Synthesis of low-pass linear-phase active circuits using distributed RC networks

An active-feedback distributed
RC
network capable of matching the magnitude response of a pair of complex-conjugate poles and simultaneously giving linear phase is described. The linearity of the phase response is further improved when exponentially tapered
\overline{RC}
networks are utilized. It is shown that such characteristics can be used for simultaneous realizations of flat magnitude response and linear phase. Butterworth magnitude responses having phase linearity associated with those of transitional Butterworth-Thomson filters and Thomson magnitude responses having better phase linearity than those achievable by active lumped RC networks can be realized by cascading these circuits. In addition, it has been found that exponential tapering substantially reduces the required gain and the
Q
sensitivity to changes in gain for a given pole position. Reduction in gain with improvement in
Q
sensitivity to changes in gain makes these circuits attractive for high-frequency applications.