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We report on the transient behavior of the charge-to-voltage conversion of a silicon drift detector with an integrated JFET in a source follower configuration, suitable for X-ray spectroscopy and imaging applications. The experimental results are based on the measurements of the JFET's source voltage in the time domain. The dependence on count rate up to 600 kcts/s and on photon energy up to 15.7 keV are presented at operating temperatures around 20°C. The charge collecting capacitance shunting the gate of the JFET is discharged by a continuous reset current, which is attributed to the I-V characteristic of the JFET's gate-to-channel junction. Its influence on the signal amplitude is discussed with respect to the voltage dependence of the charge-collecting capacitance. A set of analytical equations and an equivalent circuit fully describes the dependence of the mean source voltage, of the discharging current, and of the signal amplitude as a function of count rate and photon energy. The simulated responses show a good quantitative agreement with the measured characteristics.