Locking bandwidth equations for electrically and optically injection-locked oscillators

The two most widely used locking bandwidth equations for injection-locked oscillators, Adler´s and Kurokawa´s equations, are compared for the first time. Three differences are highlighted by the comparison: firstly, the absence of the factor 1/cosθ in Adler´s equation; secondly, larger bandwidth is predicted by Kurokawa´s equation; and thirdly, a difference in the Q factors used. It is shown that Kurokawa´s locking bandwidth equation is suitable for high-Q reflection-type electrically injection-locked oscillators employing a circulator, while Adler´s equation is suitable for reflection-type injection-locked oscillators not employing a circulator. Experimental results from measurements on an optically injection-locked oscillator show that the loaded-Q varies with injection power, and demonstrate that both Kurokawa´s and Adler´s equations, which treat the Q as a constant, are not accurate for predicting the locking bandwidth of wide locking bandwidth, injection-locked oscillators. Finally, a theoretical analysis of the optimum photodetector insertion point for a wide locking bandwidth, transmission-type indirect optically injection-locked oscillator is presented.