On Spurious Phase Modulation Caused by Second-Harmonic Terms for Digital Phase-Locked Loop

The second-harmonic term in the operation of phase detector for second-order digital phase-locked loop is studied. It unavoidably produces undesirable spurious phase modulation, which asymptotically oscillates around the would-be synchronous state, and increases the phase error, even may forbid the synchronization process. The analysis of spurious phase modulation and fast convergence problem shows, the transfer functions of loops are required to be low pass forms in order to suppress the second-harmonic term. In the presence of the second-harmonic term, the second-order digital phase-locked loop with zero spectral radius cannot achieve fast convergence, neither is stable. The results are confirmed by numerical simulations