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Although a hysteresis current control is a simple and a reliable modulation technique in switching control systems, its spectral contents around switching sideband are not distributed broadly. Random pulse width modulation (RPWM) technique is an effective scheme which distributes the spectral contents of load current and can reduce acoustic noise and mechanical vibrations of an inverter-fed motor drive. This paper presents a random-band hysteresis current control (RBHCC) technique with bipolar and unipolar modulations. Mathematical analysis and simulation results show the RBHCC with the unipolar modulation has no considerable effect on distributing the spectral contents of the load current compared to the bipolar modulation technique. Finally, the effect of the random-band hysteresis current control is analysed to determine the best hysteresis band height variation for the bipolar modulation.