New results on the PLL false lock phenomenon

Conditions, based on the multipliers of a linear differential equation with periodic coefficients, for the occurrence of false lock in a phase lock loop (PLL) are presented. Two new and powerful algorithms are presented for computing the frequency difference between the reference and voltage controlled oscillator when the loop is false locked. The first algorithm expresses omega f sup -1 as a power series in the closed loop gain. The second algorithm expresses omega sup -1 as part of a solution to a nonlinear algebraic system of equations which can be solved by numerical methods. The power of both algorithms is illustrated by application and comparison.