  The fundamental noise limit of a phase-preserving amplifier at frequency
$\omega /2\pi $ is the standard quantum limit $T_{q}=\hbar \omega /2k_{B}$. In
the microwave range, the best candidates have been amplifiers based on
superconducting quantum interference devices (reaching the noise temperature
$T_{n} \sim 1.8 T_{q}$ at 700 MHz), and non-degenerate parametric amplifiers
(reaching noise levels close to the quantum limit $T_{n}\approx T_{q}$ at 8
GHz). We introduce a new type of an amplifier based on the negative resistance
of a selectively damped Josephson junction. Noise performance of our amplifier
is limited by mixing of quantum noise from Josephson oscillation regime down to
the signal frequency. Measurements yield nearly quantum-limited operation,
$T_{n}=(3.2\pm 1.0) T_{q}$ at 2.8 GHz, owing to self-organization of the
working point. Simulations describe the characteristics of our device well and
indicate potential for wide bandwidth operation.
