An LC simulation active RC low‐pass notch filter by minimum number of capacitors

Abstract

AbstractThe most important measure in judging the advantages or disadvantages of a synthesis method for an active RC filter is the element sensitivity. One of the powerful methods for minimizing element sensitivity is the well‐known leapfrog‐type synthesis which simulates a doubly terminated LC filter.In this paper, a method for the synthesis of an LC simulation active RC filter is proposed which can realize a low‐pass notch filter with a minimum number of capacitors. First, how the signs are taken for the node voltages and inductor currents so as to minimize not only the number of capacitors but also the number of operational amplifiers is described; voltage and current relations are derived; and a circuit for realizing these relations and a method for synthesizing an odd‐order filter are shown. Next, the effects of the variation of RC elements and the GB product of the operational amplifiers are described. Finally, a fifthorder low‐pass notch filter is designed and an experiment is carried out. Furthermore, sensitivity calculation is performed using a computer and it is shown that the element sensitivity of this circuit is about 80% that of a circuit realized by conventional leapfrog synthesis.