New techniques for selecting test frequencies for linear analog circuits

Abstract : In this paper we show that the problem of minimizing the number of test frequencies necessary to detect all possible faults in a multi-frequency test approach for linear analog circuits can be modeled as a set covering problem. We will show in particular, that under some conditions on the considered faults, the coefficient matrix of the problem has the strong consecutive-ones property and hence the corresponding set covering problem can be solved in polynomial time. For an efficient solution of the problem, an interval graph formulation is also used and a polynomial algorithm using the interval graph structure is suggested. The optimization of test frequencies for a case-study biquadratic filter is presented for illustration purposes. Numerical simulations with a set of randomly generated problem instances demonstrate two different implementation approaches to solve the optimization problem very fast, with a good time complexity.