We present a model of the response of superconducting AC bolometers to signal and noise using parameters and matrix formalism that were previously adopted in modeling DC bolometers and microcalorimeters. The model was developed to investigate novel AC bolometer designs, which have properties not described by previous models. It is applicable to kinetic inductance devices, kinetic inductance thermometers, AC transition edge sensors, and other technologies based on AC read out and frequency mixing. The AC bolometer model includes the temperature and current dependence of both resistive and inductive bolometers and microcalorimeters. The bolometers may be thermal or athermal. The model compactly describes the complex relationships between electrical and thermal signals and it simplifies the associated calculations. This model is useful for characterizing bolometers, predicting the effects of various noise sources on performance and designing new detectors. Additionally, a measurement technique is developed for characterizing these devices. V C 2013 American Institute of Physics. [http://dx.