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Nonlinear analysis of a Colpitts injection-locked frequency divider

An analysis of an injection-locked divide-by-N Colpitts frequency divider is proposed. An analytical model for fundamental locking and intermodulation (or superharmonic) locking (divide-by-2 operation) is derived based on Bessel functions to account for the exponential nonlinearity existing inside the divider. The analytical model matches the simulation results obtained from a BJT implementation. The proposed method can be extended to CMOS implementation utilizing MOS transistors operating in the weak-inversion region.