Design of active RC filters with zero gain-sensitivity product

A root locus with respect to the active parameter for any second-order active RC filter is circular with center on the real axis. It is shown that for any pole pairQand pole frequencyω_0, the circular root locus centered at-2Q ω_0on the real axis and of radiusω₀√{4Q²-1}exhibits zeroQ-sensitivity and zero gain-sensitivity product (GSP) with respect to the active parameter. Furthermore, realization techniques to achieve zeroQ-sensitivity and zero GSP for prescribedQandω_0are outlined. Experimental results agree closely with the theoretical expectations.