The theory of RC transmission lines

Abstract

Interest has recently been shown in the literature, in the theory and discussion of the possible applications of network structures with distributed resistance and capacitance. Most authors in this field have restricted their studies to a few, or even one of the many such transmission lines with exact solutions. It is shown that many general results can be proved directly from the nature of the equations, without specifying any particular case. A general formulation of the problem of finding exact solutions is developed, and numerous previously unknown solutions are tabulated. An original formulation of the solutions, in terms of integral equations, is shown to provide an alternative derivation of a recently published, general series solution. Although cumbersome, this method leads to several interesting formulae. The final two chapters deal in detail with the solutions and characteristics of the simplest class of solutions. The concept of 'excess phase1 is shown to be of central importance in the theory, and in the final chapter is used in the discussion of applications of the circuits. The final chapter presents a powerful method for visualising and designing distributed networks, which makes use of a variant of the classical root locus method. Finally possible extensions to the present work are outlined.