IEEE Transactions on Circuits and Systems II:
Analog and Digital Signal Processing, vol. 46, no. 8, pp. 981-990,
Multicriteria Optimization of Analog Filter Designs
Brian L. Evans
Embedded Signal Processing Laboratory,
Department of Electrical and Computer Engineering,
Engineering Science Building,
The University of Texas at Austin,
Austin, TX 78712-1084 USA
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 non-linear optimization problem
as a sequential quadratic programming (SQP) problem.
SQP requires real-valued constraints and objective function 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, and 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 multi-criteria 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
We have released the source code for the framework on the Internet.
- an extensible, automated, multi-criteria filter optimization framework,
- an analytic approximation for peak overshoot, and
- three novel filter designs.
Last Updated 11/08/04.