Optimal Design of Filters with Bounded, Lossy Elements

This paper proposes a solution to the problem of designing a filter of given structure, incorporating nonideal elements, to meet or exceed given insertion loss specifications subject to element value bounds. This problem is reformulated as a nonlinear programming problem, i.e., minimize an objective function subject to inequality constraints, whose solution yields a filter optimal in a min-max sense. To solve this problem, a recent penalty function approach is used, which converts the constrained problem into a sequence of unconstrained minimizations. These minimizations are carried out using a recent, very efficient, descent technique. The overall method is especially amenable to computer implementation. These techniques have been applied to the computer design of cascade crystal-realizable lattice filters. The results for several designs are presented, and are uniformly good.