In an automatic gain control unit, the gain of a voltage-controlled amplifier (VCA) (25) is regulated with a closed-loop control circuit. The time constant of the control circuit is varied dependent on the magnitude (31) of the VCA output signal. As long as the magnitude (31) of the VCA output signal is small, the gain is slowly adjusted. In case the magnitude (31) of the VCA becomes so large that saturation of the analog-digital converter (28) might occur, the time constant of the control circuit is decreased, in order to allow for a quick adjustment of the amplifier's gain.