Analysis and design of a third order phase-lock loop

Abstract

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. >