Multifrequency Test and Diagnosis of Analog Circuits Using Constraint Programming and Interval Arithmetic

Analog circuits are often specified using non-linear equations, which are difficult to analyze. Therefore, test generation and diagnosis are problematic issues in practice. In this paper we propose a new method for diagnosis of analog circuits that uses combined information from tests at different frequencies. By solving simultaneously the resulting equations (one for each test frequency), we get a reliable method that decreases the number of possible answers to the diagnosis problem. The min-max optimization algorithm that we implemented for non-linear transfer functions gives good average runtime for diagnosis parametric faults. 1 Description of the Diagnosis Method The diagnosis of faults in Analog Circuits is a challenging problem with limited results currently available. The paper proposes an approach based on the solution of simultaneous equations resulting from observations at different frequencies. We consider an analog system constrained by the correct values of its parameters and its transfer function, which holds for a given range of frequencies. If an error is detected, we combine tests at different frequencies to solve them simultaneously in the constraint satisfaction problem that describes a diagnosis situation. Our innovative multifrequency test yields a reduction of the set of possible single faulty components and therefore gives a more exact answer to the diagnosis problem. The diagnosis method is presented in Fig. 1. Particularly interesting is the constraint management of this information. We combine the tests results obtained at different frequencies as new restrictions in our constraint satisfaction problem, for the same single faulty component. An overconstrained description leads to faster performance and is more likely to attain a single solution. It shows that both the number of testpoints and the number of different frequencies at which the circuit is tested are good sources of constraints to the diagnosis problem. The method was implemented in PrologIV [5]. The analog circuit tested was a biquadratic filter (see [3]) which passive components are 6 resistors and 2 capacitances. Two testpoints were considered (V3 and V5). In Table 1 encouraging diagnosis results are presented for tests at three different frequencies.