Multitone large-signal analysis of superconducting transition-edge sensors for astronomy

Abstract

A simple transition-edge sensor (TES) is governed by two coupled, nonlinear equations, which when solved give the behavior of the device given the initial conditions. The two equations describe the full electrical and thermal characteristics of the device and the way in which the device interacts with the external electrical and thermal circuits. To date these coupled nonlinear equations have been solved analytically in the small-signal limit, by linearizing the equations about some operating point. The resulting coupled linear equations contain a wealth of interesting physics, and form the principal tool by which all detectors are currently designed and modeled. In this article we describe a numerical technique for solving the coupled nonlinear equations rigorously, without any assumptions about the magnitudes of the various signals and parameters that determine the behavior of a device. The technique is based on a harmonic balance algorithm that searches, in the frequency domain, for voltage, current, and temperature wave forms that are consistent with the solid-state physics of the device. Indeed, both the small and large signal limits can be simulated, and the full harmonic content of the system retrieved. In this article, we will outline the principal features of the algorithm, and show various results such as I−V curves, saturation when signal power is modulated, impedance response when the bias current is modulated and signal power kept constant, and pulsed signal power analysis that shows the dynamics of a device. Numerous extensions of this fundamental technique are now possible including multitone nonharmonic analysis, large-signal impedance calculation, modeling of complicated thermal circuits, noise models, and frequency-domain multiplexing. We believe that our algorithm will become the principle technique for analyzing the large-signal behavior of all TES detectors and on that basis we are developing computer aided design software.