Techniques for the optimal design and synthesis of switching circuits

The variational approach to the optimal design of high-speed switching circuits is explored. The approach implements the variational calculus to obtain an expression for the vector sensitivity of a scalar performance function (e.g., delay, or switching time) to changes in the vector of design parameters. Gradient methods are established for using the vector sensitivity to iteratively update the parameter vector and obtain an optimal design. It is shown that the variational approach retains, typically, an M-fold computational advantage over conventional step-and-repeat methods in determining the sensitivity of a scalar performance function to M design parameters. The approach is shown to be well adapted for incorporation into package analysis programs with matrix formulations, and vested with sufficient generality to be applicable to a wide range of switching circuit problems (e.g., low-power or large-scale integrated circuits). It is further shown that subsumed in the general class of nonlinear parameter-value synthesis problems is the class of delay-minimization problems, and that the switching time minimization problem is a special case of the classical "time-optimal" problem.