Substrate Integrated Waveguide Bandpass Filtering with Fourier-Varying Via-Hole Walling

In this article, an optimization-driven methodology is proposed for the design of substrate integrated waveguide (SIW) bandpass filters (BPFs) with predefined passbands. The width between the metallic walls of via-holes is governed by a truncated Fourier series to achieve the desired filtering performance. The theory of rectangular waveguide is used to establish the optimization framework and obtain the series coefficients under predefined physical constraints. Two types of end-terminations are studied; specifically, with and without SIW-to-microstrip transitions. To validate the proposed methodology, two Ku-band BPF prototypes with 2.5% and 5.8% 15-dB fractional bandwidth (FBW) are designed, simulated, and measured. Furthermore, the half-mode SIW (HMSIW) concept is incorporated in one prototype to facilitate a miniaturized physical structure. Simulations and measurements are in close proximity with passband matching and transmission losses better than -15 dB and -2.5 dB, respectively. The proposed methodology allows for designing BPFs with predefined wideband or narrowband FBW by modifying the underlying physical constraints and optimization parameters. The resulting filters are planar, compact, and have wide stopband rejection. In addition, a derivation for the characteristic impedance of the SIW line is provided, which can be used to find the optimum SIW-to-microstrip transition without performing a parametric study.