An exemplary current sensor operating in accordance with the principle of compensation includes a primary winding creating a magnetic field based on a current to be measured, a secondary winding generating a magnetic field compensating the primary winding based on a compensation current. The current sensor also includes a magnetic core, a terminating resistor connected in series to the secondary winding, and sensor means. A booster circuit is connected downstream of the sensor means and feeds the compensation current to the secondary winding via the terminating resistor. The booster circuit includes a switched mode amplifier with a pulse width and density modulator that operates based on pulse width and density modulation, turning the compensation current into a pulse width and density modulated current. The switched mode amplifier having a switching frequency that is high at when the compensation current is small and low when the compensation current is high.