Prediction of autonomous nonlinear oscillations in multiple-loop active-RC networks using the Hopf bifurcation theorem

A graphical algorithm based on a reformulation of the Hopf bifurcation theorem is applied to predict autonomous nonlinear oscillations in single and multiple-loop active-RC networks. The technique is shown to be superior to other methods such as describing functions. A corrected Wien-bridge oscillator circuit and a three-amplifier state-variable bandpass filter are used as examples