Simplified two-fluid current-voltage relation for superconductor transition-edge sensors

We propose a simplified current-voltage (IV) relation for the analysis and simulation of superconductor transition-edge sensor (TES) circuits. Compared to the conventional approach based on the effective TES resistance, our expression describes the device behavior more thoroughly covering the superconducting, transitional, and normal-state for TES currents in both directions. We show how to use our IV relation to perform small-signal analysis and derive the device's temperature and current sensitivities based on its physical parameters. We further demonstrate that we can use our IV relation to greatly simplify TES device modeling and make SPICE simulation of TES circuits easily accessible. We present some interesting results as examples of valuable simulations enabled by our IV relation.