Network representation of transcendental impedance functions

The purpose of the paper is to show that the admittance or impedance of certain continuous structures, such as, for example, a finite length of transmission line of any sort, or resonant cavity, can be represented exactly at all frequencies by a network comprising lumps of constant resistance R, inductance L, conductance G and capacitance C. The network will contain an infinite number of branches, in general, although a finite number may be used if it is desired to represent only certain modes. The procedure is based upon a proposition known to students of function theory as “Mittag-Leffler's theorem,” which amounts, roughly, to an extension of rational functions to apply to transcendental functions of the type encountered in the theory of continuous structures. Several illustrative examples of the network synthesis are given.