диафрагмированные волноводные фильтры / a16f238c-a8df-4fb6-8944-c6a872c65730

Abstract — This paper presents a novel method for microwave waveguide filter design. The method assumes development of novel resonators, which can be used for the higher-order waveguide filter design. Multiple resonant frequencies can be obtained using single resonating insert. Bandpass and bandstop waveguide filters, with a single or multiple frequency bands, are developed using E-plane or H- plane printed-circuit discontinuities acting as resonating elements. They are intended to operate in the X frequency band and standard rectangular waveguide (WR-90) is used for their implementation. A solution for the compact filter design is also proposed. The application of the novel method is exemplified by various bandpass and bandstop filter models, their equivalent microwave circuit representations and laboratory prototypes. Experimental verification shows good agreement between simulation and measurement results.

Keywords — bandpass filter, bandstop filter, complementary split-ring resonator, multi-band filter, printed-circuit discontinuity, quarter-wave resonator, splitring resonator, waveguide filter.

I. INTRODUCTION

IN modern telecommunications, waveguide filters still represent significant components of the systems operating with high power and low losses, in spite of their size. Their use is required in radar and satellite systems, where they represent sustainable solutions, since the strength of the received signal should not be significantly decreased. Actually, this class of filters is characterized by a high quality factor [1]. They still gain significant attention, especially in the area of multi-band filter design

and more demanding component miniaturization. Microwave waveguide filters can be implemented using

discontinuities of various shapes and positions inside the waveguide structure [2]. Different solutions can be found in the available literature. A widespread approach regarding waveguide filter design is based on the insertion of printed-circuit boards in the E-plane of the rectangular waveguide. An example of the bandpass filter can be found in [3]. For the bandstop filter design, split-ring

This work was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia under Grant TR32005.

Snežana Lj. Stefanovski Pajoviü is with the School of Electrical Engineering, University of Belgrade, Bul. kralja Aleksandra 73, 11120 Belgrade, Serbia; Telekom Srbija, Bul. umetnosti 16, 11070 Belgrade, Serbia (e-mail: snezanastef@telekom.rs).

Milka M. Potrebiü and Dejan V. Tošiü are with the School of Electrical Engineering, University of Belgrade, Bul. kralja Aleksandra 73, 11120 Belgrade, Serbia (e-mail: milka_potrebic@etf.rs, tosic@etf.rs).

resonators (SRRs) are often used to obtain single rejection band [4], [5] or multiple rejection bands [6]. The other approach assumes placement of the printed-circuit inserts in the H-plane of the rectangular waveguide. Similarly as for the E-plane inserts, the H-plane inserts can be implemented using SRRs, for bandstop filters, or complementary split-ring resonators (CSRRs), for the bandpass filters. An example of the bandpass filter with CSRR is given in [7], while the solution with miniaturized inverters is proposed in [8]. Furthermore, bandstop filter with two rejection bands is presented in [9] and the one with miniaturized inverters is given in [10].

The objective of the research presented here is implementation of microwave waveguide filters, with multiple pass bands or rejection bands, using printedcircuit discontinuities as resonating elements. Novel method for waveguide filter design is proposed. It is explained how it can improve the existing design procedure. Numerous examples and novel solutions are provided to illustrate the applicability of the method, along with the experimental verification on the laboratory prototype.

II.NOVEL METHOD FOR WAVEGUIDE FILTER DESIGN

The novel method for the waveguide filter design assumes development of novel resonators implemented as printed-circuit inserts inside the rectangular waveguide structure [11]. The goal is to obtain one or more resonant frequencies by employing a single resonating insert, by means of optimal distribution of the resonators on the insert. Preferable solution assumes the uncoupled resonators on the inserts, since it provides the possibility to independently tune each frequency band by modifying the parameters of individual resonator. The frequency response of the resonator or filter can be changed depending on the printed-circuit insert implementation. Therefore, multi-band filter can be easily designed. The inserts are placed in the H-plane or the E-plane of the rectangular waveguide, depending on the desired implementation. There is no need to modify the waveguide structure, thus the same waveguide can be used for various implementations in the chosen frequency band.

Design of the higher-order filters is considered for the bandpass and bandstop filters with single or multiple frequency bands. The solution presented here assumes the possibility to optimally align the inserts in the H-plane of the rectangular waveguide in order to employ inverter as a corresponding waveguide section for each center frequency. For the bandpass filters, folded inserts are implemented in the H-plane, to obtain the waveguide

section length equal to a quarter of the guided wavelength. The compact filter implementation assumes miniaturized inverters and properly designed additional inserts between the inserts with resonators. For the higher-order filter design using the inserts in the E-plane, it is important to consider the position of the resonators on the insert, so their mutual coupling can be achieved.

Herein, the results of the research are presented to qualify application of the novel method for waveguide filter design, by means of various examples of bandpass and bandstop filters. SRRs, CSRRs and quarter-wave resonators (QWRs) are employed on the printed-circuit inserts, providing simple and flexible solutions, in terms of frequency response adjustment and implementation. The equivalent microwave circuit representations are provided for the chosen filter models. Simulation results are experimentally verified, so the proposed design method can be properly validated.

Considered resonators and filters operate in the X frequency band. The standard rectangular waveguide (WR-90) is used for the filter design. Dimensions of its

structure is excited by properly designed probes, i.e. monopoles placed at a distance of Ȝg/4 from the shortcircuited ends. The dominant mode of propagation, i.e. the transverse electric TE10 mode, is of interest. Threedimensional electromagnetic (3D EM) models and fullwave simulations are performed using software WIPL-D [12]. The equivalent microwave circuits are generated in software WIPL-D and AWR Microwave Office [13]. For the experimental verification, printed-circuit inserts are fabricated on the MITS Electronics FP-21T Precision machine, using available substrates. The measurements are performed using Agilent N5227A network analyzer.

III. BANDPASS WAVEGUIDE FILTERS

Bandpass waveguide filters with printed-circuit inserts are implemented using CSRRs. Novel resonators are proposed in order to obtain single or multiple resonant frequencies. These resonators are then used for the filter design. Herein, the filter models with the H-plane inserts are presented. The resonating inserts can be implemented as metal plates or multilayer planar inserts.

A. Waveguide Resonator Using Novel CSRRs

Starting from the CSRR used for the filter design in [8], [14], novel CSRR is developed by adding a central section [11], [15]. This section provides the possibility to fine-tune the frequency response, i.e. the center frequency and bandwidth. Two resonators can be made on the same insert (Fig. 1) in order to obtain two resonant frequencies, 9 GHz and 11 GHz. For the considered model, RT/Duroid 5880 microstrip board (İr = 2.2, tanį = 0.001, h = 0.8 mm, t = 0.0018 mm) is used for the printed-circuit insert. The amplitude response shown in Fig. 2 confirms possibility to independently tune each frequency band.

Fig. 1. Waveguide resonator using novel CSRRs.

Fig. 2. Comparison of the amplitude responses: blue - R1 and R2 on the insert, red - only R1 on the insert,

green - only R2 on the insert.

B. Dual-Band Waveguide Filter Using Metal Inserts with CSRRs

Design of the dual-band filter starts from the waveguide resonator with two resonant frequencies, implemented using metal inserts with CSRRs [11], [16], [17]. Folded inserts placed in the H-plane of the waveguide are introduced as important solution for multi-band filter design, because it is possible to obtain the waveguide section length equal to a quarter of the guided wavelength (i.e. a quarter-wave inverter), for each center frequency. Herein, the second-order dual-band bandpass waveguide filter is presented, as an example of the higher-order filter design, with two center frequencies, f01 = 9 GHz (B3dB-1 = 450 MHz) and f02 = 11 GHz (B3dB-2 = 650 MHz).

Fig. 3. Second-order dual-band waveguide filter.

The 3D model of the filter is shown in Fig. 3. For the filter design, two identical folded metal inserts are used. Dimensions of the corresponding CSRRs are the same for

both inserts. Also, lpl = (Ȝg 9GHz - Ȝg 11GHz)/8 = 1.84 mm. The distance between the CSRRs with the same resonant

conductivity of the metal plates is set to ı = 20 MS/m, to include the losses due to the surface roughness and the skin effect.

For the second-order dual-band filter using folded inserts, the equivalent microwave circuit is generated in software AWR Microwave Office. The circuit contains parallel RLC circuits and waveguide sections, as shown in Fig. 4. The parameters of the lumped elements are

calculated using following equations, as proposed in [15], [16]:

where Ri denotes resistance, Li inductance, Ci capacitance,

Ȧ0i is resonant frequency in [rad/s], B3dBi is 3 dB bandwidth for the i-th pass band (i = 1, 2), |s21(jȦ0i)|

denotes magnitude of s21 parameter at Ȧ0i, Z0i is port impedance, corresponding to the wave impedance of the waveguide at the resonant frequency. The values of the parameters used in these equations are obtained from the amplitude response of the 3D EM model of each individual resonator. The waveguide section of length equal to Ȝg 9GHz/4, representing inverter, is inserted between the networks. Also, in order to obtain equivalent representation of the 3D EM model, the waveguide sections are added between the resonators and ports. The

length of each section is set to Ȝg 10GHz/4 = 9.937 mm. The value of the port impedance is Z0 = 500 ȍ, which is

actually the value of the wave impedance (ZTE) of the waveguide at the operating frequency of f0 = 10 GHz, as the frequency between the considered ones (9 GHz and 11 GHz). The equivalent representation of the short plate connecting the parts of the folded insert with resonators is an inductor, connected in series between two RLC circuits. The value of the inductance is obtained by means of parameter extraction from the 3D EM model and by tuning in the software. Comparison of the amplitude responses for the 3D EM model and the equivalent circuit (Fig. 5) shows good mutual agreement.

Fig. 4. Equivalent microwave circuit of the filter shown in Fig. 3.

The next step is to develop compact waveguide filter. The solution proposed here assumes the use of miniaturized inverters between the resonators. Actually, instead of the conventional quarter-wave inverter, shorter waveguide section with properly designed metal plate is used. The goal is to preserve the original filter response.

The 3D model of the proposed compact dual-band waveguide filter is shown in Fig. 6. Two identical folded inserts are used. However, the plate connecting two parts of the folded inserts with resonators is shorter compared to the previous model and its length is set to

distance between the resonators with resonant frequency

of f02 = 11 GHz is reduced and it is set to Ȝg 11GHz/8. This means that the inverters are equally miniaturized. Because

of the shorter inverters and possible coupling, dimensions of the resonators are changed compared to the original filter model. There is additional plate for miniaturization, centrally positioned between the folded inserts. Dimensions of the slots are tuned so the original filter response can be preserved.

Fig. 5. Comparison of the amplitude responses: blue - 3D EM model (Fig. 3), red - equivalent circuit (Fig. 4).

Fig. 6. Second-order dual-band waveguide filter with miniaturized inverters.

In order to simplify fabrication and experimental verification, compact filter can be further customized. Therefore, solution with flat inserts is proposed. This means that the inserts with CSRRs, and also the additional plate used for miniaturization, are flat. However, the inverters for both center frequencies are not miniaturized in the same manner. The 3D model of the proposed compact filter is shown in Fig. 7. Two identical flat metal plates with CSRRs are used as resonating inserts. The inverter between the resonators with resonant frequency of f01 = 9 GHz is shortened and its normalized length is set to

Ȝg 9GHz/8 = 6.08 mm. However, the inverter between the resonators with resonant frequency of f02 = 11 GHz has

normalized length of 0.18Ȝg 11GHz = 6.11 mm, so it is not miniaturized in the same manner. Fig. 8 shows comparison

of the amplitude responses for the original filter and compact filters, with equal and unequal inverter miniaturization. Since the obtained results match relatively good, the proposed method for compact filter design, using inverters with unequal normalized lengths, is confirmed.

Fig. 7. Second-order dual-band waveguide filter with flat inserts and miniaturized inverters.

Fig. 8. Comparison of amplitude responses: blue - original filter, red - compact filter with equal inverter miniaturization, green - compact filter with

unequal inverter miniaturization.

(a)

(b)

Fig. 9. Photograph of the fabricated components:

(a) metal inserts and planar fixtures for precise positioning, (b) the inserts and the structure for precise positioning inside rectangular waveguide.

For the compact filter with unequal inverter miniaturization, the amplitude response is experimentally verified. The resonating inserts and additional plates for miniaturization are fabricated using metal foil of thickness 100 ȝm. In order to have stable inserts for the measurement, structure for their precise positioning inside the waveguide is proposed. Actually, this structure consists of a fixture intended to hold metal inserts on the side walls and supporting plates for the inserts. For the structure, FR-4 substrate (İr = 4.5, h = 1.0 mm, tanį = 0.02) is used. The fabricated inserts and the structure for precise positioning are shown in Fig. 9. Comparison of simulation and measurement results is shown in Fig. 10, confirming their good mutual agreement and practically negligible influence of the structure for

Fig. 10. Comparison of amplitude responses for the compact filter shown in Fig. 7: blue - simulation results, red - measurement results.

Bandpass filter can be also implemented using metal inserts with resonating slots near top and bottom waveguide walls, as proposed in [11], [18]. These resonating slots can be tuned to provide the same resonant frequencies as the previously considered CSRRs, but they are more compact in terms of dimensions, meaning that they occupy less space on the insert, compared to the regular CSRRs. Actually, it has been shown that the occupied area can be reduced up to 20 % when the resonator is attached to the waveguide wall.

IV. BANDSTOP WAVEGUIDE FILTERS

SRRs are widely implemented as resonating elements of the bandstop waveguide filters. Herein, novel resonating inserts, using SRRs or QWRs, are introduced. Multiple resonant frequencies can be obtained using single insert. Also, novel filters with H-plane or E-plane inserts are proposed. The inserts are implemented as multilayer planar structures.

A. Novel Resonating Insert Using SRR

Design of the novel resonating insert starts from the one proposed in [9], [19]. The 3D model of the waveguide resonator using printed-circuit insert across the entire transverse cross-section of the rectangular waveguide is shown in Fig. 11 (left). The insert is actually dielectric plate with printed SRR. The substrate used for the plate is RT/Duroid 5880 (İr = 2.2, h = 0.8 mm, t = 0.0018 mm).

Fig. 11. Waveguide resonator using printed-circuit insert with SRR, over the entire cross-section (left) or as a small dielectric plate (right).

Novel resonating insert is implemented as a dielectric plate whose size is significantly smaller than dimensions of the transverse cross-section of the waveguide [11], [20]. The plate with the SRR is connected to the upper and the lower waveguide walls using thin dielectric strips (Fig. 11, right). Both resonating inserts shown in Fig. 11 have the same resonant frequency of 9 GHz. Their amplitude

responses are compared in Fig. 12. It can be noticed that the resonant frequencies are slightly moved apart, however the return loss has lower value beyond the rejection band for the model with small dielectric plate, compared to the same parameter for the model with dielectric plate across the entire transverse cross-section [11], [19], [20]. This conclusion is important for the multi-band bandstop filter design using SRRs.

Fig. 12. Comparison of amplitude responses: blue - resonator in Fig. 11 left, red - resonator in Fig. 11 right.

B. Third-Order Dual-Band Waveguide Filter Using SRRs

The resonating inserts in a form of small dielectric plates with SRRs can be used for the multi-band filter design. Herein, third-order dual-band filter is considered, as proposed in [11], [21]. This filter has two center frequencies (f01 = 9 GHz, f02 = 11 GHz), i.e. it has two rejection bands, each of which has a bandwidth of 335 MHz.

Design starts from the third-order filter, with a single center frequency, 9 GHz or 11 GHz. Filter design is based on the Chebyshev approximation. It starts from the lowpass prototype and then the lowpass to bandstop transformation is applied, as explained in [22]. Microwave circuit of the considered filter contains parallel LC circuits, as resonating elements, and waveguide sections representing inverters, connected in series between them. The parameters of the SRRs in the 3D model are tuned to meet the filter specification.

The third-order dual-band filter, with center frequencies f01 = 9 GHz and f02 = 11 GHz, is designed using corresponding SRRs and placing them at the proper positions in the waveguide. Microwave circuit of this filter (Fig. 13) is generated by combining the elements of the circuits for each of the considered filters with a single center frequency. The port impedance is set to Z = 500 ȍ. Actually, this is the value of the wave impedance (ZTE) of the waveguide at the frequency of f0 = 10 GHz, which is the frequency between the considered ones (9 GHz and

11 GHz). The 3D model and the WIPL-D model of the filter are shown in Fig. 14. The inserts are made using RT/Duroid 5880 substrate (İr = 2.2, h = 0.8 mm, t = 0.0018 mm). For each considered center frequency, the SRRs are mutually separated by the distance of Ȝg/4, in order to implement quarter-wave inverters between the resonators. Therefore, the distance between the SRRs with

amplitude responses of the 3D EM model and microwave circuit is shown in Fig. 15. As can be seen, these results match relatively good.

C.Novel Waveguide Resonator with Intersected Inserts

The printed-circuit inserts in the waveguide are usually placed either in the H-plane or the E-plane. However, it is possible to obtain resonating insert by intersecting inserts in these two planes. Herein, novel waveguide resonator, using such insert, with two resonant frequencies is proposed [11], [23]. Thereby, each insert provides a single resonant frequency.

The 3D model of the novel waveguide resonator, with the resonant frequencies of f01 = 9 GHz and f02 = 11 GHz, is shown in Fig. 16a. Printed circuit inserts with SRRs are implemented using RT/Duroid 5880 substrate boards

(İr = 2.2, h = 0.8 mm).

The equivalent microwave circuit of the resonator is generated in software WIPL-D (Fig. 16b). The intersected resonating insert is represented by two parallel LC circuits connected in series. Also, waveguide sections are added between the LC circuits and the ports. The lumped element parameters are calculated using following equations [23]:

where Li denotes inductance, Ci capacitance, Ȧ0i is resonant frequency in [rad/s], B3dBi is 3 dB bandwidth for the i-th rejection band (i = 1, 2), |s11(jȦ0i)| denotes magnitude of s11 parameter at Ȧ0i, Z0i is port impedance, corresponding to the wave impedance of the waveguide at the resonant frequency. The values of the parameters used in these equations are obtained from the amplitude response of the 3D EM model of each individual resonator. The port impedance is set to Z0 = 500 ȍ, which is the value of the wave impedance (ZTE) of the waveguide at the operating frequency of f0 = 10 GHz, as the frequency between the considered ones (9 GHz and 11 GHz).

(a)

(b)

Fig. 14. Third-order dual-band waveguide filter: a) 3D model, (b) WIPL-D model.

Fig. 15. Comparison of amplitude responses: blue - 3D EM model, red - microwave circuit.

Fig. 17. Comparison of amplitude responses: blue - 3D EM model (Fig. 16a), red - equivalent microwave circuit (Fig. 16b).

D.Bandstop Waveguide Filter with QWRs and Coupling Element

Besides the use of SRRs, resonating inserts can be efficiently designed and implemented using QWRs, as proposed in [11], [24], for the H-plane waveguide resonator with multiple resonant frequencies. The bandstop waveguide filters considered so far assume the use of either SRRs or QWRs on the printed-circuit inserts. However, it is possible to use the insert with both types of resonators. Herein, novel second-order E-plane bandstop waveguide filter, with possibility to fine-tune the rejection band, is proposed [11], [25]. The presented design is based on the use of properly shaped QWRs and a coupling element in a form of SRR. For the insert, copper clad PTFE/woven glass laminate TLX-8 (İr = 2.55, tanį = 0.0019, h = 1.143 mm, t = 18 ȝm) is used.

(a)

(b)

Fig. 16. Novel waveguide resonator with intersected inserts: (a) 3D model, (b) equivalent microwave circuit.

Fig. 17 shows comparison of amplitude responses obtained for the 3D EM model and the equivalent circuit. These results match relatively good, thus verifying the equivalent representation of the proposed waveguide resonator.

Fig. 18. Second-order E-plane bandstop waveguide filter using QWRs.

Design starts from the second-order E-plane bandstop filter with center frequency of 10 GHz and the bandwidth of nearly 680 MHz. The 3D model of the filter is shown in Fig. 18. The influence of the distance D between the QWRs on the amplitude response and their mutual coupling is analyzed and the obtained results are given in Table 1. As can be seen, variation of the distance between the QWRs is not critical for the center frequency. However, by increasing the distance between the QWRs, the bandwidth becomes narrower and the coupling coefficient k decreases.

For this filter, the amplitude response is experimentally verified. The photograph of the fabricated insert, placed in the E-plane of the rectangular waveguide, is shown in Fig. 19a. Also, Fig. 19b shows comparison of the simulation and measurement results, which are in good agreement, thus confirming novel filter design.

TABLE 1: THE INFLUENCE OF THE DISTANCE BETWEEN QWRS ON THE AMPLITUDE RESPONSE AND THEIR MUTUAL COUPLING.

(b)

Fig. 19. Experimental verification for the filter shown in Fig. 18: (a) fabricated insert, (b) comparison of amplitude responses: blue - simulation results, red - measurement results.

(b)

Fig. 20. Second-order bandstop waveguide filter using QWRs and coupling element: (a) 3D model,

(b) comparison of amplitude responses: blue - original filter, red - filter with the coupling element.

Starting from the presented second-order E-plane bandstop filter, novel solution for the bandwidth finetuning is proposed. The SRR is added between the QWRs, but it does not act as a resonator and it should not increase

the filter order. Moreover, its resonant frequency is far from the center frequency of the existing filter, so it is used primarily as a coupling element. The 3D model of the filter is shown in Fig. 20a. Comparison of amplitude responses for the original second-order filter and the filter with the coupling element is shown in Fig. 20b. Practically, there is no change of the center frequency, but the rejection band is narrowed for 50 MHz, as a consequence of the insertion of the SRR between the QWRs.

The possibility to fine-tune the bandwidth using SRR is investigated in the following manner. The strip width of the SRR (c) is varied, while the positions of the QWRs remain unchanged (i.e. the distance D = 6.7 mm between them does not change). However, the distance between the SRR and each QWR (D1) varies. In order to analyze the influence of the SRR, the change of the coupling coefficient k is also calculated for each considered case. The obtained results are given in Table 2. As can be seen, variation of the strip width practically does not influence the center frequency, but it introduces small change of the bandwidth, thus providing the possibility for fine-tuning. This is in accordance with the expected role of the SRR. For example, the bandwidth can be narrowed by adding the SRR or changing its strip width, instead of increasing the distance between the QWRs and occupying more space on the insert. Also, by increasing the strip width, the coupling coefficient decreases. For both considered filters, relation between the bandwidth and the coupling coefficient is in accordance with the literature, i.e. they change in the same manner.

TABLE 2: THE INFLUENCE OF THE SRR ON THE AMPLITUDE RESPONSE AND THE COUPLING.

V.CONCLUSION

The novel method for waveguide filter design has been proposed. The use of printed-circuit discontinuities has been considered as a relatively simple solution, providing a lot of possibilities to improve the existing solutions in the area of waveguide filter design.

The novel resonating inserts have been developed using CSRRs, SRRs and QWRs, so multiple resonant frequencies have been obtained with a single insert. Furthermore, these inserts have been used for the higherorder waveguide filter design. Herein, numerous models of the bandpass and bandstop filters have been presented, to illustrate the applicability of the novel method for the filter design. For the bandpass filters, different types of metal and multilayer planar inserts with CSRRs have been considered. The inserts have been modified to meet the requirements regarding inverter implementation for each center frequency. Also, the compact filter with miniaturized inverters has been proposed. Its amplitude

response has been experimentally verified on the laboratory prototype. Novel types of multilayer planar inserts with SRRs and QWRs have been introduced for the bandstop filter design. Various solutions with E-plane and H-plane inserts have been considered. Also, the possibility to employ different types of resonators on the same insert is investigated, resulting in novel approach for bandwidth fine-tuning. The experimental verification for the chosen filter models has confirmed the applicability of the novel method for the waveguide filter design, by a good agreement of the simulation and measurement results.

The solutions presented in this paper are original, they can be easily implemented and experimentally verified. The filters have been designed to operate in the X frequency band, so they can be used in radar and satellite systems, as robust components, able to operate with high power and small losses. They can be even implemented as compact structures, as has been shown. The method can be applied for the other frequency bands as well, by scaling the corresponding dimensions of the structures. Also, the method can be further improved and adapted for the tunable waveguide filter design, which is certainly popular topic in the area of microwave filters.

ACKNOWLEDGMENT

The authors would like to thank the company WIPL-D d.o.o., Belgrade, Serbia, for providing the latest software versions and technical support during the research, free of charge.

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