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Large signal analysis of transition edge-sensors

Transition-edge sensors (TESs) are very fast and extremely sensitive detectors that can operate exceptionally well throughout the whole of the electromagnetic spectrum. We describe an algorithm based on the harmonic Newton method that is able to solve the coupled nonlinear equations that govern a TES, without any assumptions about the magnitude of input signals or parameters that control the state of the device. The harmonic balance (HB) algorithm is able to solve the coupled nonlinear equations in the small and large signal limits, and calculate the waveforms of all electro-thermal variables such as temperature and current. Full spectral analysis can be made easily with simulations that can include up to 40 harmonics. The dynamics of TESs can also be studied using pulsed signal power. This is essential to modelling calorimeters used in the X-ray region. Extensions to this algorithm such as multi-tone large signal analysis and noise models can also be made and the algorithms for these are currently being developed. The algorithm developed here can be extended, with minimum effort, to solve coupled nonlinear equations of any device such as cold-electron bolometers and general resistive thermometers.