Interval Analysis of Linear Analog Circuits

Abstract

Reliable methods for the analysis of tolerance-affected analog circuits are of great importance in nowadays microelectronics. It is impossible to produce circuits with exactly those parameter specifications proposed in the design process. Interval arithmetic can be used to obtain a worst-case analysis of the influence of component tolerances. This paper focuses on a new approach for interval-valued frequency-response analysis of linear analog circuits, which consist of current and voltage sources as well as resistors, capacitances, inductances, and all variants of controlled sources. Part and parcel of this strategy is the handling of fill-in patterns for those parameters related to uncertain components. Such systems can efficiently be solved by successive application of the Sherman-Morrison formula. The approach is also extended to complex-valued systems from frequency- domain analysis of linear circuits. Crude bounds can be obtained by treating real and imaginary part as different variables. The latter is improved by considering the correlations in order to obtain tighter enclosures of the solution.