Design of active RC filters with zero gain-sensitivity product

Abstract
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 frequency\omega_0, the circular root locus centered at-2Q \omega_0on the real axis and of radius\omega_{0}\sqrt{4Q^{2}-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 prescribedQand\omega_0are outlined. Experimental results agree closely with the theoretical expectations.

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