An automated framework for multicriteria optimization of analog filter designs

This paper presents an extensible framework for designing analog filters th at exhibit several desired behavioral properties after being realized in ci rcuits. In the framework, we model the constrained nonlinear optimization p roblem as a sequential quadratic programming (SQP) problem. SQP requires re al-valued constraints and objective functions that are differentiable with respect to the free parameters (pole-zero locations), We derive the differe ntiable constraints and a weighted differentiable objective function for si multaneously optimizing the behavioral properties of magnitude response, ph ase response, peak overshoot, and the implementation property of quality fa ctors. We use Mathematica to define the algebraic equations for the constra ints and objective function, compute their gradients symbolically, and gene rate standalone MATLAB programs to perform the multicriteria optimization, Providing closed-form gradients prevents divergence in the SQP procedure. T he automated approach avoids errors in algebraic calculations and errors in transcribing equations into software. The key contributions are: 1) an ext ensible, automated, multicriteria filter optimization framework; 2) an anal ytic approximation for peak overshoot; and 3) three novel filter designs, W e have released the source code for the framework on the Internet.