Optimal Design of PLL with Two Separate Phase Detectors

In order to improve the operation of phase-locked loops (PLL) in both the acquisition and tracking modes, loops with two phase detectors are considered. The optimization problem of choosing the phase detectors in order to minimize the, variance of loop phase error is formulated. The optimization problem is solved under several approximations. Despite the approximation, the resulting nonlinearities can be implemented and results in a PLL with improved performance in both acquisition and tracking modes.