Phase-Compensating-Circuit Design Utilizing Linear-Nonlinear Joint Optimizations

The phase-compensating-circuit (PCC) with recursive all-pass structure can be designed to approximate an ideal phase specification, but the approximation problem itself is inevitably a nonlinear optimization problem. This paper first approximates the PCC design as a linear optimization problem, and then solves the approximated linear optimization problem by using a linear-optimization solver. This linear-optimization design produces an approximate minimax solution. After the approximate minimax solution is achieved, a further step optimization using a nonlinear optimizer is executed, aiming to further enhance the PCC accuracy. These two successive optimizations yield an improved PCC and provide an alternative way for the design of performance-enhanced all-pass PCC. A comparative example is included for the comparison as well as the verification of the accuracy enhancement.