Stability conditions of a class of delayed PLL systems through linear and non-linear techniques

A study of the stability problems of a class of heterodyne second-order pha se-locked loops incorporating an additional phase modulator has been report ed in this paper. Conditions of stability of this system in terms of loop d esign parameters have been obtained through the Liapunov method, the Routh- Hurwitz method and the Nyquist method. Also reported are simulation results finding design parameters for stable operation of the system. Comparing th e results obtained through different techniques, it can be noted that linea r analytical methods provide design parameters which are consistent with si mulation results for small loop phase errors, but for large loop errors des ign parameters predicted by the Liapunov method should be used for system d esign.