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New techniques for selecting test frequencies for linear analog circuits

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.