All the substrate integrated waveguide(SIW) resonant cavities with six different boundary conditions are summarized and analyzed totally.Based on the mirror image principle and Helmholtz equations

the closed form solutions of the guided mode field of the SIW resonant cavities under different boundary conditions are given.The field distributions of the resonant cavities under all the boundary conditions are analyzed

and the results are consistent with the results given by the full wave simulation analysis

transmission line model method and empty cavity model method.The formulas for calculating the resonant frequencies of

the resonant cavities under various boundary conditions are presented.Based on the proposed theory that the transmission line added extra two boundary conditions is equivalent to the resonant cavity

the coexistence mechanism of TE mode

TM mode and TEM mode is analyzed.This paper describes the evolution of the SIW resonant cavities under different boundary conditions as well.Finally

a dual-mode SIW bandpass filter and a SIW equalizer

based on different boundary conditions are designed

fabricated and measured to demonstrate the proposed method.Two modes of the filter

TE

100

(or TEM mode) and TE

102

can be tuned independent and the measured results are in agreement with the simulation results.The relevant research results provide ways for the miniaturization design of microwave devices.