  A directional superconducting parametric amplifier in the GHz frequency range
is designed and analyzed, suitable for low-power read-out of microwave kinetic
inductance detectors employed in astrophysics and when combined with a
nonreciprocal device at its input also for circuit quantum electrodynamics
(cQED). It consists of an one wavelength long nondegenerate Josephson
parametric reflection amplifier circuit. The device has two Josephson junction
oscillators, connected via a tailored impedance to an on-chip passive circuit
which directs the in- to the output port. The amplifier provides a gain of 20
dB over a bandwidth of 220 MHz on the signal as well as on the idler portion of
the amplified input and the total photon shot noise referred to the input
corresponds to maximally 1.3 photons per second per Hertz of bandwidth. We
predict a factor of four increase in dynamic range compared to conventional
Josephson parametric amplifiers.
