Optimal Basis Functions in the Electromagnetic Analysis of Inductive Irises Accounting for Meixner’s Edge Condition
DOI:
https://doi.org/10.64915/RADAP.2026.105.%25pKeywords:
electromagnetic modeling, mode-matching technique, integral equations, iris, rectangular waveguide, field distribution, basis functions, Gegenbauer polynomials, convergence, residual error, waveguide componentsAbstract
Inductive irises are fundamental components widely applied in modern microwave filters, diplexers, polarizers, and rotators based on waveguides, as their precise electromagnetic characterization is crucial for high-performance device design. This paper presents a rigorous and comprehensive numerical investigation of the optimal selection of basis functions for the electromagnetic analysis of such irises using a hybrid mode-matching and integral equation technique. The study focuses on a comparative analysis of three distinct types of basis functions used to represent the aperture field: classical trigonometric functions, orthogonal basis functions based on Gegenbauer polynomials with a weighting function of power 1/2, and those with a weighting function of power 2/3. A key contribution of this work is the explicit demonstration that incorporating Meixner’s edge condition through the use of Gegenbauer polynomials with a weighting function of power 2/3 significantly accelerates convergence rate and improves the numerical stability of the solution. The convergence of reflection coefficient solutions is analyzed in detail, revealing that the indicated set of basis functions outperforms other sets across various iris geometries. Specifically, it is established that to achieve a residual calculation error of less than 0.5%, it is sufficient to utilize only 4 such basis functions, whereas 10 functions are required for Gegenbauer polynomials with a weighting function of power 1/2, and up to 40 functions are necessary when using trigonometric expansions. Furthermore, the paper investigates the influence of the iris window's physical dimensions, such as thickness and width, on the effectiveness of these basis functions. In addition to the convergence study, detailed amplitude distributions of the electric field within the iris window and adjacent regions are analyzed for narrower and wider windows. These distributions confirm the high physical fidelity of the model, particularly its ability to accurately capture field singularities at the sharp metallic edges. The numerical results show that at a distance of a quarter-wavelength from the inductive iris in a rectangular waveguide, the relative amplitude of the electric field of the fundamental electromagnetic mode TE10 exceeds the amplitudes of the electric field of the evanescent higher-order modes by more than 28 times. The developed mathematical model with optimal basis functions and the recommendations provided can be widely applied for the efficient computer-aided design and optimization of iris-based waveguide components such as filters, diplexers, polarizers, and rotators.
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