A new excitation technique is described for the measurement of weak magnetic fields (<0.01 Oe). The resistance variation of a magnetoresistive element due to an oscillating excitation field is converted into a voltage proportional to the environmental field. The excitation field amplitude is set large enough to saturate the magnetization during each half-cycle, greatly reducing hysteresis effects in the output signal. Both anisotropic magnetoresistance (AMR) and giant magnetoresistance (GMR) structures have been used to measure fields with sufficient accuracy for compass applications. Such devices could be made with extremely small dimensions and power requirements.