New Theorems on the Equations of Nonlinear DC Transistor Networks

Abstract

It has long been recognized that equations describing dc transistor networks do not necessarily have unique solutions. The Eccles-Jordan (flip-flop) circuit is an excellent example of one for which the dc equations may have more than one solution. Only recently, however, has a comprehensive theory concerning matters such as the existence and uniqueness of solutions of the dc equations of general transistor networks begun to take shape. This paper represents another contribution to the evolution of that theory. A key concept in the development of the recent theory is the concept of a “P0 matrix.” We give a generalization of that concept, showing that one can specify properties possessed by certain pairs of square matrices, analogous to the properties possessed by a single P0 matrix. Pairs of matrices possessing these properties are called W0 pairs. Use is made of this W0 pair concept to prove results which are more general than some of the existing ones. We provide an extension of much of the existing theory in such a manner that a broader class of dc transistor networks may be considered. In particular, the new results provide one with the ability to answer certain questions concerning the existence, uniqueness, boundedness, and so on, of solutions of the equations for any network which is comprised of transistors, diodes, resistors, and independent sources.