Minimum-Sensitivity Single-Amplifier Biquadratic Filters

Evaluating the Schoeffler criterion for Sallen-Key filters leads to expressions having two degrees of freedom and prohibitive complexity. Such expressions are normally solved only after making approximations. We show, using the lowpass filter as an example, how the two degrees of freedom can be separated by a simple non-linear coordinate transform. Exact design equations for the minimum-sensitivity filter result, revealing that this filter has the maximum allowable component spread, that its capacitor spread is larger than the resistor spread, and that the required amplifier gain does not exceed two. We then repeat the analysis for unitygain filters and show that the minimum-sensitivity filter has minimum component spreads if its pole frequency is below a certain value.