# pll system level modelling

Phase-locked loops (PLLs) are one of the basic building blocks in modern electronic systems. They have been widely used in communications, multimedia and many other applications. The theory and mathematical models used to describe PLLs are of two types: linear and nonlinear. Nonlinear theory is often complicated and difficult to deal with in real-world designs. Analog PLLs have been well modeled by linear control theory. Starting from a well-defined model in the continuous-time domain, this article introduces a modeling and design method for a digital PLL based on linear control theory. It has been proved that a linear model is accurate enough for most electronic applications as long as certain conditions are met.