Complete Modal Analysis of Planar Waveguide Junctions With a 2-D Hybrid FEM/Leontovich Framework Including Conductor Losses

A scalar 2-D finite-element-method (FEM) framework is presented for planar waveguide junctions enclosed by a non-perfect conductor, considering its complete modal spectrum at its rectangular waveguide ports. Separate formulations are first derived for the general <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {TM}^{z}$</tex-math> </inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {TE}^{z}$</tex-math> </inline-formula> modal excitations, which are combined through a modal basis transformation. Conductor losses are embedded through the Leontovich boundary condition with minimal overhead. One additional matrix is required for lateral-wall losses under <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {TM}^{z}$</tex-math> </inline-formula> excitation, while two are needed under the more involved <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {TE}^{z}$</tex-math> </inline-formula> excitation, for which specific vector test functions are introduced to maintain the scalar nature of the problem with lateral-wall losses. Lid-wall losses are captured by a perturbation method, leaving the algebraic stencil untouched. Because the analysis remains strictly 2-D, benchmarks on transformers, filters, bends, and diplexers demonstrate run-times noticeably shorter than 3-D FEM-based commercial software, while retaining full-wave accuracy.