This book develops for the first time a complete and connected nonlinear theory for the analog Phase-Locked Loop (PLL) which clarifies the obscure points of its complex non-linear behaviour. The book suggests new non-linear models for the PLL components and applies the averaging method to analyse PLL. The book presents the physical interpretation of the PLL operation, locates the difficulties presented by its operation and suggests solutions to overcome these problems. Finally it provides closed form expressions for all the important measures of the PLL and proposes new design criteria.