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 pair
Q
and pole frequency
\omega_0
, the circular root locus centered at
-2Q \omega_0
on the real axis and of radius
\omega_{0}\sqrt{4Q^{2}-1}
exhibits zero
Q
-sensitivity and zero gain-sensitivity product (GSP) with respect to the active parameter. Furthermore, realization techniques to achieve zero
Q
-sensitivity and zero GSP for prescribed
Q
and
\omega_0
are outlined. Experimental results agree closely with the theoretical expectations.