Johnson Noise Suppression in AC-Biased Transition-Edge Sensor Bolometers: A Thévenin-Equivalent Circuit Analysis

Abstract: Transition-edge sensor (TES) bolometers operate under strong electrothermal feedback, wherein power deposited on the bolometer is compensated by a corresponding change in electrical power dissipation. We present a comprehensive analysis of Johnson noise suppression that extends previous theoretical frameworks to the general case of AC-biased linear circuits with arbitrary parasitic impedances. Using a Th\'evenin-equivalent circuit formulation -- consisting of an ideal voltage source and complex series impedance external to the bolometer thermal island -- we derive analytical expressions for the noise-equivalent current in the presence of both bolometer and parasitic Johnson noise sources. Our analysis demonstrates that while the electrothermal feedback loop effectively suppresses Johnson noise originating from the bolometer resistance, it provides no suppression of Johnson noise from external series resistance. In the limit of high loop gain, the bolometer Johnson noise contribution vanishes while the parasitic contribution remains unsuppressed.