Analysis and experiment of substrate integrated waveguide cavity of four sidewalls of cylinders and solid top and bottom walls

Given in this paper are the equivalence formulas to convert the substrate integrated rectangular waveguide (SIW) resonant cavity of cylinder sidewalls (and solid top- and bottom-walls) to its equivalent rectangular wavguide cavity of solid sidewalls. The equivalence is analytical, therefore it should be excellent as long as the radius of the cylinders and their separation are small in terms of wavelength. Two prototypes are fabricated to demonstrate the validity of the equivalence formula. Excellent agreement of the measured and analytical resonant frequencies of TE₁₀₁ mode has been observed in the substrate integrated rectangular waveguide resonant cavity, indicating the accuracy of the proposed equivalence theory. Such equivalences are convenient for the design of small waveguides, of millimeter wave, in a multilayer circuit structure, such as the LTCC.