Mathematical modeling of the field electron emission from the metal cathode with the modulated voltage is carried out. Theory and calculations show that the density of the external electron energy distributions is linear in relation to the modulated voltage. Numerical results for the potential barrier transmissivity with image forces potential is obtained as solution of Shroedinger equation. WKB approximation of the potential barrier transinissivity is also considered for the analytical extraction of the harmonic component from the field emission signal. Analytical results can be applied to the determination of the potential barrier transmissivity on experimental data.