A closed loop magnetic sensor system for measuring an input magnetic field from a magnetic field source has a compensation circuit, which can be for example a printed wire board, and a magnetic sensor, such as a Magnetoresistive (MR) sensor, for measuring an input magnetic field. Preferably, the magnetic sensor is magnetically coupled to the compensation circuit by arranging the magnetic sensor in an air gap provided in the compensation circuit. The compensation circuit has a compensating conductor, arranged on or in a dielectric medium, which can be configured as a plurality of nested coils. Electrical control circuitry, electrically, coupled to the magnetic sensor and compensating conductor, is adapted and arranged to drive a feedback current through the compensating conductor according to the output of the magnetic sensor such that the input magnetic field is substantially compensated at the magnetic sensor. The magnetic system can serve as current sensor for sensing current through a primary conductor.