This paper reports a novel analytic model of a plasma synthetic jet actuator (PSJA), considering both the heat transfer effect and the inertia of the throat gas. Both the whole cycle characteristics and the repetitive working process of PSJA can be predicted with this model. The frequency characteristics of a PSJA with 87 mm3 volume and different orifice diameters are investigated based on the analytic model combined with experiments. In the repetitive working mode, the actuator works initially in the transitional stage with 20 cycles and then in the dynamic balanced stage. During the transitional stage, major performance parameters of PSJA experience stepped growth, while during the dynamic balanced stage, these parameters are characterized by periodic variation. With a constant discharge energy of 6.9 mJ, there exists a saturated frequency of 4 kHz/6 kHz for an orifice diameter of 1 mm/1.5 mm, at which the time-averaged total pressure of the pulsed jet reaches a maximum. Between 0.5 mm and 1.5 mm, a larger orifice diameter leads to a higher saturated frequency due to the reduced jet duration time. As the actuation frequency increases, both the time-averaged cavity temperature and the peak jet velocity initially increase and then remain almost unchanged at 1600 K and 280 m/s, respectively. Besides, with increasing frequency, the mechanical energy incorporated in single pulsed jet, the expelled mass per pulse, and the time-averaged density in the cavity, decline in a stair stepping way, which is caused by the intermittent decrease of refresh stage duration in one period.