Linear Analog Circuits Problems by Means of Interval Analysis Techniques

Abstract

Inevitable fluctuations in the manufacturing processes and environmental operating conditions of linear analog circuits cause circuit parameters to vary about their nominal target values. The mathematical model of an engineering system evaluated by a transfer function (e.g. of an active and even passive circuit) never describes exactly the system’s behavior. The changes in the performance of linear circuit due to the variations in circuit parameters are of great practical importance in engineering analysis and design. The tolerance problem for linear analog circuit have been extensively studied and many results have been published, e.g. (Antreich et al., 1994; Spence & Soin, 1997). Because of uncertainties, the values of the parameters of a given circuit may be treated as belonging to some intervals. In recent years, interval analysis becomes powerful tool for tolerance computations of some design problems (Kolev et al., 1988; Femia & Spagnuolo, 1999). Some results have been reported using algorithms for linear interval equations for solving tolerance problems (Tian et al., 1996; Garczarczyk, 1999; Shi et al., 1999; Tian & Shi, 2000). The structure of the chapter is the following: section 2 explains an interval analysis techniques for linear analog tolerance problem. In that approach we are interested in calculation tolerances (the range of values) for real and imaginary part of transfer function with respect to change of one parameter of the circuit. Section 3 deals with the problem of computing the frequency response of an uncertain transfer function whose numerator and denominator are interval polynomials. Studying a solution set of corresponding 2×2 linear interval equation one can obtain bounds on the frequency response. Using Kharitonov polynomials family and complex interval division it’s also possible to evaluate the bounds. In this section we compare results obtained by applying presented approaches. Numerical studies are also reported in order to illustrate presented methods.