Motion or displacement transducers of the two-terminal magnetoresistive type are well known.  These devices employ a semi-conductor material whose electrical resistance increases in the presence of a magnetic field.  This characteristic is exploited in detecting the presence or variation of magnetic flux fields produced either by current flow or relative motion in the magnetic fields of electromagnets or permanent magnets.  Examples of magnetoresistive transducer arrangements are described in such U.S. Pat.  Nos.  as: 3,853,377; 3,753,202; 3,267,405, 3,260,932, and 3,172,032. 
These patents generally disclose transducer configurations for detecting motion relative to a magnetic field and techniques for obtaining controlled output signals.  In each of these arrangements, the output capabilities of the transducers severely limit positional accuracy because of gradual change of the flux fields, the generally low signal levels, and sensitivity of the semiconductors to gap and temperature variations.  The semiconductor devices need effective flux concentration and their output signals usually require amplification, even though biased to the sensitive portion of the response curve. 
These limitations have hampered adaptation of the magnetoresistors as indicators of small displacements.  For instance, when the devices are used to detect displacement along a toothed member of relatively small pitch, the magnitude of the output signal tends to distort and produce an asymmetrical waveform as the device approaches and crosses tooth surfaces and edges, because of the fringing flux.  The effect of this deficiency has been diminished by using center-tapped or dual magnetoresistors in a bridge circuit, but there remains sufficient distortion to make accurate position deflection difficult and uncertain.