Sensitivity of 2nd-order Sallen-key-type active RC filters

The sensitivity, to μ−1 (where μ is the open-loop amplifier gain), of the Q factor of a 2nd-order Sallen-Key circuit can be reduced from the conventional value 2Q2/μ to 3Q/μ by increasing the closed-loop gain from 1 to 4/3. However, this increases the sensitivity to passive-element variations. An optimum engineering solution is found by minimising, for given maximum component variations, the resulting variation of Q, rather than the sensitivities. This makes single-amplifier circuits usable for higher Q factors than previously, which is of particular interest for microelectronic realisations of such circuits.