The qualitative form of optimum transient test signals for analog circuits derived from control theory methods

In this paper a new fundamental result concerning the form of optimum transient signals for testing general analog circuits is presented. It is shown for the first time, that an optimum test signal for a general analog circuit must be a piecewise constant signal. For a general analog circuit only a piecewise constant signal is able to maximize an arbitrarily chosen merit functional, which is based on the circuit states. Thus, a test signal also called test stimulus of this form is optimal with respect to the detection of a given fault set by means of a predefined merit functional representing a fault detection criterion. This result is obtained by the application of optimal control theory methods, in particular the maximum principle of Pontrjagin, to the test signal generation problem of finding optimal test stimuli. The test signal generation problem is formulated as an optimal control problem. With the knowledge of the qualitative form of optimal test signals it is possible to develop efficient tools for the test of analog circuits.