Compact half-mode substrate integrated waveguide bandpass filters with capacitively loaded complementary single split ring resonators

A novel compact half-mode substrate integrated waveguide (HMSIW) filter with capacitively loaded complementary single split ring resonators (CSSRRs) is presented in this article.The proposed structure demonstrates lower resonant frequency and enhanced miniaturization compared to the HMSIW with conventional CSSRRs due to the additional capacitance generated by an additional conductor connected to the inner metal disk and overlaid across the ground plane of the CSSRR. Even lower resonant frequency and greater miniaturization can be achieved conveniently by increasing the area of the overlap or using thin dielectric substrate and the technique can readily be realized in a range of multilayer technologies. The equivalent circuit model for the proposed structure of the HMSIW with the capacitively loaded CSSRR is derived and a second-order bandpass filter with the proposed structure, operating at 4.92 GHz, is designed and fabricated. Excellent agreement is achieved between the simulation and the measurement. The proposed HMSIW filter with capacitively loaded CSSRRs shows good selectivity, low loss, and compact size, with the total size being only 9.8 × 7 mm² (0.17 λ₀ × 0.115 λ₀) without the feed lines.