Analysis and design of a third order phase-lock loop

The author examines the analysis and design of a third-order phase-lock loop (PLL). Although it offers superior noise rejection and lower steady-state error than a second-order PLL, its stability is difficult to analyze in the region of nonlinear operation. The author treats the third-order PLL as a nonlinear control system, first examining the small-signal (linear) operation and then extending the analysis to the nonlinear region. The second method of Lyapunov and LaSalle´s theorem are used to derive stability conditions for the nonlinear model. It is concluded that Lyapunov stability techniques are adequate, thus removing the chief disadvantage of designing third-order PLLs