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An interval-mathematic approach is presented for frequency-domain simulation and sensitivity analysis of linear analog circuits under parameter variations. With uncertain parameters represented as intervals, bounding frequency-domain responses is formulated as the problem of solving systems of linear interval equations. The formulation is based on a variant of modified nodal analysis, and is particularly amenable to interval analysis. Some characterization of the solution sets of systems of linear interval equations are derived. With these characterizations, an elegant and efficient algorithm is proposed to solve systems of linear interval equations. While the widely used Monte Carlo approach requires many circuit simulations to achieve even moderate accuracy, the computational cost of the proposed approach is about twice that of one circuit simulation. The computed response bounds contain provably, or are usually very close to, the actual response bounds. Further, sensitivity under parameter variations can be computed from the response bounds at minor computational cost. The algorithms are implemented in SPICE3F5, using sparse-matrix techniques and tested on several practical analog circuits.

Simulation and sensitivity of linear analog circuits under parameter variations by Robust interval analysis