A Closed-Form Formula for Dispersion Characteristics of Fundamental SIW Mode

An accurate closed-form formula is derived from an analytical method to calculate dispersion properties of the substrate integrated waveguide (SIW). The derived equation which is a function of geometrical parameters is used to accurately estimate the cutoff frequency of the dominant mode at a low leakage condition. The unit cell of an SIW can be considered as two consecutive rectangular waveguide sections with the specific difference in their widths. The propagation constant is extracted by applying the Floquet theorem to the overall transmission matrix of the single unit cell. The proposed formula agrees well with numerical solutions as well as reported empirical equations in a wide range of structure parameters.