A sensor includes: a reference magnetic field generator configured to generate a reference magnetic field that is modulated at a first frequency, a first magnetic field sensing element that is configured to generate a first internal signal that is modulated at a second frequency, and a second magnetic field sensing element that is configured to generate a second internal signal that is modulated at the second frequency. A first amplifier is configured to receive the first internal signal and output a first amplified signal; and a second amplifier is configured to receive the second internal signal and output a second amplified signal. A gain adjustment circuit is configured to produce a gain adjustment signal and adjust a gain of at least one of the first amplifier and the second amplifier based on the gain adjustment signal.