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Context: Bolometers are high sensitivity detector commonly used in Infraredastronomy. The HFI instrument of the Planck satellite makes extensive use ofthem, but after the satellite launch two electronic related problems revealedcritical. First an unexpected excess response of detectors at low opticalexcitation frequency for {\nu} < 1 Hz, and secondly the Analog To digitalConverter (ADC) component had been insufficiently characterized on-ground.These two problems require an exquisite knowledge of detector response. Howeverbolometers have highly nonlinear characteristics, coming from their electricaland thermal coupling making them very difficult to modelize.  Goal: We present a method to build the analytical transfer function infrequency domain which describe the voltage response of an Alternative Current(AC) biased bolometer to optical excitation, based on the standard bolometermodel. This model is built using the setup of the Planck/HFI instrument andoffers the major improvement of being based on a physical model rather than thecurrently in use had-hoc model based on Direct Current (DC) bolometer theory.  Method: The analytical transfer function expression will be presented inmatrix form. For this purpose, we build linearized versions of the bolometerelectro thermal equilibrium. And a custom description of signals in frequencyis used to solve the problem with linear algebra. The model performances isvalidated using time domain simulations.  Results: The provided expression is suitable for calibration and dataprocess- ing. It can also be used to provide constraints for fitting opticaltransfer function using real data from steady state electronic response andoptical response. The accurate description of electronic response can also beused to improve the ADC nonlinearity correction for quickly varying opticalsignals.

Building the analytical response in frequency domain of AC biased bolometers Application to Planck/HFI