Normed Distances and Their Applications in Optimal Circuit Design

A new geometric method for optimal circuit design is presented. The method treats the optimal design problem through the concept of normed distances from a feasible point to the feasible region boundaries in a norm related to the probability distribution of the circuit parameters. The method treats directly the nonlinear feasible region boundaries without any region approximation. The normed distances are found through the solution of a nonlinear optimization problem. The sufficient optimality conditions for this optimization problem are established and an ordinary explicit formula for the normed distance is also derived. An iterative boundary search technique is used to solve the nonlinear optimization problem concerning the normed distances. The convergence of this technique is proved. Practical circuit examples are given to test the method.