Four-phase characteristics of a multimode oscillator with second and third harmonic oscillations

This paper describes the multimode synchronisation of an oscillator having three resonators of fundamental, second and third harmonic frequencies with an external signal injected. Assuming that the current/voltage relationship of the nonlinear conductance is given by a third-order polynomial, the simplified equations for the amplitude and phase of oscillation are derived by using the method of equivalent linearisation. It is found that four output phases exist which are separated by ¿/2 from one another at the fundamental frequency when an external signal is applied at frequency close to the second harmonic of the oscillator.