A switching half-bridge has two field-effect transistors and a supplementary circuit arranged upstream of a gate terminal of a first field-effect transistor and formed of a first circuit branch having a damping resistor and an inductor connected in series with the damping resistor and a second circuit branch being connected in parallel with the first circuit branch and having a series resistor and an auxiliary switch connected in series with the series resistor. The half-bridge can be switched from a first switching state to a second switching state, wherein while the auxiliary switch is open, a change in the control voltage causes the first circuit branch to temporarily change the gate-source voltage of the first field-effect transistor from the switch-on level to a second switch-off level greater than a first switch-off level, with the gate-source voltage thereafter returning to the first switch-off level.