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In this paper, the 2-D electrostatic field software, POISSON, is used to calculate the characteristic impedance of a BPM (beam position monitor) for a high current proton linac. Furthermore, the time-domain 3-D module of MAFIA with a beam microbunch at a varying offset from the axis is used to compute the induced voltage on the electrodes as a function of time. Finally, the effect of low 13 beams on the induced voltage, the sensitivity and the signal dynamic range of the BPM are discussed.