Modal analysis of multilayers conductors in multilayers dielectric strip line

The analysis of a multiconductor strip line embedded in multilayer dielectric media has received considerable attention. Most of the work done in this area is based on quasi-TEM analysis employing Green's function or field modal expansion and a suitable numerical technique. This obtains an approximate solution to the strip line parameters such as the characteristic impedance and the propagation constant valid only at low frequencies. To this author's knowledge, no complete modal analysis for all hybrid modes valid for all frequencies for the multilayer conductors in a multilayer dielectric strip line has been published. It is the objective of this paper to present a general technique which could apply to various types of structures both symmetric and non-symmetric. Further, the technique could also determine the field distribution within the structure which allows for the determination of the characteristic impedance for quite a large number of different microstrip line structures. The technique is based on employing the reciprocity theorem for traveling waves inside the strip line. The expression used is variational with respect to the propagation constant, and upon the application of the Rayleigh-Ritz optimization technique, both the propagation constant and the field components are readily obtained to a high degree of confidence.