Multifilter Phase-Lock Loop Nonlinear Analysis and Design Criterion

In this paper a nonlinear analysis of a multifilter phase-lock loop (MPLL) by using the method of "harmonic balance" is presented. The particular MPLL considered has a low-pass filter and a bandpass filter in parallel. An analytic expression for the relationship between the input signal phase deviation and the phase error is determined for sinusoidal FM in the absence of noise. The expression is used to determine bounds on the proper operating region for the MPLL and to investigate the "jump phenomenon" previously observed. From these results the proper modulation index, modulating frequency, etc., used for the design of an MPLL is determined. Data for the loop unlock boundary obtained from the theoretical expression are compared to data obtained from analog computer simulations of the MPLL.