Power flow for Josephson elements

A Josephson element is a nonlinear lossless element that is characterized by an internal frequency, ω0;, the autonomous frequency, proportional to the dc voltage across the element. Detection, mixing, generation, harmonic generation and mixing, and parametric amplification are possible using such an element. We present here general relations for the power flow at the frequencies of interest in such an element. These general power flow relations depend upon whether the autonomous frequency is phase-locked, either harmonically or subharmonically, to a frequency in the system or is unlocked. The results here generalize those given previously by Russer for the harmonically locked case.