Forced oscillations in a class of self-biased multimode oscillators

The behavior of a class of multimode oscillators, having two nonlinear elements and operating under the influence of an external signal, is analyzed, using approximation procedures of Krylov, Bogoliubov, and Mitropolsky. Although features of the basic circuit are chosen to conform to the general characteristics of common self-biased oscillators, the procedures employed are applicable to a large class of problems involving two nonlinear elements. Through the approximating procedure, the system of nonlinear differential equations, describing the basic circuit, is replaced by a new, more tractable system of three first-order nonlinear differential equations. Phase-space solutions of the approximating system are then used to predict and analyze several features of forced oscillator operation, including frequency entrainment, pulling, and super-regenerative detection. The results of the theoretical analysis are in very close agreement with the actual behavior of an experimental oscillator.