveguide transition is shown in Fig. 9(c). The coaxial transition structure has been optimized using commercial EM simulators (CST MWS) by varying depth of intaglio (de) and width of intaglio (wi) in Fig. 9(c). Note that the diameter of the coaxial probe is 4.1 mm. The resulting values of “de” and “wi” are 6.78 and 5.7 mm, respectively. Frequency responses obtained by simulation and measurement of the partial -plane filter are shown in Fig. 10, showing a good 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 of types 1 and 2, are presented in Section III. Even though partial -plane filters of types 1 and 2 have the same frequency characteristics and transversely reduced dimension as one-quarter of those of the - and -plane filters, they still have problems in

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

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

Therefore, here, we propose the partial -plane filter of type 3. The partial -plane filter of type 3 is designed by modifying the type 1 filter. The type 3 filter utilizes two different structures 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 by the - and -inverter circuits, respectively. The length of the resonator between the short and open ends should also be a quarter-wavelength. The half-wavelength resonator filter like types 1 and 2 is coupled - or -inverters on both ends, while the quarter-wavelength resonator filter like type 3 is coupled alternately by - and -inverters. Fig. 12 shows the equivalent circuit 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 bandpass filter of type 3 and resonator lengths are given by [10]

or

(14)

(15)

Fig. 16. Broadband responses of partial H-plane filter type 3 compared to the ones of types 1 and 2. (a) Simulation. (b) Measurement.

Using the same design method as those of types 1 and 2, we have designed a partial -plane filter of type 3. Their specifications are: 1) 5-GHz center frequency; 2) 0.01-dB passband ripple; 3) five poles; and 4) 5% relative bandwidth. Inserted metal vane thickness of designed filters was fabricated to be 0.5 mm. Type 3 has been fabricated as shown in Fig. 14 and their designed sizes are listed in Table III. The designed results indicate that type 3 has the reduced length by 28.7% resonators evanescent waveguides over that of the type 1 filter. The measured and simulated responses of type 3 with designed sizes, describing a good agreement, are shown in Fig. 15. The frequency responses of the types 1–3 filter are compared in Fig. 16. The quarter-wavelength resonator filters have a second passband center at instead of , as is the case of half-wave- length resonator filters [10]. In detail, types 1 and 2 consisted of a half-wavelength resonator having the first spurious mode at 8.1 GHz, while that of type 3 with a quarter-wavelength resonator occurs at 11 GHz. As a result, type 3 has the sharp skirt characteristic and superior spurious response compared to the other filters, as shown in Fig. 16.

REFERENCES

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Dong-Won Kim was born in Seoul, Korea, in 1977. He received the B.S. degree from Myoungji University, Yongin, Korea, in 2003, and the M.S. degree from Hongik University, Seoul, Korea, in 2005, both in electronic and electrical engineering.

Since 2005, he has been with the Mobile Communication Department, LG Electronics Institute of Technology, Seoul, Korea. His current research interests include microwave/millimeter-wave circuits.

Dong-Jin Kim was born in Daegu, Korea, in 1981. He received the B.S. degree in electronic and electric engineering from Hongik University, Seoul, Korea, in 2005, and is currently working toward the M.S. degree 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 National University, Seoul, Korea, in 1985 and 1988, respectively, and the Ph.D. degree in electrical engineering from the University of California at Los Angeles, in 1996.

From 1993 to 1996, he was a Visiting Scientist with General Atomics, San Diego, CA, where his major research concerned the development of a millimeter-wave diagnostic system. Since 1996, he has been with Hongik University, Seoul, Korea,

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