Influence of active device nonlinearities on the determination of Adler´s injection-locking Q-factor

The problem of the correct evaluation of Q-factor appearing in Adler´s equation for injection-locking is addressed. Investigation has shown that recent results presented in the literature, while extending applicability of the original method, do not completely account for nonlinear effects occurring when two-port active devices are involved. To overcome such limitation, use can be made of a newly developed theory in the dynamical complex envelope domain, capable of providing first-approximation exact dynamical models of driven quasi-sinusoidal oscillators. Some preliminary results are presented here concerning a class of injection-locked oscillators with single-loop feedback type configuration. The proposed procedure permits evaluation of the nonlinear oscillator Q-factor, either analytically or numerically, depending on the complexity of the nonlinear active device model involved. The example worked out, a MOST-equipped driven Colpitts scheme, clearly illustrates the accuracy improvement achieved in the determination of the locking bandwidth stemming from the newly defined effective Q-factor, without the need to resort to the very time consuming full numerical transient envelope simulations otherwise required to this purpose.