This brief deals with soft-fault diagnosis of analog circuits. Both ac and dc linear circuits, as well as dc nonlinear circuits with limited number of test points are considered and the presence of component tolerances is taken into account. An approach using the linear-programming concept and the simplex method is developed. Contrary to the other methods which use optimization techniques for diagnosis, no optimization process for evaluating the parameters deviations is performed. In fact, only phase 1 of the simplex method is applied to check the existence of a feasible solution. It enables us to state whether the actual parameters are within tolerance ranges or some components are faulty. Identification of the faulty elements is achieved using a similar idea. Three numerical examples illustrate this approach.
The paper offers a universal method for finding a unique or multiple DC operating points of nonlinear circuits. The developed method is based on the theory known as a linear complementarity problem (LCP) and the homotopy concept. It is a combination of Lemke's method for solving LCP and some variant of the homotopy method. To express the problem of finding DC operating points in terms of LCP, an appropriate piecewise-linear approximation of diode characteristic is proposed. Although the method does not guarantee finding all the DC operating points, usually it finds them. The method is very fast and remarkably efficient. Numerical examples, including practical BJT and CMOS circuits having a unique or multiple DC operating points are given.
The paper deals with nonlinear dynamic circuits containing MOS transistors. The problem of global and local stability of a class of these circuits is considered in detail. It is shown that any circuit belonging to this class is Lagrange stable. In a special case where no independent sources act in the circuit, it is proved that the origin is the only equilibrium point and the circuit is globally asymptotically stable. Special attention has been paid to the circuits driven by dc sources, having multiple equilibrium points. A simple tool for proving asymptotic stability of equilibrium points is developed and illustrated by numerical examples.
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