Synthesis Design of Inductively-Coupled 3-D Bandpass Frequency-Selective Structures Based on Equivalent SOL-Extracted Circuit Model

Abstract

In this article, an accurate and unified synthesis method for a class of 3-D bandpass frequency-selective structures (FSSs) is proposed. Each element of the presented 3-D FSSs is composed of stacked planar slotline sections cascaded with inductively coupled structures. Here, each inductively coupled structure is modeled as an equivalent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> -inverter, and each stacked slotline section is regarded as an equivalent transmission-line resonator. By defining three ideal calibration standards, i.e., short circuit, open circuit, and matched load in a commercial electromagnetic full-wave simulator, a numerical short-open-load calibration technique is utilized to effectively extract all the equivalent circuit parameters involved in the presented 3-D FSS. Furthermore, a generalized synthesis design procedure is presented by mapping the proposed 3-D FSS topology onto an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> th-order bandpass filtering network. To verify the feasibility of this design concept, two groups of design examples, including a single-polarized third-order Chebyshev bandpass FSS and two dual-polarized second-order ones, are, respectively, synthesized and designed. Finally, two prototypes of the designed 3-D FSS examples are fabricated, assembled, and then tested by using a free-space measurement method. The measured results exhibit good agreement with the predicted ones. The proposed 3-D FSSs feature simple topologies with high-order bandpass filtering responses and stable filtering responses under a large variation of incident angles of spatial waves.