Academic and Theoretical Aspects of Circuit Theory

Abstract

This paper discusses various types of realizability problems in electric circuit theory, with particular attention to the role of necessary and sufficient conditions. The first example is the general realization of an arbitrary driving-point impedance function discovered by Brune, together with his introduction of the use of the positive real function. Next comes the remarkable synthesis of the same problem by Bott and Duffln, with their complete elimination of all transformers. A brief survey is then given of subsequent efforts to simplify the original networks prescribed by Bott and Duffin, together with various alternative conditions which are sufficient but not necessary. All of this is then illustrated by application to the relatively simple case of the biquadratic impedance function. The other chief example discussed is the current work on the realization of a given real matrix as the open-circuit impedance matrix, or closed-circuit admittance matrix, of a network composed entirely of ordinary resistors. Particular attention is given to the work of Cederbaum in this field. It would seem that, although complete necessary and sufficient conditions have not yet been obtained, this problem is almost at the point of being solved.