Background: Kinetic Inductance Travelling Wave Parametric Amplifiers (KITWPAs) are a new variant of superconducting amplifier that can potentially achieve high gain with quantum-limited noise performance over broad bandwidth, which is important for many ultra-sensitive experiments. In this paper, we present a novel modelling technique that can better capture the electromagnetic behaviour of a KITWPA without the translation symmetry assumption, allowing us to flexibly explore the use of more complex transmission line structures and better predict their performance. Methods: In order to design a KITWPA with optimal performance, we investigate the use of different superconducting thin film materials, and compare their pros and cons in forming a high-gain low-loss medium feasible for amplification. We establish that if the film thickness can be controlled precisely, the material used has less impact on the performance of the device, as long as it is topologically defect-free and operating within its superconducting regime. With this insight, we propose the use of Titanium Nitride (TiN) film for our KITWPA as its critical temperature can be easily altered to suit our applications. We further investigate the topological effect of different commonly used superconducting transmission line structures with the TiN film, including the effect of various non-conducting materials required to form the amplifier. Results: Both of these comprehensive studies led us to two configurations of the KITWPA: 1) A low-loss 100 nm thick TiN coplanar waveguide amplifier, and 2) A compact 50 nm TiN inverted microstrip amplifier. We utilise the novel modelling technique described in the first part of the paper to explore and investigate the optimal design and operational setup required to achieve high gain with the broadest bandwidth for both KITWPAs, including the effect of loss. Conclusions: Finally, we conclude the paper with the actual layout and the predicted gain-bandwidth product of our KITWPAs.

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Broadband ultra-low noise amplification is important for many fundamental physics experiments. In our case, we aim to develop a quantum limited Josephson Travelling Wave Parametric Amplifier (JTWPA) for dark matter search experiments. In this paper, we focus on the development of the JTWPA, in particular to optimise the performance of the amplifier with a simplified fabrication prospect. We present our methodology for the optimisation process, focusing on three important aspects, namely utilising the minimal number of tunnel junction required, maximising the operational bandwidth and achieving a 50 Ω characteristic impedance. We first explore the relations between the important circuit parameters of the JTWPA and its performance indicators. Using the information obtained, we perform our optimisation process to search for the optimal design parameters. We then compare the gain bandwidth performance of the different optimised models, and present our findings with further analyses. We demonstrate that our optimised model requires 4× less tunnel junctions compared to the conventional model, and we are able to improve the operational bandwidth by 68% while maintaining the characteristic impedance of the device at 50 Ω.

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