Circle/Popov criteria in phaselock loop design

Phaselock loops are generally designed by a combination of linear techniques, phase plane plots, rule of thumb, and simulation. It was only rather recently that Lyapunov´s second method was formally applied to the design of phaselock loops. The method however, is not suitable for phaselock loops with high order filters. This note is intended to call the attention to the use of circle/Popov criteria for the design of phaselock loops, which has been made possible by the available power for numerical computation