Microwave theory of Josephson oscillators

In this paper, we deal with a model of a specific Josephson microwave circuit, that of a Josephson oscillator, and show that the RF behavior of a real Josephson oscillator may be predicted from a knowledge of the experimentally measured microwave circuit parameters, the junction critical current, and junction shunt resistance. Based on observations made with an electronic analog, we present an approximate analytical method for calculating the junction impedance or, rigorously speaking, the appropriate single sinusoidal-input describing function. Emphasis is placed on the proper use of the impedance, for example, in calculating the operating point and the expected output power of the oscillator. The circuit model used is that of a junction, described by the resistively shunted junction model, coupled to a series
LCR
resonance. Further confirmation of the validity of the circuit-theory approach is obtained by using the injection-locked oscillator theory of Kurokawa to predict the in-lock amplitude variation of a Josephson oscillator exposed to a weak synchronizing signal. Experimental data describing the amplitude variation and output power of an oscillator consisting of a point-contact junction placed in a 9.72-GHz coaxial resonator are presented. The data demonstrate the reasonable agreement obtained when the measured critical current and shunt resistance are used with the analytical expression for the junction impedance and the circuit theory to predict the RF behavior of a Josephson oscillator. Circuits more complex than our specific example may be handled by means of describing function techniques recently developed in the area of nonlinear solid-state microwave devices.