RF Phase Control in Pulsed Magnetrons

This paper describes the behavior of a magnetron oscillator started in the presence of an externally applied rf exciting signal whose frequency is not greatly different from the unperturbed steady-state frequency of the magnetron. Two points of view are presented: First, quasi-steady-state starting is assumed, and a differential equation representing the system within this limitation is derived. Solutions obtained specify the phase of the oscillator as a function of time subsequent to starting. Second, the inhomogeneous Van der Pol equation is used to describe the system. The oscillator is represented as a parallel RLC circuit shunted by a negative, nonlinear conductance. Approximate analytical and differential analyzer solutions of this equation are used to investigate the frequency and phase transients during starting and distortion of the build-up envelope by the exciting signal. The initial conditions for both equations are established in terms of the exciting signal-topreoscillation noise ratio. Results of the two analyses are essentially in agreement; details of the solutions are different since reactive beam loading has been neglected in the latter case. The phase transient initiated during starting may have a duration which is long compared to the build-up time of the rf voltage on the magnetron anode. Preoscillation conditions which fix the initial phase play an important part in determining the phase for a considerable time subsequent to starting.