Noise Considerations in Circuit Optimization

Noise can cause digital circuits to switch incorrectly and thus produce spurious results. It can also have adverse power, timing and reliability effects. Dynamic logic is particularly susceptible to charge-sharing and coupling noise. Thus the design and optimization of a circuit should take noise considerations into account. Such considerations are typically stated as semi-infinite constraints in the time-domain. Semi infinite problems are generally harder to solve than standard nonlinear optimization problems. Moreover, the number of signals to be checked and the number of sub-intervals of time during which the checking must be performed can potentially be very large. Thus, the practical and realistic incorporation of noise constraints during circuit optimization is a hitherto unsolved problem.

This paper describes a novel method for incorporating noise considerations during automatic circuit optimization. Semi-infinite constraints representing noise considerations are first converted to ordinary equality constraints involving time integrals, which are readily computed in the context of circuit optimization based on time-domain simulation. The gradients of these integrals are computed by the adjoint method. By using an augmented Lagrangian optimization merit function, the adjoint method is applied to compute all the necessary gradients required for optimization in a single adjoint analysis, no matter how many noise measurements are considered and irrespective of the dimesionality of the problem. The technique is applicable in both dynamic and static circuit optimization contexts. Numerical results are presented in the dynamic case.