An Exact Formula for the Pull-Out Frequency of a 2nd-Order Type II Phase Lock Loop

The pull-out frequency of a Phase Lock Loop (PLL) quantifies the loop´s ability to remain frequency locked under abrupt changes in the reference input frequency. This parameter is very critical in many applications e.g. FSK demodulator, multicarrier, and frequency-hopping based systems. In most cases, this parameter must be determined numerically or approximated using asymptotic techniques. Either of the methods needs special knowledge, skill and tools. An exact formula is derived for computing the pull-out frequency for a 2nd-order Type II PLL that employs a triangular characteristic phase detector. With this formula, the pull-out frequency of such PLLs can easily be calculated using a current day scientific calculator.