William F. Egan


William F. Egan is an expert and author in the area of PLLs. The first and second editions of his book
Frequency Synthesis by Phase Lock
as well as his book Phase-Lock Basics
are references among electrical engineers specializing in areas involving PLLs.

Egan's conjecture on the pull-in range of type II APLL

In 1981, describing the high-order PLL, William Egan conjectured that type II APLL has theoretically infinite the hold-in and pull-in ranges., This conjecture can be found in various later publications, see e.g.,. In general, the hold-in and pull-in ranges of type II APLL for a given parameters may be either infinite or empty, thus, since the pull-in range is a subrange of the hold-in range, the question is whether the infinite hold-in range implies infinite pull-in range. For the second-order type II APLL the conjecture is valid,.
From a mathematical point of view, that means what the loss of global stability in type II APLL is caused by the birth of self-excited oscillations and not hidden oscillations. A similar statement for the second-order type I APLL with lead-lag filter is known as Kapranov's conjecture on the pull-in range.
In general, his conjecture is not valid and the global stability and the pull-in range for the type I APLL with lead-lag filters may be limited by the birth of hidden oscillations.
For control systems, a similar conjecture was formulated by R. Kalman in 1957.