Nonlinear dynamics of first-order DPLL with FM input

In previous work the author considered the nonlinear dynamics of first- and second-order digital phase-locked loops (DPLLs), paying particular attention to the effect of frequency quantization within the loop. The input to the loop in that work consisted of a single sinusoidal signal. In this paper the author begins the extension of previous work to the case where the input signal to the DPLL is a frequency modulated (FM) signal. This is restricted to the case of the uniformly-sampled first-order DPLL, both with and without frequency quantization. It is seen that even in this relatively simple case the dynamics can be extremely complex