Using a Genetic Algorithm to Optimize Capacitance Ratio Approximations in SC Filters

Abstract

Accurate capacitance matching is one of the main design issues in switched-capacitor (SC) filters. Using identical unit capacitors in parallel to implement each filter capacitor, combined with a careful layout design, can provide an accuracy of 0.1% in the filter coefficients. The disadvantage of this technique is the fact that it can be directly applied only if the coefficients can be expressed as ratios of integer numbers. As a result, coefficient approximations are required, leading to frequency response errors. In this paper, a genetic algorithm (GA) is used to find the optimum capacitance ratio approximations by rational numbers that minimize the total number of unit capacitors for a given error tolerance in the frequency response. Design examples in 0.35 µm CMOS are presented and simulated to illustrate the proposed approach and verify its effectiveness.

Transistor‐level optimization methodology for the complete design of switched‐capacitor filter circuits

“…Commonly used algorithms for the design and optimization of SC filters include gradient descent, 9 simulated annealing, 4,8,18 differential evolution, 10 linear programming, 8 GAs, 7,19 among others. Gradient descent algorithms are not guaranteed to find the global minimum, since the algorithm can, depending on the step size, get stuck when a first‐order critical point is found.…”

“…Most methods found in the literature either optimize the circuit from an ideal standpoint [3][4][5][6][7][8] (i.e., consider the switches and the amplifiers as ideal elements) or use simplified models [9][10][11] to predict the behavior of the real SC circuit, which can limit the accuracy of the optimized frequency response. In Ruiz-Amaya et al, 11 a method to model the settling-time of SC circuits, implemented using the two-stage Miller-compensated amplifier, is described.…”