Phase-locked loop simulations using the latency insertion method

In this paper we present a novel and simple behavioral model based simulation method for PLLs. We also demonstrate the use of LIM for simulating PLLs. The methods exploit the latency in the PLL formulation and utilize a leapfrog time-stepping discretization scheme to solve for the transient response of the PLL. Various PLL dynamic responses such as lock-in, pull-in and pull-out conditions are simulated and comparisons with analytical solutions are depicted when available. Due to the formulation in the voltage-phase domain, the method does not suffer from the dual time scale problem which is a main issue in full transistor level simulations of PLLs.