Analytical equivalence between substrate-integrated waveguide and rectangular waveguide

Rectangular waveguide (RW) with sidewalls of vertical conducting cylinders (i.e. SIW, substrate-integrated waveguide) becomes popular with the advent of low-temperature co-fired ceramic structure; its analysis is usually numerical, or modal, leading to empirical design formulas. However, its analytical equivalence to the common RW of the solidwall is identified; in other words, analytical design formulas of the SIW and the equivalent RW of solid sidewalls are the same. The equivalence is established on comparing the surface impedances along the side walls, of the SIW and of an RW through analytical continuation. The equivalence formulas, propagation and cut off frequency show very good agreement with the results from both numerical simulations and measurements of hardware experiments, and over wide frequencies. The good agreements are easily understood on the basis of the conformal maps and the variational principle.