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arXiv:2509.01850

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

T. de Haan

Published Sep 2, 2025• 0 citations
arXivHTMLPDF

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 Thévenin-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.

DOI
10.48550/arxiv.2509.01850

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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 Thévenin-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.
We present a theoretical analysis and experimental evaluation of a transition-edge superconducting bolometer for detecting infrared and millimeter waves. The superconducting film is voltage biased and the current is read by a superconducting quantum interference device ammeter. Strong electrothermal feedback maintains the sensor temperature within the transition, gives a current responsivity that is simply the inverse of the bias voltage, and reduces the response time by several orders of magnitude below the intrinsic time constant C/G. We evaluated a voltage-biased bolometer that operates on the Tc∼95 mK transition of a tungsten film with a thermal conductance of G∼1.2×10−9 W/K. As expected, the electrical noise equivalent power of 3.3×10−17/W√Hz is close to the thermal fluctuation noise limit and is lower than that of other technologies for these values of G and temperature. The measured time constant of 10 μs is ∼100 times faster than the intrinsic time constant.
We present a detailed analysis of the fundamental noise sources in superconducting transition-edge sensors (TESs), ac voltage biased at MHz frequencies and treated as superconducting weak links. We have studied the noise in the resistive transition as a function of bath temperature of several detectors with different normal resistances and geometries. We show that the "excess" noise, typically observed in the TES electrical bandwidth, can be explained by the equilibrium Johnson noise of the quasiparticles generated within the weak link. The fluctuations at the Josephson frequency and higher harmonics contribute significantly to the measured voltage noise at the detector bandwidth through the nonlinear response of the weak link with a sinusoidal current-phase relation.
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Numerical and experimental modeling of the characteristics (sensitivity, constant time, noise properties) of high-Tc transition edge superconducting bolometers, operating in the various modes with an electrothermal feedback, are carried out: the mode with constant bias current, i.e. passive positive electrothermal feedback, the mode with constant bias voltage, i.e. passive negative electrothermal feedback and the mode with active electronic negative electrothermal feedback . It is shown, that in the modes with negative electrothermal feedback it is possible essentially to reduce constant time of bolometers till 5-15 of times in at some prize of the noise equivalent power on high frequencies. The estimation of influence of various noise components on a performance of the bolometers, operating with positive or negative electrothermal feedbacks, is carried out at the variation of bolometer parameters.
We systematically study the analysis and simulation of ac-biased superconductor transition-edge sensor (TES) circuits. In these ac-biased circuits, the current and voltage of the TES experience large swings in both directions, and small-signal analysis around a dc steady state does not apply. To understand their electrical and thermal behavior, we rely on concepts and techniques from radio-frequency circuit simulation and introduce the periodic steady state and perform periodic ac analysis. We also construct TES device models based on a comprehensive two-fluid physical model and investigate the behavior of ac-biased TES circuits using advanced circuit simulators. By relating our findings to results for the analysis of dc-biased TES circuits, we give appropriate definitions for the current and temperature sensitivity of the TES in ac-biased circuits. Our work not only builds a rigorous foundation for theoretical analysis of ac-biased TES circuits but also introduces powerful simulation techniques valuable for their design and research.
We report the experimental evidence of the ac Josephson effect in a transition edge sensor (TES) operating in a frequency domain multiplexer and biased by ac voltage at MHz frequencies. The effect is observed by measuring the non-linear impedance of the sensor. The TES is treated as a weakly linked superconducting system and within the resistively shunted junction model framework. We provide a full theoretical explanation of the results by finding the analytic solution of the non-inertial Langevian equation of the system and calculating the non-linear response of the detector to a large ac bias current in the presence of noise.