Radial Wave Excitation and the Radiation Condition in Planar Microwave Circuits

In a detailed rigorous analysis it is shown how the radiation condition can be incorporated into the hybrid mode formulation of planar circuit boundary value problems. The analysis presented is based on the fact that the spectral domain Green's function of covered planar structures can be expressed in terms of radial wave eigenfunctions. It considers lossy substrates for the limiting case of vanishing losses and throws some light on the mechanism of the excitation of radial waves in planar circuits. Numerical results are presented for the microstrip case.