Phase regeneration characteristic of a three–mode oscillator with second and third harmonic resonators

Abstract

This paper discusses the phase regeneration characteristics of the three‐mode oscillator with two‐phase PSK signal injection composed of three resonators for the fundamental, second and third harmonics and a negative resistor. As the basic synchronization property of the oscillator, it is shown that two stable phase synchronization modes exist as follows. When the oscillator oscillates synchronously to the fundamental and the third harmonic frequencies, and the external signal with the frequency equal to the second harmonic is injected, synchronization takes place migrating among three frequencies with two stable phases. Then the phase regeneration of the oscillator for the injected phase‐modulated signal is discussed. When the change of the input signal phase is small, the oscillator output phase tends to remain at the original stable phase. When, however, the input phase approaches the other stable phase, the output phase changes stepwise to the other stable phase. Thus, the output signal has the phase fixed to either of the two stable phases. Such a phase regeneration phenomenon is demonstrated by the numerical solution for the simplified equation for the amplitude and phase of the oscillator. Finally, a three‐mode oscillator is constructed which oscillates at the fundamental frequency of 3.5 MHz. It is verified experimentally that the characteristics as analyzed by the theory are realized.