Theoretical study on the number of solutions and the stability on transistor circuits

点击翻译按钮获取中文摘要

This study aims to pursue two subjects on nonlinear active circuits including transistor circuits. One is to investigate the maximum number of solutions of transistor circuits under the prescribed topology. This problem was proposed by the Technical Committee on Nonlinear Circuits and Systems of the IEEE CAS Society several years ago.. The other is to investigate the stability conditions for general active circuits including transistor circuits. The main results of this research are summarized as follows:1.We showed that the algebraic equations which have two variables and whose nonlinear terms are exponential functions of the variables have at most five solutions. This type of equations come from transistor circuits.. The above result show that the well-known conjecture does not hol in general.2.We give some sufficient conditions for the denominator polynomial of active RC circuits including transistor circuits not to yield negative coefficients due to parasitic elements. This result then shows some conditions for stability of this class of circuits.3.We give the necessary and sufficient conditions for a one-dimensional discrete-time cellular neural network, which is a class of active analog circuits.4.We give the necessary and sufficient condition for the second-order differential equations to be globally stable.