Hybrid mode analysis of end effects of planar microwave and millimetrewave transmission lines

The phase shift associated with the reflection of a guided wave at the abrupt open end of planar strip and slot waveguides is determined numerically by solving the relevant frequency-dependent hybrid-mode boundary-value problem. In addition, nonideally short-circuited ends are considered, i.e. those where the planar guiding structure terminates in a metallisation layer. The method of analysis employed is a Galerkin approach in conjunction with a spectral-domain Green's function interpolation technique and especially suited expansion functions. Its main features are described, and numerical results are presented for most of the technically important types of planar waveguides (microstrip, suspended substrate, slot/fin and coplanar lines). The results are compared with published measured data and quasistatic computations, as far as these are available. The frequency-dependent behavior of the different end effects is discussed. In an Appendix, it is shown how the numerical approach of this paper can be extended to the analysis of planar n-ports.