Frequency dependence of sensitivities in second-order RC active filters

This paper presents that gain and phase sensitivities to some element in biquadratic filters approximately constitute a circle on the complex sensitivity plane, provided that the quality factor Q of the circuit is appreciably larger than unity. Moreover, the group delay sensitivity is represented by the imaginary part of a cardioid. Using these results, bounds of maximum values of gain, phase, and group delay sensitivities are obtained. Further, it is proved that the maximum values of these sensitivities can be simultaneously minimized by minimizing the absolute value of the transfer function sensitivity at the center frequency provided that w(0)-sensitivities are constant and do not contain design parameters. Next, a statistical variability measure for the optimal-filter design is proposed. Finally, the relation between some variability measures proposed to the present time is made clear.