Qualitative properties of resistive networks containing multiterminal nonlinear elements: No gain properties

This paper is concerned with several qualitative properties of nonlinear multiterminal resistors and nonlinear resistive networks. The concept of no-gain elements is generalized to include multiterminal elements. The main result obtained is that an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -terminal element possesses the no-gain property if, and only if, at each operating point, a connected network of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n-1</tex> positive linear two-terminal resistors exists which has the same operating point. This generalization is then used as a basic tool to derive bounding regions for the two most useful nonlinear resistive network characterizations; namely, the driving point (DP) and the transfer characteristic (TC) plots. The sharpest possible bounding regions are obtained for a large class of nonlinear networks-including networks which use operational amplifiers as one of the main elements. The concepts of locally no-gain n-ports and locally no-gain networks are introduced and it is shown that these concepts are related to the classical <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -port resistor synthesis problem.