Ⅰ. Introduction
1. Introduction
The rapid development of wireless communication systems has led to an increasing demand for high-performance bandpass filters with sharp frequency selectivity, compact size, and wide stopbands (Krishna and Mukherjee, 2021;Shen et al., 2010). These filters are crucial for suppressing unused signals and ensuring clear and efficient communication (Shen, 2018;Wang et al., 2024). Substrate integrated waveguide (SIW) technology, realized using planar dielectric substrates with linear arrays of metallic via-holes, offers several advantages such as low cost, high Q-factor, and easy integration with other planar circuits (Feng et al., 2021;Lin and Dong, 2022). However, the large area of traditional SIW filters poses a challenge for high-density integration (Wang et al., 2024;Liu et al., 2023).
To address this issue, half-mode SIW (HSIW) structures have been introduced to achieve miniaturization while maintaining performance (Zhu et al., 2021;Pelluri and MV, 2020). The HSIW structure reduces the size of the filter by utilizing only half of the mode volume of a full SIW cavity (Tang et al., 2022;Wu et al., 2023). Furthermore, the incorporation of a co-planar strip (CPS) resonator and T-shaped slot in the HSIW cavity provides additional degrees of freedom in filter design to achieve better frequency selectivity and a wide stopband.
In this paper, we propose a novel design of a compact HSIW bandpass filter that combines the benefits of HSIW, CPS resonator and T-shaped slot. The filter is designed to operate at a center frequency of 3.8 GHz with a bandwidth of 0.4 GHz. The T-shaped slot and half-wavelength CPS resonator contribute to the compact size and enhanced frequency selectivity, realizing two transmission zeros at 2.95 GHz and 4.75 GHz. The wide stopband characteristic, extending up to 6.0 GHz with a 30 dB rejection level, is achieved due to the different harmonic resonant frequencies of HSIW, CPS, and T-shaped slot. This feature is particularly important for suppressing unwanted signals and harmonics in communication systems.
The filter was designed using electromagnetic simulation software (Ansys HFSS) and fabricated on a Taconic TLX-8 substrate with a relative permittivity of 2.55 and a thickness of 1 mm. The measured S-parameters of the fabricated filter are in good agreement with the simulated results, validating the design approach. The proposed filter achieves a compact size of approximately 26.0 × 48.8 mm², making it suitable for integration into compact communication devices.
Ⅱ. Configuration and design methods
1. Design of HSIW Filter
<Fig. 1> shows the physical structure of the proposed HSIW filter, and the corresponding coupling topology is shown in <Fig. 2>. An explicit expression is provided to establish the relationship between the coupling elements and the transmission zero Ω, offering insights into the control of the transmission zero in the doublet filter configuration (Liao et al., 2007)
where Ms1 and Ms2 represent the external coupling coefficients of the nodes 1 and 2, respectively, and M23 is the coupling coefficient between the nodes 2 and 3. The locations of two transmission zeros are contributed to the sign of Ms12 -Ms22. When Ms12 -Ms22＞0, two transmission zeros can be realized. According to the coupling scheme shown in <Fig. 2a>, two transmission zeros located in the upper and lower stopbands can be obtained in the HSIW filter to enhance frequency selectivity. The center of the filter passband is at 3.8 GHz, and the bandwidth is 0.4 GHz. It is well established that the magnetic field reaches its maximum around the via-holes in the HSIW cavity. Furthermore, the magnetic field of the half-wavelength CPS achieves a minimum at its open ends. Consequently, coupling occurs between the T-shaped slot and the HSIW cavity, whereas no coupling is observed between the half-wavelength CPS and the HSIW cavity. <Fig. 2b> illustrates the equivalent circuit model of the proposed HSIW filter, which is employed to characterize its overall performance. In this model, the inductance Ld and capacitance Cd represent the metallic holes, while the series Lc and Cc correspond to the patch of SIW. Additionally, Lr and Cr denote the T-shaped slot, and Cx presents the mutual coupling capacitance.
All the elements of the HSIW filter are fine-tuned by EM simulator (Ansys HFSS), and the final parameters are optimized. <Fig. 3> shows the simulated S-parameters, where the value of the reflection coefficient S11 remains below -18.0 dB, and the transmission coefficient S21 is within -1.5 dB. The total electric field distribution of HSIW filter at 3.8 GHz are plotted in <Fig. 4>, and it is concentrated around the T-shaped slot, half-wavelength CPS and the center of SIW cavity. Their sizes are mainly used to control the performance of the filter.
<Fig. 5> shows the simulated S21 parameters with different values of g. As shown in <Fig. 2>, MS1 is implemented by the coupling between the probe and half-wavelength CPS. The coupling MS1 becomes larger with smaller g, and then, bandwidth will get wider. Meanwhile, the transmission zeros below and above the passband will move to lower frequency.
2. Prototype and experimental results
The HSIW filter was fabricated on Taconic TLX-8 with relative permittivity and thickness is 2.55 and 1 mm, loss tangent is 0.0019, respectively. As shown in <Fig. 5>, the area of filter without feed lines is around 26.0 × 48.8 mm2. The diameter of the via-holes is 1 mm, and the horizontal and longitudinal pitches between adjacent via holes are 2 and 2.05 mm, respectively.
The measured S-parameters of HSIW filter are shown in <Fig. 6>. The measured center frequency of passband is around 3.8 GHz, and the filter has 25 dB rejected level up to 6.0 GHz.. Minimum insertion loss in the passband is 1.15 dB, 0.43 dB larger than the simulated one, which is mainly due to the loss of connectors. Return loss better then 11 dB in the passband is realized. There are two transmission zeros appeared at 2.87 and 4.72 GHz.
Ⅲ. Conclusion
In this paper, a compact half-mode substrate integrated waveguide (HSIW) bandpass filter with a wide stopband has been demonstrated. The design integrates a CPS resonator and a T-shaped slot on the top metal surface, effectively achieving miniaturization while enhancing frequency selectivity. The wide stopband characteristic is attributed to the distinct higher-order resonant frequencies of the HSIW, CPS, and the T-shaped slot. The proposed filter was designed, fabricated, and experimentally validated. The measured S-parameters exhibit good agreement with the simulated results. The filter operated at a center frequency of 3.8 GHz with a bandwidth of 0.4 GHz and exhibits two transmission zeros at 2.95 GHz and 4.75 GHz, ensuring a rejection level of 30 dB up to 6 GHz. These characteristics show the effectiveness of the proposed approach in achieving high-frequency selectivity and wideband suppression, enhancing its capabilities in future wireless communication applications.
