  The RCSJ (Resistor-Capacitor Shunted Junction) model provides us an
analytical formula for the conversion efficiency for a resonant Josephson
effect mixer. An external rf signal is applied to a long Josephson junction
operating in the fluxon oscillating regime. The sine-Gordon equation is used to
investigate the dynamics of the phase-locking between the fluxon oscillations
and the external signal. We obtain that it is possible to have conversion
efficiency greater than unity.
