Foster-Distributed-Lumped Network Synthesis

Sufficient conditions are developed for the realizability of frequency-domain nonrational immittance functions. The networks consist of distributed and lumped elements (
RC
and
RL
) and have Foster-type topologies. The approach used is to classify functions by their singularities. The functions may have a discontinuity across a line on the negative real axis of the s plane. This class includes positive real branches of multivalued functions with branch points as their singularities. The theory utilizes properties of integrals with Cauchy-type kernels evaluated along the line of discontinuity. The functions could also have a countably infinite number of poles on the negative real axis. Mittag-Leffler's theorem gives representations for such functions, which yield Foster-type infinitelumped networks.