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Effect of Various CSRR Meta-resonator Geometries on the Bandwidth of C- band Waveguide Filters
Conference Paper · October 2023
DOI: 10.1109/ASYU58738.2023.10296556
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2023 Innovations in Intelligent Systems and Applications Conference (ASYU) | 979-8-3503-0659-0/23/$31.00 ©2023 IEEE | DOI: 10.1109/ASYU58738.2023.10296556
Effect of Various CSRR Meta-resonator Geometries on the Bandwidth of C-band Waveguide Filters
Abdullah GENC
Department of Mechatronics Engineering Isparta University of Applied Sciences Isparta, Türkiye abdullahgenc@isparta.edu.tr
Abstract—Recently, split ring resonator (SRR) or complementary split ring resonator (CSRR) meta-resonator structures have been widely used in waveguide filter designs. These waveguide filters with meta-resonator have some advantages over conventional waveguide filters using iris and post as follows: easy to make the equivalent circuit model, a wide range of applications, miniaturization, and low cost. In this work, the bandwidth impact of three widely used CSRR metaresonator structures with different geometries (ring, rectangular, and crescent shapes) is investigated at C-band. The analyses are performed numerically in CST Microwave Studio (MWS) and Rogers 5880 is used as a substrate. According to the results, the narrowest band design is the rectangular-shaped filter while the widest band design is the crescent-shaped filter.
Keywords— waveguide filters, meta-resonators, complementary split ring resonator (CSRR), C-band
I. INTRODUCTION
Filters that are indispensable components of communication equipment are frequency-selective circuit elements that select/suppress the desired and/or unwanted frequency components of the input signals and transfer them to the output. There are various types of filters (Butterworth, Chebyshev, Bessel or Elliptic-Cauer) with mathematically different functions. The Butterworth filter has as flat frequency response as possible in the bandpass region, whereas the frequency characteristic of the Chebyshev filter is more undulating in this region. The Butterworth filter has a flatter bandpass region than the Chebyshev and Elliptical filters, but higher-order designs are needed for a sharper transition to the stop band region. Ideally, all filter types should have a sharp transition. Sharp transitions require an increase in the order of the designed filter and therefore a more complex (multilayer) structure. This not only increases the design and manufacturing costs but also introduces additional losses in the circuit. Chebyshev filters are generally preferred in filter designs where a sharp transition is required [1, 2].
In normal circuit technology, filters are designed using lumped elements such as R, L, and C. In radio frequency and microwave circuits, filters are designed using structures such as microstrip and waveguides. Waveguides are rectangular or circular hollow metal structures, which are widely used especially in the high-frequency region due to their highpower handling capacity and low loss characteristics. However, the disadvantage of this type of waveguide filter is its large physical size at low frequencies. Waveguide filters, which have an important role in communication systems in sectors such as agriculture, defense, security, and telecommunications, have been extensively studied in the literature in terms of compactness, low cost, power carrying capacity, weight, operating frequency region, thermal stability, etc. [3-5].
Habib DOGAN
Department of Information Systems and Technology
Mehmet Akif Ersoy University
Burdur, Türkiye hdogan@mehmetakif.edu.tr
Different design techniques have been developed for waveguide filter construction in the microwave and millimeter-wave frequency region. In traditional waveguide filter applications, metal irises and posts are added to the waveguide, while in some new applications, substrateintegrated circuits (SICs) are designed on the substrate to eliminate the size disadvantage [6]. The disadvantages of conventional waveguide filters are their electrically large size, difficulty in manufacturing, cost, and the need for separate filters for applications requiring different bandwidths and filter orders. In order to overcome these disadvantages, recently, designs having meta-resonator structures (due to their unique, unnatural electromagnetic properties) inside the waveguide have started to be used [7, 8]. These metaresonator structures enable the creation of a spatial microwave filter within the waveguide and further miniaturization of the dimensions. The number of meta-resonators to be added in the waveguide corresponds to the order of the filter due to the cascade circuit. That is, the number of meta-resonators in the waveguide determines the order of the designed filter. In this way, it is possible to obtain filters of the desired degree by increasing the number of meta-resonators [9]. In the study in the literature, a bandpass filter for a rectangular waveguide was designed using CSRR. By varying different geometrical parameters of the CSRR, the resonant frequency, bandwidth, and quality factor (Q) are investigated, and a filter with a pass band of 2 GHz (11.6-13.6 GHz) is proposed with the appropriate selection of the relevant parameters [10].
Moreover, split ring resonators (SRR) and complementary split ring resonators (CSRR), a type of meta-resonator structure, play an important role in microwave filter design. SRR and CSRR meta-resonator structures can be used in waveguides as band-stop and bandpass, respectively [11]. Also, there is a need for designs of waveguide filters that exhibit both narrowband and broadband characteristics. Narrowband designs are used in applications requiring noise suppression and higher sensitivity, while wideband designs are preferred in applications where more power transfer is required [12]. Although there are intensive X-band studies in the literature, C-band applications are almost non-existent. In this study, the effect of three widely used CSRR metaresonator structures with different geometries (ring, rectangular and crescent-shaped) on the bandwidth is numerically investigated at C-band.
II. DESIGN OF CSRR META-RESONATORS FOR C-BAND
APPLICATIONS
The advantages of waveguide filters designed using CSRR structures compared to conventional filters can be summarized as follows: easy to obtain the equivalent circuit model, various application areas, miniaturization, and low cost. Different geometrical structures of the meta-resonator
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(ring, rectangle, and crescent) affect the bandwidth to be narrow or wide. Even if it is not possible to tune the desired bandwidth, narrow/medium/wideband designs can be made by changing the geometry type. The frequency response of a typical bandpass filter and various filter types are given in Figure 1. Depending on the filter bandwidth, the quality factor is given in (1).
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In Figure 1, f0 is the operating frequency and BW3dB is the desired bandwidth. The frequency response of a typical bandpass filter is given in Figure 1a. Here, f1 and f2 are the lower and upper cut-off frequencies respectively. Also, f3 and f4 indicate the stop bandwidth. In the design of a bandpass and stopband filter, the characteristics of the filter such as center frequency, bandwidth, filter type, return loss and insertion loss, quality factor must primarily be determined. The sharpness of the transition between the pass-band and the stopband of the filter determines the order (n) of the filter. The higher the order of the designed filter is, the higher both the cost and the performance of the filter is [13].
capacitance and inductance in the transmission line. On the other hand, based on the duality theorem and Babinet's principle, CSRR structures can also be used as bandpass filters [14]. The design parameters of the CSRR resonators designed in the C band are given in Table 1. In all designs, Rogers 5880 plate is used as substrate due to its low loss.
Fig. 1. a) Frequency response of a typical bandpass filter, b) various filter types
Furthermore, Figure 2 shows both the shapes and the equivalent circuit models of various CSRR meta-resonators such as ring, rectangular, and crescent. The equivalent circuit model of each of the meta-resonators, as well as the SRRs, can be represented by a parallel LC circuit. The dielectric and conductive (copper) materials are colored green and orange respectively in Figure 2. The circuit model of SRR elements can be used to design band-stop filters with parallel
Fig. 2. Various CSRR meta-resonators such as ring, rectangular and crescent and equivalent circuit models
TABLE I. |
DESIGN PARAMETERS OF CSRR META-RESONATORS FOR |
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C-BAND APPLICATIONS |
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CSRR resonator |
Parameters |
Dimensions |
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types |
(mm) |
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d |
2 |
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Ring shape |
c |
1.19 |
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r1 |
6 |
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r0 |
4.81 |
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l |
2.978 |
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g |
2.67 |
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Rectangle shape |
w |
11.289 |
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c1 |
0.816 |
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c2 |
0.816 |
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G1 |
2.6 |
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Crescent shape |
G2 |
1 |
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R0 |
8.5 |
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R1 |
9.75 |
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The rectangular waveguide in which the CSRR resonators will be placed is WR-159, suitable for the C band. The waveguide is filled with air and the internal dimensions are b (20.193 mm) × a (40.386 mm). The cutoff frequency (fc) for TE10 mode is calculated by (2) and the waveguide operates within this range of 1.25 fc < f < 1.89 fc. The wavelength inside the guide (λg) is obtained by (3). Here, λ0 is the wavelength at the center frequency of 6 GHz.
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Authorized licensed use limited to: Isparta Uygulamali Bilimler University. Downloaded on November 01,2023 at 12:10:59 UTC from IEEE Xplore. Restrictions apply.
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III. SIMULATION RESULTS
All simulations are performed with the CST Microwave Studio (MWS) program. Simulation setup and boundary conditions are given in Figure 3. Boundary conditions are chosen to be open (add space) in the wave propagation direction and perfect electric conductor (Et = 0) in other directions. In addition, the performance results of the metaresonators are improved by using the "parametric sweep" features of the simulation program. Frequency solver is preferred as the solver type which uses Finite Element Method (FEM) in order to solve the Maxwell's equation.
Fig. 3. Simulation setup and boundary conditions
The frequency response of the CSRR structured waveguide filters for a center frequency of 6 GHz is given in Figure 4. In this study, three different bandwidth bandpass filters are designed using different meta-resonator geometries (rectangular, ring and crescent). According to the results obtained, the bandwidths of rectangular, ring, and crescentshaped structures are 106 MHz (BWrect = 1.8%), 338 MHz (BWring = 5.7%), and 1143 MHz (BWcresc = 11.8%), respectively. According to (1), the bandwidth and quality factor are inversely proportional and the quality factor for the first order filter (n = 1) with a center frequency of 6 GHz are 55.55, 17.54, and 8.45, respectively. Furthermore, the insertion losses of the rectangular, ring, and crescent-shaped filters are found to be |S21| ≥ - 0.67 dB, |S21| ≥ - 0.53 dB, and |S21| ≥ - 0.47 dB, respectively. The performance comparison of the three waveguide filters is given in Table 2. According to these results, the rectangular/ring and crescent geometries are recommended for narrow/medium and wideband applications, respectively. It should be noted that the reason for the wide bandwidth of the crescent geometry filter is because of the equivalent circuit model.
Fig. 4. Frequency response of CSRR waveguide filter with different geometries for the center frequency of 6 GHz
TABLE II. |
PERFORMANCE COMPARISON OF THREE WAVEGUIDE |
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FILTERS WITH RECTANGULAR, RING, AND CRESCENT-SHAPED |
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META-RESONATOR |
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CSRR |
Bandwidth |
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Quality |
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resonator |
S-parameter |
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factor (Q) |
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types |
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Rectangle |
%1.8 |
|S21| ≥ - 0.67 dB |
55.55 |
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shape |
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Ring |
%5.7 |
|S21| ≥ - 0.53 dB |
17.54 |
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Crescent |
%11.8 |
|S21| ≥ - 0.47 dB |
8.45 |
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shape |
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Fig. 5. Parametric analysis of three types of waveguide filters depending on the geometry a) for Ring shape, b) for Rectangular shape, and c) for Crescent shape
Authorized licensed use limited to: Isparta Uygulamali Bilimler University. Downloaded on November 01,2023 at 12:10:59 UTC from IEEE Xplore. Restrictions apply.
The Parametric analysis of three types of waveguide filters depending on the geometry are given in Figure 5. When Figure 4a is examined, while the effect of d and c parameters of Ring shape on the operating frequency is low, ri and r0 parameters have a greater effect on operating frequency. On the other hand, In Figure 4b, four parameters (l, g, w, c1) of Rectangular shape has a significant effect on the center frequency. As the g parameter increases, f0 increases. Lastly, In Figure 4c, other parameters except G1 affect f0 value to a certain extent. While G2 parameter is directly proportional to f0, R0 and R1 parameters are inversely proportional to f0. As a result, the reason for the difference between the bandwidth of the structures is that equivalent circuit models of three CSRR meta-resonators are different.
IV. CONCLUSIONS
In this study, three different waveguide filters with rectangular, ring, and crescent shapes in the C band are designed and simulation results are compared with each other. The results show that rectangular waveguide filters should be used in applications requiring narrowband noise suppression. Crescent-shaped waveguide filters should be preferred in wideband applications where more power transfer is required. The equivalent circuit model of a single-designed metaresonator behaves as a parallel LC. The resonant frequency of these LC circuits depends on the proper choice of their geometrical dimensions. Besides, high-frequency microwave resonant circuits behave like RLC elements at low frequencies, which can be excited by an external magnetic source. In future work, designs that allow both frequency shifting and variable filter orders will be physically realized.
ACKNOWLEDGMENT
This study is carried out within the scope of the project numbered 123E108 supported by TUBITAK (The Scientific and Technological Research Council of Türkiye)
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