The mechanism of sub-harmonic generation in a feedback system

A theory is presented for the mechanism of sub-harmonic generation in a non-linear feedback system. This phenomenon is the occurrence of components, in the output of a system, whose frequency is a fraction of the input frequency. This sub-harmonic component is regarded as an oscillation of the closed-loop feedback system in the Nyquist sense. The parameters of the system are modified to allow continuous oscillation by the action of the input signal on the non linear element. A connection is shown to exist between the open-loop frequency response and the conditions necessary for sub-harmonic oscillation. From this, sufficient limitations are obtained to ensure the absence of this phenomenon. Experimental work on a system with a cubic characteristic is included.