A Simulation Program for Higher-order Nonlinear PLLs

Abstract

Phase-locked loops (PLLs) are widely used in modern communication and control systems. Several books and many papers have been published in this field. In the paper the higher-order nonlinear loops will be examined. The state variable method has been applied for describing the operation of a PLL in time-domain. The state equations are first-order nonlinear( and stochastic if noise is present) differential equations A simulation program has been developed to analyze the transient behaviour of a phase locked loop in the absence or in the presence of additive Gaussian noise. The program uses the Runge-Kutta algorithm for solving the differential equations under the given initial conditions. As a result, the transient phase error, which is an important characteristic of a PLL and the locking tine can be computed. When noise is present in the loop, the program can also plot the empirical probability density functions of the phase error. The Gaussian noise is generated by the random function of the computer. The simulation program has been written in BASIC for an HP 9845 computer. It can be used to simulate almost all types of analogue phase-locked loops and control systems having models equivalent to PLLs.