Stability analysis and pull-in behavior of modified dither optical phase-lock loop with loop propagation delay

This paper analyses the stability of a modified dither optical phase-lock loop (OPLL), which contains all the components of a standard dither OPLL in conjunction of an additional electro-optic phase modulator in the phase-locking branch, taking loop delay into account. Applying Nyquist criteria, expression for maximum allowable loop propagation delay of the modified dither OPLL is derived. Relative stability of the modified loop is studied in terms of the Gain margin and Phase margin of the OPLL. Also, Pull-in behavior of modified dither OPLL is analyzed in the presence of loop propagation delay. Expressions are derived analytically for computing the pull-in voltage, pull-in range and acquisition time for a second-order type-II modified dither OPLL that employs an active low pass loop filter. The influences of the dither signal, electro-optic phase modulator and loop propagation delay on the acquisition of the loop are shown. It is found that the electro-optic phase modulator completely eliminates the false locking phenomenon due to loop delay, decreases the acquisition time of the loop and allows pull-in from larger frequency offset. Simulation results are given in support of the analytical results.