Computing the half-plane pull-in range of a PLL

A second-order PLL based on a triangular-characteristic phase detector and lead-lag loop filter is found in many applications where simplicity and economics are important. For these loops, the half-plane pull-in range Ω2 is of interest. In the existing literature, an algorithm is described for approximating Ω2; it requires the numerical integration of the nonlinear differential equation that describes the PLL. This numerical integration requirement is removed here by the development of an exact formula for Ω2.