Transient Analysis of a Phase-Locked Loop Optimized for a Frequency Ramp Input

This paper considers the nonlinearity of the multiplier in the phase-locked loop which is optimized for a frequency ramp input. The third-order system with this nonlinearity is analyzed for transient response. Equilibrium points and stability are considered from eigenvalues, and transient response is determined using norm in phase space vs phase-space variables. The technique of getting error, error derivative, etc., vs time curves is described in great detail. Comparative study is made for the exact linear model, practical linear model and practical nonlinear model.