A tunable resonator in the gigahertz‐range using circular sine‐Gordon fluxons or pulsons on a lossy large‐area Josephson junction with a circular impurity in the Josephson current density is proposed. To obtain steady tunable oscillations in a lossy medium, one must supply energy (’’negative’’ resistance). We propose to control the constant bias current with an autonomous pulson velocity‐sensitive switch. One possibility for fine tuning the oscillations is to vary the strength of the Josephson impurity current.