Minimizing the Worst-Case Drift of an Active Bandpass Filter,

This report presents a technique for designing active bandpass filters that will be relatively insensitive to drifting circuit components including the op amp. The procedure can be applied to the design of single stage, two pole bandpass filters or individual stages of multiple pole filters. The filter circuit requires only one op amp and employs positive feedback that can be increased to make the filter less sensitive to the op amp characteristics however this makes the circuit more sensitive to the passive component values. In order to determine the optimum amount of positive feedback, formulas are derived which describe the approximate sensitivities of the filter transfer function to the passive component values and to three op amp parameters, as functions of the positive feedback ratio. These sensitivity formulas are combined to yield an expression for the worst-case drifts of three filter parameters center frequency, Q, and gain. Optimization techniques are applied in order to determine the positive feedback ratio that minimizes the worst-case drift of a selected filter parameter.