Designing the Width of Substrate Integrated Waveguide Structures

A new formula for the effective width design of substrate integrated waveguide (SIW) structures is presented. Contrary to another formulation of similar accuracy, which requires an iterative process or solution of a fifth-order polynomial, the new equation allows the direct design of the SIW's width for a given cutoff frequency. The presented formula is obtained by minimizing the reflections from the junction between the SIW and an all-dielectric waveguide of equivalent width. A mode-matching approach is used to derive the equation which is verified by comparison with μWaveWizard for three SIW examples. Further optimizations in CST Microwave Studio and μWaveWizard demonstrate the robustness of the new formula.