Design of a uniplanar resonance phase-matched Josephson traveling-wave parametric amplifier

In this paper, we present the design of a resonance phase-matched Josephson travelling-wave parametric amplifier that have a 12 GHz 3 dB-bandwidth centred near 10 GHz. Our design utilises a unilateral planar circuit structure which requires only a single layer of thin superconductor film deposited on a supporting substrate to reduce the fabrication complexity. The nonlinear medium of the device is provided by a series of Josephson junctions embedded in a coplanar waveguide with integrated shunt capacitor, and the dispersion of the transmission line is controlled by quarter wavelength resonators coupled capacitively to the feedline. Here, we describe in detail the electromagnetic designs of the various components of the amplifier, and the coupled-mode equations model that governs the three-wave mixing process. We extract the required circuit parameters of the amplifier through electromagnetic modelling, and determine the parametric gain-bandwidth product of the amplifier using an analytical model. Finally, we discuss the various design aspects that affect the overall performance of the amplifier.