In the application of atmospheric pressure plasma jet, because the frequency of AC power supply is limited in the kHz range, the research on the influence of power supply electrical parameters on discharge is basically aimed at the variation of plasma jet characteristics with a single driving electrical parameter ( such as voltage and frequency). However, the discharge power usually changes with a single electrical parameter changing, which can undoubtedly affect the discharge performances including the plasma physical parameters and generated reactive species, resulting in the failure to reflect the influence of the single driving parameter on the discharge. In this study, an atmospheric pressure argon plasma jet is driven by a home-made AC power supply with adjustable pulse modulated duty cycle. And combining the diagnosis of the optical emission spectrum and the optical absorption spectrum, the influences of the voltage, frequency and pulse modulated duty cycle parameters on the gas temperature T_g, electron excitation temperature T_exc, electron density n_e, and OH radical particle number density of the plasma jet are studied under a constant discharge power of 2 W. The results show that at the constant power, the electron density n_e does not change with the variation of electrical parameters as the linkage change of electrical parameters will offset the influence of a single parameter on the electron density, while the gas temperature T_g, electron excitation temperature T_exc, and OH radical particle density are most affected by the pulse modulated duty cycle, followed by driving voltage, and the frequency effect is the smallest. Under the constant power, as the frequency decreases, the voltage will increase, and also the gas temperature T_g, electron excitation temperature T_exc, and OH radical particle number density will increase. On the contrary, although the voltage also increases as the pulse modulated duty cycle decreases, the gas temperature T_g, electron excitation temperature T_exc, and OH radical particle number density are all reduced. In addition, the results indicate that reducing the duty cycle of AC power can make the atmospheric pressure plasma jet produce more OH radicals at lower gas temperature. This study provides a new insight into the influence of electrical parameters on the characteristics of atmospheric pressure plasma jets under constant power, and also presents a guidance for choosing power parameters of plasma jets with low gas temperature and high density of reactive species, which is conducive to the development of atmospheric pressure plasma jets in biomedicine and other fields.