Test and Diagnosis of Analog Circuits Using Moment Generating Functions

The function of a circuit under test (CUT) is represented as a transformation on the probability density function of its input excitation, which is a continuous random variable (RV) with Gaussian probability distribution. Probability moments of the output, now a transformed RV, are used as metrics for testing catastrophic and parametric faults in circuit components. The proposed use of probability moments as test metrics with white noise excitation as input addresses three important problems of analog circuit test, namely, it 1) reduces complexity of input signal design, 2) increases resolution of fault detection, and 3) reduces production test cost as it has no area overhead and may even marginally reduce the test time. We also propose a method to diagnose circuit elements with catastrophic faults based on unique relationships between specific moments of the output and circuit elements. We present a theoretical framework, test and diagnosis procedures and SPICE simulation results for a benchmark elliptic filter and a low noise amplifier. We are able to detect all catastrophic faults and single components that deviate from their nominal values by just over 10%. We diagnose all catastrophic faults in the example circuits.