The Egan Problem on the Pull-in Range of Type 2 PLLs

In 1981, famous engineer William F. Egan conjectured that a higher-order type 2 PLL with an infinite hold-in range also has pull-in range, and supported his conjecture some third-order implementations. Although it is known for the second-order PLLs are both infinite, this brief shows not valid in general. We provide implementation of PLL, which experiences stable oscillations. This naturally pose problem, we will call problem: to determine class implies range. Using direct Lyapunov method cylindrical phase space suggest sufficient condition infiniteness, provides solution problem.