Abstract <p>Analytical expressions have been obtained describing the spatio-temporal dynamics of terahertz pulses in a medium with refractive index dispersion, representing a single-period oscillation of the electric field have been obtained. The calculation results made it possible to approximate the actual radiation from a photoconductive semiconductor antenna based on LT-GaN. Comparison with experimental spectra showed that the proposed formulae successfully describe the single-period emission of terahertz pulses generated by photoconductive antennas under the action of femtosecond laser pulses. It is shown that in the far-field diffraction zone, terahertz pulses undergo diffractive broadening, acquiring the character of a one-and-a-half-period oscillation.</p>