A magnetic-field-to-voltage transducer includes a Hall element and a digitally gain-controlled Hall-voltage amplifier that produces an analog signal voltage Vsig having excursions of one polarity corresponding to the passing of magnetic articles. The gain of an AGC Vsig amplifier is only decreased in small sequential gain increments during an initial interval defined as that in which two excursions in Vsig have occurred, and the gain remains unchanged thereafter. Vsig is applied to the input of a peak-referenced-threshold signal detector that generates a binary output voltage, Vout, having transitions of one direction and the other direction corresponding respectively to the approach and retreat of the passing articles. The peak-referenced-threshold signal detector includes a dual-threshold-voltage comparator which is set to a large threshold at start-up. When just after start-up an excursion in the signal Vsig at the output of the amplifier exceeds a predetermined reference voltage, a small threshold obtains. Such an automatic threshold adjustment is made only in a brief initial period following start-up and not again until the proximity detector has been powered down and then started up again. This automatic dual-mode threshold feature prevents false detection due to "overshoots" that may be present in the transducer signal when the air gap is small, and leads to accurate detection over a wide range of air gaps between the transducer and the passing magnetic articles.