A Method of Designing Simulative Networks

In communication work it is often necessary to design a simple lumped network, the impedance of which approximates at all frequencies that of a certain distributed circuit, such as a transmission line. The present treatment includes a clarified method of making such a design. Former design methods have the common fault that negative circuit constants may be called for. This paper presents a simple method by which the difficulty is avoided. Moreover the best design under the particular circumstances in question may be arrived at quickly and directly. The impedance functions of two common forms of simulative networks are developed and design equations for the establishment of the parameters are presented. Since four elements are to be established it is possible to specify four arbitrary conditions. This is most conveniently handled by specification of the vectorial impedance at two frequencies. The major portion of this paper is concerned with the relation which must exist between these impedances in order that the calculated circuit parameters will all be positive. For the sake of completeness conditions leading to negative parameters are also considered.