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A mathematical model for an energy-dispersive X-ray spectrometer is proposed, which is based on the analysis of the radiation transport in a sample and in a detector, and an electron transport in the detector. The results obtained by using this model are compared with experimental data. The influence of parameters of sources of the primary X-rays, and the thickness and material of the detector on the signal-to-background ratios, was estimated. These ratios limited by electron and photon transport were compared. It is shown that the signal-to-background ratio can vary by several orders of magnitude at changing conditions of recording, and there are conditions when the use of Si or Ge detector is preferable.

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