Abstract
In a-c servomechanisms, many compensation problems can be handled by the biquadratic transfer function G(s)=(s2+2ω1s+ωc2)/(s2+2ω2s+ωc2). The R-C Twin-T network is one network which realizes this function, and many synthesis methods have already been reported. Presently available methods usally require the use of cumbersome design charts. G. Weiss showed that realizability conditions for the Twin-T network are ω2>ω1, and ωc2-(ω2-2ω1)ωc-2ω1(ω2-ω1)<0.
Also, Sallen and Key developed the synthesis method for the active filter with the symmetrical Twin-T network in the special case of ω1=0.
In this paper, realization of the biquadratic transfer function using the Sallen-Key type filter with the general Twin-T network is discussed based on consideration of the realizability. By means of this filter, the biquadratic transfer function for arbitrary values of ω1, ω2 and ωc is realizable with no design charts. The output impedance of the filter can be decreased by making that of the active element in the filter smaller. This filter can be used as a phase-lead network or a phase-lag network. Furthermore it is shown that the design is simplified by using the phase curves derived from the transfer function of the carrier process with obtained realizability curves.
