Reciprocity based transmission line equations for higher order eigenmodes in lossy waveguides

An important branch in electromagnetic research is the construction of circuit models for devices starting from electromagnetic field simulations. Among the first of such descriptions was the transmission line representation of TEM fields along a coaxial cable, the so-called telegrapher's equations. Although the transmission line representation directly follows from Maxwell's equations only in the pure TEM and, at low frequencies, also in the quasi-TEM situations, many authors have published representations that are valid for the propagation at arbitratry frequencies in general waveguides. These representations usually are based on the assumption that equal complex power is propagated in both the waveguide and the transmission line. However, this leads to problems regarding the reciprocity of such transmission line representations. About 10 years ago Prof. de Hoop suggested the present authors a solution to these problems. In honor of the celebration of Prof. de Hoop's 75th anniversary, we present in this paper these “reciprocity based transmission line representations” in a new and concise manner and apply them to a new problem dealing with higher order eigenmodes in single conductor waveguides. It is shown that again reciprocity leads to simple and hence esthetically pleasing results.