This work consists of a detailed thermal modeling of two different radiometers operated at cryogenic temperatures. Both employ a temperature sensor and an electrical-substitution technique to determine the absolute radiant power entering the aperture of a receiver. Their sensing elements are different: One is a germanium resistance thermometer, and the other is a superconducting kinetic-inductance thermometer. The finite element method is used to predict the transient and steady-state temperature distribution in the receiver. The nonequivalence between the radiant power and the electrical power due to the temperature gradient in the receiver is shown to be small and is minimized by placing the thermometer near the thermal impedance. In the radiometer with a germanium resistance thermometer, the random noise dominates the uncertainty for small incident powers and limits the ultimate sensitivity. At high power levels, the measurement accuracy is limited by the uncertainty of the absorptance of the cavity. Recommendations are given based on the modeling for future improvement of the dynamic response of both radiometers.

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