Abstract
To enhance filter performance in terms of stopband, we propose a wide-stopband substrate-integrated waveguide filter based on the rejection of higher-order modes. The filter establishes the inner and outer coupling windows at the mode’s weakest electric field to achieve mode suppression. Simultaneously, we employ the electromagnetic hybrid coupling theory to analyze the electromagnetic distribution of the particular modes and determine the dimensions of the coupling circular apertures and slits based on the extracted coupling coefficients to attain suppression of the specific modes. The filter successfully suppresses all higher-order modes having resonant frequencies below that of the TE150 mode, as demonstrated by simulation results. We conducted measurements and found that the filter has a center frequency of 4.78 GHz, a bandwidth of 100 MHz with a -3 dB attenuation, and a stopband of -25 dB that extends up to 16.62 GHz (i.e., 3.48 times the center frequency). Simulation and measurement results demonstrate a good correlation. This method, compared to other SIW filters, is easy to design, has a wider stopband range, can be readily applied to practical microwave communication systems, and has potential applications.
1. Introduction
For microwave device design, substrate-integrated waveguide (SIW) is an optimal option because of its high-quality factor, small size, low loss, and low cost. It is extensively utilized in the design of different microwave gadgets, including filters, couplers, diplexers, and antennas [1–7]. Nevertheless, since SIW exhibits inherent multimode resonance characteristics, filters designed using it frequently fall short of providing an adequate stopband width. To solve this issue, researchers have suggested multiple approaches to broadening the stopband of SIW filters.
To enhance the stopband width of the filter, multiple methods have been explored by researchers. In a study mentioned in [8], distinct shapes of SIW cavities were utilized to mitigate harmonic coupling. While this promotes out-of-band rejection performance, it also elevates the complexity of the filter design. Literature [9] suggests using cascaded low-pass filters to widen the filter stopband, but this method results in increased circuit size and loss, which is not ideal for integrating with communication systems. Literature [10] proposes setting the external or internal coupling window at the weakest electric field of a particular mode, but it only suppresses the TE120 higher-order mode. Literature [11] utilized an open/short-filled step impedance resonator to achieve a dual-pass band filter, which possesses a wide stopband width. However, due to the microstrip filter limitations, this method results in increased insertion loss at higher frequency bands. Literature [12] suggests a method for implementing a bandstop filter via dual-radial substrate-integrated waveguide resonant cavities. However, the shape of the filter acquired through this technique is more specialized and challenging to integrate into communication systems. In literature [13], researchers discovered that by etching complementary split-ring resonators (CSRRs) inside the upper surface of a substrate-integrated waveguide, bandstop filters could be achieved. However, when this method is used to extend the stopband width of a bandpass filter, it results in significant insertion loss. In literature [14], the introduction of transmission zeros for harmonic suppression leads to increased out-of-band suppression. However, limiting the number of transmission zeros also limits the expansion of resistance bandwidth. In literature [15], a method for achieving a wide stopband in a filter involves selecting a cavity of a specific size to separate the first harmonic passband from the main mode passband, as well as staggering the higher-order harmonic couplings. However, this approach is constrained by the need for a cavity with a unique aspect ratio, making it suitable only for a narrow range of scenarios. In previous research [16], a multilayer coupling structure was used to create a wide stopband filter, but the filter only achieved a stopband of twice the center frequency, which was clearly inadequate. Subsequent research [17] addressed mode orthogonality by introducing offset port coupling, which was shown to improve stopband range. Nevertheless, the stopband extension range remained limited.
In light of the aforementioned research background, existing filters struggle to attain a well-rounded balance between stopband range, out-of-band rejection level, circuit structure, and design methodology. Therefore, this paper proposes a two-layer structure for a wide-stopband SIW bandpass filter. First, we eliminate higher-order modes (TE120/TE210, TE220, TE230/TE320, TE140/TE410, and TE240/TE420) by positioning the inner and outer coupling windows at the spot with the weakest electric field. Next, using the electromagnetic hybrid coupling theory, we study the electromagnetic distribution of particular modes (TE130, TE310, and TE330) with coupling coefficients. We then design the dimensions of the coupling circular holes and slits rationally. When the levels of electric and magnetic coupling are balanced, the TE130/TE310 and TE330 higher-order modes can be sufficiently suppressed, leading to enhanced filter performance in terms of wider stopband and increased rejection levels. Afterward, we conducted processing and testing of the filter. The experimental results demonstrate high consistency between simulated and measured results, thus confirming the feasibility of the proposed design method.
2. Structure of the Filter
This study employs a substrate-integrated waveguide cavity structure with a double layer, as illustrated in Figure 1. It consists of three metal layers and two dielectric layers. The material used in the dielectric layer is ZYF300CA-P, which has a relative permittivity of 3, a loss tangent of 0.0018, and a thickness of 0.762 mm. The rectangular-shaped substrate-integrated waveguide cavity comprises two resonant cavities in each layer, as shown in Figure 1, labeled 1, 2, 3, and 4. The upper layer features resonant cavities 1 and 4, whereas the lower layer includes resonant cavities 2 and 3. Each resonant cavity is rectangular and operates in TE110 mode. The energy coupling between cavities no. 1 and no. 2 and no. 3 and no. 4 is through circular holes and gaps etched in the middle metal layer. Between cavities no. 2 and no. 3 in the lower layer, energy coupling occurs through a window at the center of the common edge. The input and output ports are placed in the middle of the sidewalls in resonant cavities no. 1 and no. 4, respectively. Both of them utilize coplanar waveguides to facilitate the energy coupling between the source or load and the filter. The shape of the metal layer of the filter is shown in Figure 2. Following simulation optimization through the HFSS software, the filter’s ultimate structural parameters are listed in Table 1.
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3. Filter Design and Principle Analysis
3.1. SIW Resonant Cavity Theory
The SIW is a novel waveguide-like construct that exhibits electromagnetic field transmission characteristics similar to those of a rectangular waveguide. Nevertheless, the sidewalls of the SIW contain metallized through holes arranged in a periodically spaced pattern. This arrangement truncates the current that propagates along the longitudinal direction, generating a radiation effect. Thus, the transmission of the transverse magnetic wave TMmn0 mode is not possible in the SIW. In contrast, the transverse electric wave TEmn0 mode has solely a magnetic field component in the direction of longitudinal propagation, with no electric field component. Hence, the SIW rectangular resonant cavity can solely transmit TEmn0 modes, and the frequency equation for resonance is as follows: where is the speed of light in a vacuum, is the dielectric constant of the dielectric substrate, and are the number of modes along the width and length directions, respectively, and and are the equivalent width and length of the SIW structure, which are defined as follows: where the center distance between two rows of circular holes on the wide side of the cavity is denoted by , the center distance between two columns of circular holes on the long side of the cavity is denoted by , the diameter of the circular holes is denoted by , and the circumcentric distance between adjacent circular holes is denoted by .
In this design, the filter operates in the 5G n79 band. Therefore, the initial resonant frequency of the TE110 mode is assumed to be 4.75 GHz by setting mm and mm. The cavity dimensions can then be initially calculated following Eqs. (1) and (2).
It is widely acknowledged that SIW resonant cavities possess an infinite number of resonant modes. In comparison to similar microwave filters, the harmonic passbands of the SIW are situated closer to the main mode passbands, which consequently restricts the stopband. To broaden the stopband range of the SIW filter, it is essential to suppress additional higher-order modes. The TE modes in the SIW rectangular resonant cavity occur in the following order as frequency increases: TE110, TE120/TE210, TE220, TE130/TE310, TE230/TE320, TE140/TE410, TE330, TE240/TE420, and so forth. Table 2 displays their corresponding resonant frequencies. In order to achieve the wide stopband performance of the SIW filter, it is necessary to suppress the higher-order modes based on their resonant frequencies, from low to high.
3.2. Analysis of Suppression Methods for Modes
The study employs a methodology of establishing external excitation ports and internal coupling windows at the weakest electric fields of specific modes in the SIW resonant cavity to fundamentally suppress the resonant coupling of higher-order modes. External excitation ports and internal coupling windows are located at the center of the sidewalls, i.e., at a and b in Figure 3. This design not only ensures the strongest magnetic coupling of the TE110 mode but also effectively suppresses other modes such as TE120/TE210, TE220, TE230/TE320, TE140/TE410, and TE240/TE420. The input port is positioned at the center of the resonant cavity sidewalls, preventing the excitations of TE120, TE220, TE320, TE140, and TE240/TE420 modes in the resonant cavity 1. The coupling window located at the sidewall’s center suppresses the coupling of the TE210, TE220, TE230, TE410, and TE240/TE420 modes between the resonant cavity 2 and the resonant cavity 3. However, electromagnetic hybrid coupling theory is necessary to suppress the coupling of the TE130/TE310 and TE330 modes.
When only electrical or magnetic coupling exists between the two resonators, the coupling coefficient “” can be determined by using the following equation: where and represent the odd-mode and even-mode resonant frequencies, respectively, that are generated when the two resonators are coupled. If there is both electric and magnetic coupling between two resonators, the total coefficient of coupling can be expressed through the following equation: where is the magnetic coupling coefficient, which has a positive value, and is the electric coupling coefficient, which has a negative value. Suppression of a mode can be achieved by introducing equal amounts of electric and magnetic coupling into the coupling of the two resonators so that the total coupling coefficient is approximately zero.
Based on the theory presented above, a coupling structure was designed in the SIW cavity (as shown in Figure 4) according to the electromagnetic field distribution of the TE130/TE310 and TE330 modes. The coupling structure includes one coupling circular hole located at the center of the cavity and four coupling slits symmetrically distributed in the center. The coupling circular hole has a diameter of , and the coupling slits have a width of . To achieve independent control over the degree of suppression of the TE130, TE310, and TE330 modes, distinct lengths are assigned to the coupling slits. Furthermore, the coupling structure between the resonant cavities of no. 1 and no. 2 is designed to suppress the TE130 and TE310 modes, while the coupling structure between resonant cavities no. 3 and no. 4 is intended to suppress the TE330 mode.
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In the distribution of electromagnetic fields in a resonant cavity, the magnetic field is weaker in areas where the electric field is stronger and stronger in regions where the electric field is weaker. Using the TE130 mode as an illustration, the circular orifice with diameter , along with the upper and lower pair of slits with length , are strategically situated where the electric field is more potent to establish an electrical coupling. Conversely, the left and right pairs of slits with length are positioned where the electric field is weaker and the magnetic field is stronger to facilitate magnetic coupling. When appropriate values for , , and are selected, the electric and magnetic couplings can be balanced, resulting in a total coupling coefficient of 0 for the TE130 mode and effectively suppressing it. This approach can also be extended to suppress the TE310 and TE330 modes.
Based on the electric field distribution of the TE130, TE310, and TE330 modes, a simulation model was created using HFSS software to obtain the mode coupling coefficients, as depicted in Figure 5. The simulation model was used to extract the coupling coefficients for the TE130, TE310, and TE330 modes, thereby confirming the feasibility of the electromagnetic hybrid coupling method. To ensure the optimal transmission performance of the primary TE110 mode within the passband, was set to 4.4 mm. Figure 6 depicts the influence curves resulting from changes in and on the coupling coefficients of TE130 modes extracted through simulation. The data suggests that , the coupling coefficient of the TE130 modes, is primarily influenced by changes in , with a comparatively smaller impact by changes in . This is due to the fact that the electric coupling of the TE130 mode is mainly provided by the circular hole located in the center of the cavity (the strongest electric field), and the electric field strength at the gap of length is much smaller compared to that at the circular hole, so the influence of the change of on the coupling coefficient is relatively small, while the magnetic field at the gap of length is the strongest, and the change of which results in a larger change of the magnetic coupling. When is set at 2.6 mm, the electric and magnetic couplings become nearly equal, resulting in a minimum value for the total coupling coefficient (). Figure 7 shows the influence curve of and on the coupling coefficient of TE310 mode. It can be seen that the coupling coefficient () of TE310 mode is mainly affected by the change of , and the change of has a smaller influence on it for the same reason as mentioned above. The reaches its minimum value when . Figure 8 displays the impact of the variation in on the coupling coefficient of TE330 mode. It is evident that attains its minimum value at mm.
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The SIW filter design, utilizing the electromagnetic hybrid coupling suppression method, enables targeted mode suppression, resulting in a wider stopband for the filter. Additionally, the coupling level of the filter can be flexibly controlled, allowing for adjustable filter bandwidth.
4. Results and Discussion
Figure 9 illustrates a comparison between the filter S-parameters obtained through simulation by solely utilizing the electric coupling of round holes between the no. 1 and no. 2 resonance cavities and between the no. 3 and no. 4 resonance cavities and the S-parameters obtained via simulation employing the electromagnetic hybrid coupling method in this particular design. When using only the electric coupling of round holes, it is evident that the weakest electric field method is efficient in suppressing higher-order modes. The TE120/TE210, TE220, and TE140 modes can be suppressed better by the weakest electric field method, while the TE230/TE320, TE410, and TE240/TE420 modes are not sufficiently suppressed. The higher-order modes TE130/TE310 and TE330 exhibit a stronger output currently, as they cannot be suppressed by the weakest electric field method. However, using the electromagnetic hybrid coupling method improves the suppression of not only the TE130/TE310 and TE330 higher-order modes but also the TE230/TE320, TE410, and TE240/TE420 higher-order modes. The preceding findings support the efficacy of the electromagnetic hybrid coupling technique for targeted suppression of higher-order modes and enhancement of the filter stopband width.
Based on the dimensions listed in Table 1, the physical filter was processed by the PCB process, and the two layers of SIW cavities were mounted by screws to press the gap between the upper and lower cavities to prevent the leakage of electromagnetic energy. The physical filter is shown in Figure 10. To conduct the physical examination, solder SMA-KHD coaxial connectors on the filter’s input and output ports and connect them to an Agilent E8363C model network vector analyzer for measurement. Figure 11 displays the simulated and measured S-parameters of the filter. The measured and simulated S-parameter curves display overall consistency, revealing a center frequency of 4.78 GHz, a bandwidth of 100 MHz at -3 dB, and a stopband at -25 dB that can be extended up to 16.62 GHz (i.e., 3.48 times the center frequency). The simulation exhibits an insertion loss of approximately -0.47 dB in the passband, while the measured insertion loss is 0.8 dB lower than the simulated value. Processing error, dielectric loss, and conversion structure loss are the primary reasons for the discrepancy between the measured and modeled values.
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Table 3 presents a comparison of our proposed filter’s performance with the SIW filters in the references. The filter proposed in this paper shows significant advantages in terms of insertion loss and blocking bandwidth, and the design methodology used is simple and easy to implement. Additionally, the filter employs a cascade structure that results in a more compact design for seamless integration into the communication system.
5. Conclusions
To enhance the filter’s stopband performance, this paper proposes a wide-stopband filter for substrate-integrated waveguides that rejects higher-order modes. The filter effectively suppresses the mode by placing the inner and outer coupling windows at the mode’s weakest electric field. Meanwhile, the paper presents the applications of electromagnetic hybrid coupling theory in analyzing the electromagnetic distribution of specific modes and in designing the size of coupling circular holes and slots based on the extracted coupling coefficients to achieve specific mode suppression. The results demonstrate that the filter center frequency is 4.78 GHz, with a -3 dB bandwidth of 100 MHz and an extended -25 dB stopband of 16.62 GHz (i.e., 3.48 times the center frequency). All higher-order modes with resonant frequencies below the TE150 mode’s resonant frequency are effectively suppressed by the filter. Compared to other SIW filters, this approach features a simple design and a broader stopband range. It can be easily implemented in real-world microwave communication systems and has promising applications.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that there is no conflict of interest regarding the publication of this paper.
Acknowledgments
This work is supported by the Chongzuo Science and Technology Program Project (No. 2023ZC025654), the School-level Research Project of Guangxi Minzu Normal University (No. 2022SP007), the first batch of the 2021 Industry-University Cooperation Collaborative Education Project of the Department of Higher Education, Ministry of Education (No. 202101139002), the Basic Research Ability Improvement Project for Young and Middle-aged Teachers in Guangxi Universities (No. 2023KY0793), and the Guangxi Natural Science Foundation (No. 2022JJB150010).