Numerical analysis of a three-wave-mixing Josephson traveling-wave parametric amplifier with engineered dispersion loadings

The recently proposed Josephson traveling-wave parametric amplifier (JTWPA) based on a ladder transmission line consisting of radio-frequency SQUIDs and exploiting three-wave mixing (3WM), has great potential in achieving both a gain of 20 dB and a flat bandwidth of at least 4 GHz. To realize this concept in practical amplifiers we model the advanced JTWPA circuit with periodic modulation of the circuit parameters (engineered dispersion loadings), which allow the basic mixing process, i.e., ${\omega }_s={\omega }_p-{\omega }_i$, where ${\omega }_s$, ${\omega }_p$, and ${\omega }_i$ are the signal, the pump, and the idler frequencies, respectively, and efficiently suppress propagation of unwanted higher tones including ${\omega }_{2p}=2{\omega }_p$, ${\omega }_{p+s}={\omega }_p+{\omega }_s$, ${\omega }_{p+i}={\omega }_p+{\omega }_i$, etc. The engineered dispersion loadings allow achieving sufficiently wide $3$ dB-bandwidth from $3$ GHz to $9$ GHz combined with a reasonably small ripple ($\pm 2$ dB) in the gain-versus-frequency dependence.