Plasma immersion ion implantation applies a series of negative high-voltage pulses to a target immersed in a plasma. An analytical model of the currents and potentials induced before, during, and after the negative bias in a planar geometry is presented. The effect of multiple pulses on the results is also studied. The model determines the time-varying ion current, electron current, total current, total dose, and sheath thickness for a piecewise linear voltage pulse. The sheath collapse is found to be important for high repetition rate pulses. Implementation of the model is done in SPICE, a circuit simulator. Comparison with experimental data has demonstrated the accuracy of the model.