Characterization of planar discontinuities in open dielectric waveguides - Application to the study of passive microwave components

Discontinuities in planar dielectric waveguides are treated as perpendicular to the propagation direction of the EM wave. The propagating signal, when encountering a discontinuity, will display reflected and transmitted modes. The discontinuities are characterized by coefficients expressing the energy coupling for each of the modes, and the model is dependent on the geometry of the discontinuity, of the coupled waveguides, the type of incident mode, and the working frequency. The problem is analytically described by formulating the state space into two half-spaces separated by the discontinuity plane. Continuity equations are defined for the transverse electric and magnetic fields. A Neumann series is employed to iteratively solve the equations, which are similar to the Fredholm equations. The resonant conditions of cylindrical dielectric resonators are obtained. Sample problems are presented for the cases of TM and TE modes and for interacting discontinuities, showing the accuracy of the model when compared to laboratory measurements.