Discretization and discrimination methods for design, verification, and testing of analog/mixed-signal circuits

This paper describes how the difficult problems of designing verifying and testing analog circuits in presence of variability can be converted to easier ones by discretizing the search spaces or discriminating one case from another. For instance discretizing the continuous design space of analog circuits enables the use of an efficient predictive global circuit optimizer. Also discretizing the initial condition space of a circuit enables one to establish its global convergence property over the entire space by exploring only a small number of samples. Lastly discriminating the test responses of the circuit with and without a fault in consideration of the underlying statistical distribution provides a formal guide on how to quantify the fault coverage of analog/mixed-signal circuit tests. It is noteworthy that it is variability that introduces the cross-correlations in the performance metrics convergence behaviors and test responses between two nearby candidates in consideration and therefore enables the use of discretization and discrimination methods listed in this paper. The proposed methods are demonstrated on the practical examples of sizing an operational amplifier verifying the correct start-up of a coupled ring oscillator and composing a test suite for screening faults in a digitally-controlled phase interpolator circuit.