An approach to the analysis of injection-locked oscillators

By combining the instantaneous phase shift of a twosinusoid-input describing function with a phase response of the tuned circuit it has been possible to develop the locking equation for single-stage LC injection-locked oscillators ILO. The locking range as well as steady-state phase shift of an ILO are calculated for subharmonic, fundamental, and harmonic locking, the dc transfer characteristic of a nonlinear device being approximated, at the dc operating point, by a third-order polynomial. The phase plane representation is included. Experimental results are given to support some of the theoretical relations derived.