Cascaded R–C Networks and Phase-shift Oscillators

Abstract

This article briefly describes the salient features of the simple three section C–R phase-shift oscillator which is met quite early in electronics laboratory courses. The frequency of operation and the gain required for oscillation are shown to depend on the output impedance of the amplifier which feeds the C–R network. By using a directly coupled cathode follower, the C–R network can be driven under almost ideal conditions where the C–R network determines the frequency and gain requirement. A simple and rapid method for calculating the frequency and gain for a cascade of ‘n’ identical sections is given, in general form, along with a graph of gain and frequency/no. of sections. A three section C–R network with tapered sections is analysed from the point of view of the gain required for the limiting case of extremely steep taper. The R–C transmission line with distributed parameters is considered and the gain required for the open-circuit line type of oscillator is shown to be – coshπ. The limiting gain required for a large number of identical sections appears to approach — coshπ, but this is not proved.