Circle Equation-Based Fault Modeling Method for Linear Analog Circuits

Abstract

Owing to the lack of feasible fault modeling method, hard (open and short) faults and discrete parameter faults are still the mostly used fault models. These models cannot characterize all soft faults occurring in analog circuits because the parameters of analog element are continuous. To address this concern, a new circle equation-based modeling method is developed. In a linear analog circuit, we prove that the real and imaginary parts of voltage phasor at any test node satisfy circle equation with respect to any network element. The equation is independent from the value of element to be modeled, and uniquely determined by its location and the nominal values of the remaining elements in the circuit under test. Hence, the circle equation can model any continuous parameter shifting (soft) or hard fault occurs to linear and piecewise linear circuits. Three points are sufficient to determine a circle; therefore, only three simulations corresponding to three distinct faulty parameters are enough to model all parameter shifting faults that occur in any network element. The effectiveness of the proposed approach is verified by simulation and comparison with other modeling methods.