Dynamics of an antiferromagnetic spintronic oscillator phase-locked loop-based frequency synthesizer, which generates terahertz oscillations in a wide frequency range under the influence of direct current, was investigated. By the method of slowly varying amplitudes, a dependence of the gain on the ring of the phase locked loop on the difference in frequencies of synchronized oscillations at different division coefficients in the feedback circuit is obtained. It is shown that as the division coefficient increases, the band of synchronized oscillations decreases with unchanged parameters of the antiferromagnet-based spintronic oscillator.