Genetic algorithms applied to the design of robust biquadratic filters

This work presents a design methodology for discrete active RC biquadratic filters based on genetic algorithm (GA). The main difference with other methods is the consideration of the passive sensitivities during the optimization process. The GA delivers the values of resistors and capacitors (from E series) that comply with the desired specifications and minimize at the same time the sensitivities. This characteristic leads to filters that exhibit low deviations in their functional parameters, despite drifts in the values of passive components. Additionally, the method allows the designer to establish the gain in the passband. In this way, it overcomes the problem of low gain values observed in some of the solutions given by other authors. The paper presents an evaluation campaign that considers 12 designs for showing the robustness of the method. This study analyses the results delivered by the GA at transfer function level using MATLAB. Subsequent evaluations validate these results by using SPICE simulations. Following these procedures, it is observed a proper matching between the behaviors of the filters predicted by the GA and the simulated ones. The performance comparison with other heuristics (solving the same problem) shows that our proposal is well suited for the design of active filters. The stochastic nature of the GA allows obtaining different design alternatives in each run. This feature gives the designer the possibility to choose between several options that are more appropriate for a particular design problem. The paper also provides a simple guideline for dealing with the results from the iterative executions of the GA. The design method requires tools that are usual to find in the industry. Practitioners can straightforwardly implement it, even those that are nonspecialists in heuristics.