The mechanism affecting the saturation frequency of plasma synthetic jet actuators is still unclear, which has led to the great hindrance of the application of plasma synthetic jet actuators on supersonic aircraft. Discharge parameters affecting the saturation frequency of plasma synthetic jet actuator and the average Helmholtz frequency are analyzed based on a novel coupling model in this paper. The model couples the phenomenological energy source term model with the mechano-acoustical analogy model. The Helmholtz frequency at each moment during the formation of the synthetic jet can be calculated. The effects of the electrical energy, the discharge duration and the instantaneous discharge power on the formation of the synthetic jet in a single discharge are investigated. The results show that the average Helmholtz frequency could not be used to evaluate the saturation frequency of the plasma synthetic jet actuator because they have different trends as electrical energy increases. The average Helmholtz frequency increases linearly with the increase of electrical energy, while the saturation frequency decreases in power function. The discharge duration on the microsecond scale and the instantaneous discharge power have little effect on the saturation frequency.