Impedance matching is a crucial feature of an amplifier used to increase its instantaneous bandwidth and is typically achieved using static LC resonators. Here we show an approach toimpedance matching in parametric amplifiers using arrays of unequal Josephson-junction-based elements (rf/dc SQUIDs, SNAILs, etc). The elements act either as small-footprint flux-tunable inductors forming an impedance-matching circuit, or ‚active‘ amplifier elements which result in amplifier gain. We develop an analytical theory describing these systems, predicting a quasi-non-periodic amplifier frequency and gain modulation with applied flux and the broadening of gain bandwidths. We demonstrate this in devices using arrays of flux-focused SNAILs where flux biasing varies across the array. We find instantaneous bandwidths of 200 MHz with >17 dB of gain centred at ∼5.4 GHz in a device without a static impedance matcher. This broadening of amplifier bandwidth is stable with >100 MHz bandwidth at 17 dB gain across >1.2 GHz tunable bandwidth. Our analytical model captures flux dependence and qualitatively reproduces gain-bandwidths giving confidence in our understanding of these systems and allowing operational figures of merit to be optimised in future devices.
We have simulated the performance of the Josephson Travelling Wave Parametric Amplifier (JTWPA) based on the one-dimensional array of RF SQUIDs. Unlike the ideal model in which allSQUIDs are assumed to be identical, we allowed variation of the device parameters such as the geometric inductance of the SQUID loop, capacitance to ground, Josephson junction capacitance and critical current. Our simulations confirm the negative effects of variation of the device parameters leading to microwave reflections between individual cells and the shift of the flux bias from the optimal point. The strongest effect is caused by the variation of the geometric inductance as it varies both the wave impedance and the flux bias. The most detrimental, however, are point defects, such as shorts to ground making the circuit opaque to microwaves. This imposes stringent requirements on the fabrication process making it extremely challenging. We highlight the strict limitations on parameter spread in these devices while also discussing the robustness of the scheme to variation
We present an analysis of wave-mixing in recently developed Josephson Travelling Wave Parametric Amplifiers (JTWPAs). Circuit simulations performed using WRspice show the full behaviourof the JTWPA allowing propagation of all tones. The Coupled Mode Equations (CMEs) containing only pump, signal, and idler propagation are shown to be insufficient to completely capture complex mixing behaviour in the JTWPA. Extension of the CMEs through additional state vectors in the analytic solutions allows closer agreement with WRspice. We consider an ordered framework for the systematic inclusion of extended eigenmodes and make a qualitative comparison with WRspice at each step. The agreement between the two methods validates both approaches and provides insight into the operation of the JTWPA. We show that care should be taken when using the CMEs and propose that WRspice should be used as a design tool for non-linear superconducting circuits such as the JTWPA.