диафрагмированные волноводные фильтры / abc294dc-6ba4-4dae-ac61-6c8a12503ab5

Abstract—This paper presents partial -plane filters with multiple transmission zeros using a narrow -plane slot of open-ended evanescent waveguide. Each narrow -plane slot operates as an admittance inverter and, simultaneously, provides the attenuation pole due to its resonance behavior at a particular frequency. Thus, the number of transmission zeros is equal to that of the -plane slots. The filters with multiple transmission zeros are simply implemented without any additional coupling and extra modification of the filter structure. Two filters are designed by halfand quarter-wavelength resonators, respectively. The measured results are in good agreement with simulated results.

Index Terms—Admittance inverter with attenuation pole, partial -plane filter, partial -plane waveguide, transmission zero.

I. INTRODUCTION

W AVEGUIDE filters with transmission zeros out of passband are applied to variously wireless filtering systems where the high rejection and sharp skirt characteristics of the

stopband are required. These waveguide filters are implemented by numerous coupling structures such as generally folded crosscoupling [1]–[3], direct coupling between the source and load [4], [5], bypass coupling [6], stub iris [7], and particular structure in waveguide [8], [9]. However, the above waveguide filters have disadvantages in that they require the folded structure or imperative extra space, although they offer the transmission zeros out of passband. In this paper, the partial -plane filters [10], [11] with multiple transmission zeros are proposed without additional coupling or extra space.

The narrow -plane slot of an open-ended evanescent waveguide employed in partial -plane filters acts as an admittance inverter and an attenuation resonator simultaneously. Thus, the number of transmission zeros is equal to that of the -plane slots. The bandpass filters do not also require cross coupling or modification of the waveguide structure. Furthermore, the filters are very compact because these are implemented by a partial -plane waveguide [12], which has one-quarter cross section compared with a conventional rectangular waveguide.

Two partial -plane filters using admittance inverters with an attenuation pole are designed by halfand quarter-wave- length resonators, respectively. The half-wavelength resonator filter consisting of only -plane slots of open-end evanescent waveguides has good spurious responses, as well as sharp skirt

Manuscript received October 16, 2007; revised March 26, 2008. First published June 20, 2008; last published July 9, 2008 (projected). This work was supported by the Seoul Research and Business Development (R&BD) Program, Korea.

The authors are with the Department of Electronic and Electrical Engineering, Hongik University, 121-791 Seoul, Korea (e-mail: jeonglee@hongik.ac.kr).

Digital Object Identifier 10.1109/TMTT.2008.925237

Fig. 1. Unit cell of narrow -plane slot and its -equivalent circuit of admittance inverter.

characteristics because the multiple attenuation resonances of admittance inverters can occur at the frequencies of spurious modes besides both sides of the center frequency. Another filter using quarter-wavelength resonators utilizes two different structures of evanescent waveguides and has transmission zeros on both sides of the center frequency. The detailed design procedures of two filters will be discussed.

II. ADMITTANCE INVERTER WITH ATTENUATION POLE

-plane slots of an open-ended evanescent waveguide, which

circuit is represented by an admittance inverter. Usually, the susceptance of of the -plane slot can be described with an inductive component. However, the -plane slot has a resonant characteristic if its width is narrower and/or its depth is deeper. Thus, the susceptance of should be represented by a parallel L–C resonant circuit. Therefore, each narrow -plane slot of the open-ended evanescent waveguide acts as an admittance inverter, and simultaneously offers the attenuation pole due to its resonance behavior. The number of the attenuation poles is also determined by that of the narrow -plane slots.

Figs. 2 and 3 show the frequency responses with the width and depth of the narrow -plane slot in the -band by

full-wave simulation. The cross section and vane length

of the partial -plane waveguide are set to be 23.8 mm

12 mm and 19.16 mm in the -band, respectively. As shown in these figures, the frequency of attenuation resonance is downshifted if the depth is deeper and width is narrower. This means that the frequency of attenuation resonance is determined by the size of the -plane slot.

Fig. 4 illustrates the tendency of the normalized inverter value depending on depth and width of the -plane slot at several frequencies. In general, the normalized admittance inverter value and electrical length for an open-ended evanescent waveguide are calculated by [13]

(1)

(2)

where is the wave admittance of a partial -plane waveguide. Each susceptance value depends on width or depth

of the evanescent waveguide. The normalized inverter value is equal to zero when the susceptance of of the -plane slot is zero, indicating that attenuation resonance occurs. At the frequency of in Fig. 4, the susceptance of has a positive value

downwards in Fig. 4 since the resonance occurs at the upper frequency of , which corresponds to a smaller value of and a larger value of . As shown in Fig. 2 and 3, the -plane slot with a smaller value of and a larger value of causes the resonance frequency to up-shift. Similarly, at the lower frequency

which gives the required admittance inverter value and the desired frequency of the attenuation pole. Assuming that the value

of is required at the center frequency in the filter design, the size of the -plane slot is determined by points 1 and 2, as indicated in Fig. 4. If the desired frequency of the attenuation pole is larger than the center frequency , the size of the -plane slot is chosen by points 1 since it corresponds to attenuation resonance. On the other hand, if the desired frequency of the attenuation pole is smaller than the center frequency , the size of the -plane slot is chosen by points 2. Therefore, it is possible that the bandpass filter having multiple transmission zeros can be implemented with the different sizes of -plane slots without any cross coupling or additional modification of the waveguide structure.

III. HALF-WAVELENGTH RESONATOR FILTER

Using the previously described -plane slot of the open-ended evanescent waveguide, the half-wavelength resonator filter is designed in the -band. The specifications of filter are: 1) center frequency of 5 GHz; 2) passband ripple of 0.01 dB; 3) four-pole; and 4) fractional bandwidth of 4%. Fig. 5 shows the structure of the partial -plane filter, which consists of half-wavelength resonators. The designed bandpass filter consists of five -plane slots with different sizes and four half-wavelength resonators. Thus, five transmission zeros are expected to be obtained. The length of the half-wavelength resonator is given by [13]

(3)

where is the guide wavelength at center frequency. The designed filter is compared with a conventional -plane filter and their designed sizes are listed in Table I. The thickness of the inserted metal vane is 0.5 mm. Two bandpass filters consist of half-wavelength resonators, but the proposed filter is implemented by open-ended evanescent waveguides, while the conventional -plane filter is constructed by short-ended evanescent waveguides. In addition, the proposed partial -plane filter has one-quarter cross-section size compared with that of the conventional filter even though the total lengths are similar as listed in Table I.

The normalized inverter values for the equal-ripple bandpass filter are defined by [13]

(4)

where are element values for a equal-ripple low-pass prototype and is a normalized cutoff frequency. , , and are guide wavelengths at center frequency and the lower and upper passband edge frequencies, respectively. is a relative bandwidth for guide wavelength. Usually, to satisfy the above design equations, the conventional bandpass filter is designed by a symmetrical structure. However, the proposed partial -plane filter is materialized by an asymmetrical structure because the -plane slots with different sizes can have the same inverter values as discussed in Fig. 4. This indicates that the filter can have the same number of transmission zeros as that of -plane slots since each -plane slot generates its own attenuation resonance.

The designed filter consisting of half-wavelength resonators has sharp skirt characteristics and excellent spurious responses due to five attenuation resonances of -plane slots. As shown in Fig. 6, five transmission zeros are generated. In detail, two transmission zeros at the upper (5.85 GHz) and lower (4.50 GHz) center frequency are generated by the second and third -plane slots of evanescent waveguides. The first, fourth, and fifth -plane slot of the open-ended evanescent waveguide also produce attenuation poles at 7.25, 7.40, and 8.85 GHz, respectively, and suppress spurious responses.

Theoretically, the transmission zero of the proposed filters can be freely placed since the size of the -plane slot (width and depth) determines the frequency of the transmission zero, as discussed in Figs. 2 and 3. As shown in Figs. 2 and 3, the frequency of the attenuation pole is lower as the -plane slot gets narrower, thus the transmission zeros, which are generated by the first, second, fourth, and fifth slots at the upper band rather than the center frequency can be placed near the passband by

Fig. 6. Frequency responses of half-wavelength resonator partial -plane filter with five transmission zeros and conventional -plane filter.

Fig. 7. Measured and simulated frequency responses of half-wavelength resonator partial -plane filter with five transmission zeros.

adopting the narrower -plane slot. For instance, if the narrower -plane slot rather than the second slot in Table I is implemented as the second admittance inverter, the transmission zero is theoretically located closer to the edge of the passband. However, in this case, the variation rate of the inverter value with frequency, which is a quantitative index of frequency dependence of the inverter, is too large to design the filter. Thus, the desired filtering characteristics cannot be obtained. In general, the variation rate of the inverter value with frequency is getting smaller with the number of resonators so that it is easy to place the transmission zero near the edge of the passband.

In order to calculate the insertion loss due to conduction loss, the conductivity of 5.8 10 is assumed. The insertion loss of the proposed filter is larger than that of the conventional -plane filter because the factor of the partial -plane filter is lower than that of the -plane filter due to its compactness and presence of a metal vane. In detail, the calculated insertion loss of the proposed filter is 0.15 dB, while that of the conventional -plane filter is 0.032 dB.

To verify our approach, the open-ended partial -plane filter has been fabricated. Fig. 7 shows frequency responses obtained by simulation and measurement. The measured insertion loss is 0.73 dB. It is confirmed that the measured data are in good agreement with simulated data. The filter has a steep skirt and excellent spurious responses.

IV. QUARTER-WAVELENGTH RESONATOR FILTER

The proposed admittance inverter with attenuation resonance implemented by the -plane slot can also be applied to the quarter-wavelength resonator filter. In general, the quarter-wavelength resonator filter has advantages, which are that the length of the filter is shorter than that of the half-wave- length resonator filter. It has good spurious response since the second passband center is at instead of [14]. The quarter-wavelength resonator is employed in a compact partial -plane filter, but it does not has transmission zeros [10]. In this section, a quarter-wavelength resonator partial -plane filter with two attenuation poles at the upper and lower portions

Fig. 8. Structure of quarter-wavelength resonator partial -plane filter with two -plane slots and three -plane septa.

of center frequency introduced by two narrow -plane slots is designed, as shown in Fig. 8. The designed filter is constructed using two different types of evanescent waveguide because the quarter-wavelength resonator is coupled alternately by impedance and admittance inverters. The impedance inverter, which acts as a short-ended evanescent waveguide, is materialized by the -plane septa. The admittance inverter, which acts as an open-ended evanescent waveguide, is materialized by the -plane slot. This -plane slot provides a transmission zero of the filter, as discussed earlier.

The normalized impedance inverter value and electrical length are calculated by

(5)

(6)

where is the wave impedance of a partial -plane waveguide and are reactance values of the impedance inverter represented by a T-equivalent circuit [10], [11]. The normalized

Fig. 9. Measured and simulated responses of quarter-wavelength resonator partial -plane filter with two transmission zeros.

inverter values and resonator length of the equal-ripple quarter wavelength resonator filter are also given by

or

(7)

(8)

where is the electrical length of the impedance inverter if is one of the admittance inverters. is the electrical length of the admittance inverter if is also one of the impedance inverters.

The quarter-wavelength resonator filter with attenuation poles is designed with the same specifications of the half-wave- length resonator filter discussed in Section III. Its sizes are listed in Table II. In order to satisfy design equations of the equal ripple bandpass filter, normalized admittance inverter values of two -plane slots should be the same. However, the same inverter values can be obtained with different sizes of -plane slots and, thus, the designed filter has two transmission zeros at the upper (5.4 GHz) and lower (4.6 GHz) portions of the center frequency. The attenuation resonance poles at 4.6 and 5.4 GHz are generated by -plane slots with the depths of 16.27 and

14.15 mm, respectively. The described results indicate that the filter with attenuation poles can be implemented without any additional modification of the structure. Furthermore, the designed bandpass filter is very compact because it consists of quarter-wavelength resonators and is constructed by a partial -plane waveguide. The measured and simulated responses of the designed bandpass filter are shown in Fig. 9. As shown, two transmission zeros due to -plane slots occurs at the frequencies of 4.61 and 5.41 GHz, respectively, and the measured insertion loss is 0.84 dB. The results show excellent agreement.

V. CONCLUSION

Two partial -plane filters having multiple transmission zeros have been proposed. The open-ended evanescent waveguide, which is embodied by a narrow -plane slot, acts as an admittance inverter of the bandpass filter and, simultaneously, offers the attenuation resonance at a particular frequency. Thus, the number of transmission zeros is equal to that of the -plane slots. The half-wavelength resonator filter consisting of five admittance inverters with attenuation poles has been designed. Its spurious responses are improved by attenuation resonances of narrow -plane slots. The quarter-wavelength resonator filter using two narrow -plane slots has two transmission zeros at both sides of center frequency. Two filters have been fabricated in the -band and the measured data show excellent agreement with theory.

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Dong-Jin Kim was born in Daegu, Korea, in 1981. He received the B.S. and M.S. degrees in electronic and electrical engineering from Hongik University, Seoul, Korea, in 2005 and 2007, respectively, and is currently working toward the Ph.D. degree at Hongik University.

His current research interests include the mi- crowave/millimeter-wave circuits.

Jeong-Hae Lee (M’98) received the B.S. and M.S. degrees in electrical engineering from Seoul National University, Korea, in 1985 and 1988, respectively, and the Ph.D. degree in electrical engineering from the University of California at Los Angeles (UCLA), 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 mil- limeter-wave diagnostic system and to study plasma wave propagation. Since 1996, he has been with

the Department of Electronic and Electrical Engineering, Hongik University, Seoul, Korea, where he is currently an Associate Professor. His current research interests include microwave/millimeter-wave circuits, millimeter-wave diagnostics, and meta-material RF devices.