Transient Analysis of Regenerative Frequency Dividers

The regenerative frequency divider provides an output sinusoid whose frequency is times that of an input sinusoid, where is an integer. A simple mathematical model of such a divider is proposed, and its approach to the steady state is analyzed for an input of constant amplitude and phase. Two types are considered. In the first the steady-state input-output characteristic is double-valued for input amplitudes greater than a certain threshold; in the second it is single-valued. In both, the output decays to zero if the input amplitude is less than the threshold, but in the first type of divider additional conditions on the initial values of the output signal must hold in order for the output not to decay to zero when the threshold on the input amplitude is exceeded. An appendix deals with the effect of a memoryless nonlinearity on a quasi-harmonic (narrow-band) signal.