On equivalent circuit representations for radiating systems by means of complex-valued network elements

In the development of equivalent circuit representations for radiating systems the question arises whether it is necessary and physically meaningful to employ generalized network elements which, in particular, may become complex. Analytically, this problem has been investigated by methods which are based on the Singularity Expansion and the Eigenmode Expansion Method. We reconsider this problem in the light of recent advances in the formulation of generalized transmission line theories and compare the structure of both approaches. It is seen that the essential steps which lead from electric field integral equations to equivalent circuit representations for radiating systems are similar. Differences exist in the spatial integration procedures which allow to reduce the relevant field problem to a network problem, leading to equivalent circuit representations which consist of either infinite ladder networks with lumped elements or per-unit length network parameters, both of which may become complex if radiating systems are considered.