Chaudhuri, SaptarshiVadapalli, Pranav2025-08-072025-08-072025-04-28https://theses-dissertations.princeton.edu/handle/88435/dsp01m613n205fExcess noise in amplifiers poses a significant limitation on scan rate in the comprehensive search for axion dark matter. For this reason, the quantum-limited parametric amplifier is essential to axion detection experiments. Due to its ability to provide broadband, quantum-limited amplification at hundreds of MHz, the KI-TWPA is the amplifier of choice for low-frequency applications such as the Princeton Axion Search. Despite experimental progress in the use of these devices, a rigorous analytical model for quantum noise does not exist for KI-TWPA systems. In this paper, a simplified quantum noise model for the KI-TWPA is formulated from the ground up, and some basic implications of such a model are discussed.enPrinceton University Senior Theses