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The model of a photoacoustic gas-microphone signal in the time domain recorded in a transmission configuration using a minimum volume cell is derived. This model takes into account the inertial thermal relaxations of both the sample and the gas filling the cell by means of the generalized hyperbolic theory of heat conduction. With the introduction of electro-thermal analogy for the thin sample and short microphone length cavity, characteristic quantities are defined, which can be used in solving the inverse problem in time-domain photoacoustic in both cases, when thermal relaxations are neglected as well as when they are considered. The derived model that includes thermal relaxation explains the experimentally observed occurrence of overshoots and undershoots as well as an oscillatory approach to the steady values of the recorded signal in high-resolution time-domain photoacoustic measurements of thin semiconductor membranes, which will be presented in detail in Paper II of the paper. [ABSTRACT FROM AUTHOR]