We introduce an exponentially tapered Josephson flux-flow oscillator t
hat is tuned by applying a bias current to the larger end of the junct
ion. Numerical and analytical studies show that above a threshold leve
l of bias current the static solution becomes unstable and gives rise
to a train of fluxons moving toward the unbiased smaller end, as in th
e standard flux-flow oscillator. An exponentially shaped junction prov
ides several advantages over a rectangular junction including: (i) sma
ller linewidth, (ii) increased output power, (iii) no trapped flux bec
ause of the type of current injection, and (iv) better impedance match
ing to a load.