Abstract
Sufficient conditions are developed for the realizability of frequency-domain nonrational immittance functions. The networks consist of distributed and lumped elements ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RL</tex> ) 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.
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