Lyapunov redesign of classical digital phase-lock loops

The author (1990) has previously established that Lyapunov redesign is effective in designing an analog phase-locked loop for which the nonlinear model (in the signal phase space) is guaranteed to be stable. This paper extends that concept to what are commonly called classical digital phase-locked loops. These loops, which are very common in high speed digital communications systems, use digital phase detectors but analog filters and VCOs.

[1]  R. E. Kalman,et al.  Control System Analysis and Design Via the “Second Method” of Lyapunov: I—Continuous-Time Systems , 1960 .

[2]  Solomon Lefschetz,et al.  Stability by Liapunov's Direct Method With Applications , 1962 .

[3]  D. Abramovitch.  Analysis and design of a third order phase-lock loop , 1988, MILCOM 88, 21st Century Military Communications - What's Possible?'. Conference record. Military Communications Conference.

[4]  N. Eva Wu,et al.  Circle/Popov criteria in phaselock loop design , 1998 .

[5]  C.R. Hogge.  A self correcting clock recovery circuit , 1985, IEEE Transactions on Electron Devices.

[6]  Daniel Y. Abramovitch,et al.  Phase-locked loops: a control centric tutorial , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[7]  Roland E. Best.  Phase-locked loops : design, simulation, and applications , 2003 .

[8]  C. Hogge.  A self correcting clock recovery curcuit , 1985, Journal of Lightwave Technology.

[9]  Behzad Razavi.  Clock Recovery from Random Binary Signals , 1996 .

[10]  P. Parks,et al.  Liapunov redesign of model reference adaptive control systems , 1966 .

[11]  Roland E. Best.  Phase-Locked Loops , 1984 .

[12]  N. E. Wu.  Analog phaselock loop design using Popov criterion , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[13]  Dan H. Wolaver,et al.  Phase-Locked Loop Circuit Design , 1991 .