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FAIMS's ion separation mechanism is based on analyte's characteristic nonlinear relationship between its ion mobility and applied electric field strength. Present characterization methods for this nonlinear relationship are based on precarious assumptions which incur substantial errors under many circumstances. A rigorous method for solving the second and fourth taylor series coefficient of this relationship based on dispersion voltage value (assuming half-sinusoidal waveform) and associated compensation voltage value of spectrum peak is presented, alongside with rigorous analytical functions. FAIMS spectrums were obtained for ethanol, metaxylene and n-butanol using custom-built FAIMS spectrometer, and corresponding second and fourth taylor series coefficients were obtained with the proposed method. Evaluation shows that this method substantially reduces the RMS error between interpolated and measured peak compensation voltage values under different dispersion voltages, confirming its superiority over present methods. This rigorous method would help improve spectral resolutions of FAIMS spectrometer, facilitating high precision FAIMS spectrum database construction and accurate analyte discrimination.