This paper presents the activities performed for the modelling and experimental characterisation of a pyroelectric infrared detector. The work focuses on a LiTaO3 sensor which has been used as detector in the Long Wavelength Channel of a double channel IR spectrometer devoted to the study of Mars atmosphere, the MarsExpress Planetary Fourier Spectrometer, PFS. The need for an experimental characterization arise from the need of modelling the complete spectrometer for a correct interpretation of the scientific data collected while orbiting around Mars. The sensor of interest has been characterised along with its amplifying and conditioning proximity electronics. Because of the final use of the detector, i.e. FTIR spectrometry, the experimental characterization focuses on the frequency response and non-linear behaviour which respectively affects spectral responsivity and the presence of spectral features ghosts. Mathematical models available in literature describing the pyroelectric phenomena usually neglect the dependence of thermal characteristics on temperature and are intrinsically linear, therefore unfit for our needs. Because of the lack of information about the detector building characteristics, an accurate a priori model could not be straightforward implemented. An a posteriori model, derived from an identification process based on the detector testing has been developed and validated in order to have a simulation tool for the full spectrometer. The sensor exhibit nonlinearities, depending on all factors influencing the sensing element average temperature: incident infrared power, housing temperature. These nonlinearities can be traced back to the dependence on temperature of thermal characteristics of the sensing element, pyroelectric coefficient and the thermal capacity of LiTaO3 and on the nonlinearity of the radiative heat exchanges.