Analog Multiplier Based on the Hall Effect

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Abstract
The Hall effect is shown to be well fitted for electronic multiplication of voltages—one of the most cumbersome operations in analog computation. The use of this effect yields a very simple instrument with good accuracy and speed. The rise time—corresponding to a 0.2% error in amplitude—for the response of a step voltage of maximum value (100 volts) applied to the slower of the two inputs, can be kept down to about 1 msec. This time is dictated only by the feeding circuits and is linearly dependent on the amplitude of the step. Thus a step of 5 volts gives a rise time of 50 μsec. Most semiconductors are investigated with respect to their capabilities of accurate multiplication. Silicon is found to be the best choice. The choice of dimension of the semiconductor crystal is discussed from the solution of a potential problem with skew boundary conditions which determines the Hall voltage. The output of a silicon crystal may be as high as about 0.5 volt for an applied magnetic induction of 5000 gauss, a current through the crystal of about 5 ma, and with a simple thermal contact between the crystal and the core of the magnet, without having errors greater than 0.1%. The output voltage is amplified with a chopper amplifier to 20 volts.

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