Interval Methods for Analog Circuits

Abstract

Concepts of interval analysis are suitable for solving some problems for linear and nonlinear analog circuits. The effects of circuit parameter uncertainties on circuit performance are always of great concern to the system designer. It is desirable to know a priori estimates of the circuit response, subject to parameter uncertainties. In the first section of this chapter a problem of calculating of the operating regions (solutions) for linear circuits with parameters done as interval numbers is considered. Such circuits are described by linear interval equations. The set of all possible operating points of the circuit may have a very complicated structure and it is usually impractical to calculate it. Applying ideas of interval analysis it is possible to calculate multidimensional rectangular region bounding the set of operating points. In the paper an algorithm of iterative evaluation of the bounds of operating regions is applied. The second section deals with the finding DC solutions of nonlinear, inertialess circuits. Using idea of a continuation method one can solve nonlinear equations describing circuit by tracing so-called solution path. A version of the predictor-corrector method for computing points of continua‐ tion path of a nonlinear equation is presented. The target of this approach is to control the corrector step in such a manner that the predictor step is sufficiently large but that the corrector step does not jump to another continuation path. Additionally interval analysis offers possi‐ bility to solve that problem by applying generalized bisection method based on some interval operator associated with nonlinear equation. In the section Krawczyk operator is used in ndimensional box-searching of all solutions. For both sections numerical studies are reported in order to illustrate and verify presented approach.