Foundations of computer- aided circuit design by singular imbedding

Although computer-aided circuit analysis has advanced quite rapidly in the last few years, there is considerable room for applications of network theory to the computer-aided design of electronic networks. In this paper the scope of network theory is generalized to include multiterminal networks in which the voltages and currents are related by inequality as well as equality relations. Two classes of new singular elements useful in electronic network design are introduced. The first class generalizes the allowed
v-i
pairs of a nullator and its multiterminal counterparts. The second constrains the allowed pairs of the norator and its multiterminal counterparts. The new singular elements are used to constrain network variables and to represent bounded adjustable elements. In this way the role of the objectives and element constraints are handled in a unified scheme. By imbedding these elements in a network, the synthesis problem is transformed into a problem of analysis of a circuit containing singular elements. Although the method is applicable to a wide variety of circuits, only the dc linear case is treated here. By keeping a linear formulation throughout, the analysis can be done with linear programming techniques with the corresponding theoretical and computational advantages. On-line programs for interactive time-share use have been written, and their flow charts are given in the paper. They provide a very efficient on-line design system that avoids the iterative analysis optimization approach. The gains achieved in computation time are of several orders of magnitude, and the solutions are guaranteed to be found.