Design Optimizaion Of Gm-C Filters Via Geometric Programming

This paper presents a design optimization method for a Gm-C active filter via geometric programming (GP). We first describe a GP-compatible model of a cascaded Gm-C filter that forms a biquadratic output transfer function. The bias, gain, bandwidth, and signal-to-noise ratio (SNR) of the Gm-C filter are described in a GP-compatible way. To further enhance the accuracy of the model, two modeling techniques are introduced. The first, a two-step selection method, chooses whether a saturation or subthreshold model should be used for each transistor in the filter to enhance the modeling accuracy. The second, a bisection method, is applied to include non-posynomial inequalities in the filter modeling. The presented filter model is optimized via a GP solver along with proposed modeling techniques. The numerical experiments over wide ranges of design specifications show good agreement between model and simulation results, with the average error for gain, bandwidth, and SNR being less than 9.9%, 4.4%, and 14.6%, respectively.