An automated framework for multicriteria optimization of analog filter designs

This paper presents an extensible framework for designing analog filters that exhibit several desired behavioral properties after being realized in circuits. In the framework, we model the constrained nonlinear optimization problem as a sequential quadratic programming (SQP) problem. SQP requires real-valued constraints and objective functions that are differentiable with respect to the free parameters (pole-zero locations). We derive the differentiable constraints and a weighted differentiable objective function for simultaneously optimizing the behavioral properties of magnitude response, phase response, peak overshoot, and the implementation property of quality factors. We use Mathematica to define the algebraic equations for the constraints and objective function, compute their gradients symbolically, and generate standalone MATLAB programs to perform the multicriteria optimization. Providing closed-form gradients prevents divergence in the SQP procedure. The automated approach avoids errors in algebraic calculations and errors in transcribing equations into software. The key contributions are: 1) an extensible, automated, multicriteria filter optimization framework; 2) an analytic approximation for peak overshoot; and 3) three novel filter designs. We have released the source code for the framework on the Internet.