New Uses for Hall-Effect Modulators
January 17, 1964 Electronics Magazine Article

January 17, 1964 Electronics [Table of Contents] Wax nostalgic about and learn from the history of early electronics. See articles from Electronics, published 1930 - 1988. All copyrights hereby acknowledged.

According to author Albert Hilbinger, dynamic range down to DC and circuit simplicity offset the low efficiency of Hall-effect modulators. The mixer circuit output has a suppressed carrier signal, making it a true product of the two inputs (fLO ± IF in the frequency domain). Evidently the scheme never gained wide acceptance in the industry because a search of the term does not produce much - other than this article. Achieving a suppressed carrier with standard diode mixers requires a quadrature arrangement using two mixers and a pair of 90° power splitters, which nowadays is done handily within a single integrated circuit. Sensors are the main exploitation for the Hall effect these days. They are widely used as proximity sensors, speed sensors, position sensing, and current sensing.

New Uses for Hall-Effect Modulators

By Albert R. Hilbinger

Aircraft Armaments Inc., Cockeysville, Maryland

Dynamic range down to d-c and circuit simplicity offset the low efficiency of Hall-effect modulators. Output is a suppressed carrier signal, a true product of the two inputs

Hall Efficiency

The main trouble with Hall-effect multipliers at present is their low efficiency. Whether or not this efficiency can ever be substantially raised is problematical, since it depends on a materials constant called the Hall coefficient. The Hall coefficient is much higher for semiconductors than it is for metals but still leaves much to be desired. But efficiency is only one parameter, and Hall multipliers have some important advantages.

Hall effect devices are useful as modulators since their output voltage is proportional to the product of two input voltages or currents.^{1, 2, 3, 4} In spite of an inherently low efficiency, Hall-effect multipliers offer the advantages of simplicity and wide dynamic range.

Circuit - Hall output voltage, as indicated in Fig. 1A, is

E_h = (R_hI_cB/t) X 10^-8 volt                                (1)

where R_h = Hall coefficient (a semiconductor material constant) in cm³/coulomb, I_c = semiconductor element control current in amperes, B = magnetic flux density in gauss, and t = semiconductor element thickness in centimeters.

Flux density produced in an air gap in a ferromagnetic core operated below saturation can be expressed as

B ≈ 0.4πNI_b/L_g                                   (2)

where N = number of turns in coil wound on core, I_b = coil current in amperes, and L_g = length of air gap in core in centimeters.

Substituting Eq. 2 for B in Eq. 1 and combining constants yields

E_h = KI_cI_b                                           (3)

where K = 0.4 πNR_h X 10^-8/t L_g

Thus the Hall voltage is a true product of two applied currents. If the currents are expressed in terms of the voltages which produced them

E_h = K'E_cE_b                                             (4)

where K' = K/R_c R_b; and R_c = resistance of control-current input circuit and R_b = resistance of field-current input circuit.

Modulation - If the two inputs are sinusoids E_c = E_oc cos ω_ct and E_b = E_ob cos ω_ct, the resulting output product is

E_h/K' = E_cE_b = E_ocE_ob cos ω_ct cos ω_bt                             (5)

Letting E_oc E_ob = E_o and applying the appropriate trigonometric identity

E_h/K' = (E_o/2)[cos (ω_c + ω_b)t + cos (ω_c - ω_b)t]                                (6)

If E_c is a carrier frequency and E_b a modulating signal, Eq. 6 represents a modulated wave. The equation has two sideband terms, (ω_c + ω_b) and (ω_c - ω_b) and no carrier term (a term in ω_c only). Thus the resulting output is a suppressed carrier or balanced modulator signal; the Hall-effect multiplier is inherently a balanced modulator.

Applications - A number of applications employing Hall-effect modulators have been investigated and three will be described. In all cases the same basic physical construction was used. A rectangular indium arsenide (InAs) element is cemented to a ferrite disk and then lapped to the desired thickness. Four electrical connections are made to the semiconductor element as shown in Fig. 1 B. The ferrite disk-semiconductor element assembly then becomes an integral part of the magnetic structure, as shown in Fig. 1C. The magnetic field through the semiconductor element is produced by a current flowing in a coil wound on a bobbin which is mounted around the center ferrite post of the assembly.

In one application a carrier frequency of approximately 1-Mc is modulated with a fixed frequency of 400 cps. Theoretically, either signal could be applied to either input. The practical choice, however, is to use the carrier frequency as the control current and the 400 cps as the magnetic-circuit drive, as shown in Fig. 2A. Core losses in the ferrite material used would be high at 1-Mc whereas the semiconductor element is essentially a pure resistance. The magnetic field coil is then series resonated to minimize the input power. Output is applied to a load of approximately 15 pf. Since input frequencies are fixed, it is possible to resonate the capacitance with a high-Q inductance that is link-coupled to the output of the Hall-effect multiplier.

With no modulating voltage applied, but with maximum carrier input, the output voltage is nulled with R₁. This minimizes the in-phase component of what is generally called the zero-field voltage. This voltage also contains a quadrature component that is eliminated by adjusting C₁. After potentiometer R₁ is adjusted, maximum modulating signal amplitude is applied and C₁ is adjusted for zero output at the points of modulation envelope cross-over.

In many Hall-effect modulator applications the leakage component inductively coupled from the magnetic field to the output must be removed. In this application this component was eliminated by the narrow-band output circuit.

Modulator output voltage is linear within one percent of full scale from zero to peak-field excitation of ±12 ampere-turns. With 850 milliwatts of carrier power and peak-field excitation of 12 ampere-turns, a modulated 100 volts peak-to-peak was obtained. The output could be increased by using a multiplier ferrite core material with a higher saturation flux density or by using a higher Q output transformer. A 50-percent increase in output level could be achieved with presently available optimum core materials for both multiplier and output transformer, with no increase in input power.

Pulse Circuit - In a second application a Hall-effect multiplier was used to produce bursts of audio-frequency signals, is indicated in Fig. 2B. Audio response of the unit is from d-c and is down 3db at 20 kc; there is no low-frequency cutoff. Pulse input requirements are one ampere peak at a maximum duty cycle of 0.1. For lower duty cycles peak current can be increased, with the restriction that the average pulse power dissipated in the semiconductor element does not exceed 2 watts. Resistor R₁ provides the audio bandwidth and matches the audio input to a particular voltage source. Resistor R₂ matches the pulse input to a 50-ohm pulse source. Potentiometer R₃ is adjusted for minimum pulse output with no audio applied; potentiometer R₄ is adjusted for minimum audio output between pulses. For both R₃ and R₄, infinite resolution trimming potentiometers are used.

Results obtained with one-ampere peak pulses and 10 volts rms audio input include an output of 350 mv peak-to-peak, with the output more than 65 db down between pulses.

The audio input could be increased to 100 volts rms without distortion, giving an output of 3.5 volts peak-to-peak. But the audio rejection between pulses would be degraded by approximately 20 db. Also, the peak pulse current could be increased in accordance with the power restrictions mentioned. Operation at greater pulse amplitudes with the audio input voltage held constant would improve audio rejection between pulses. For maximum audio rejection under any conditions, the pulse source should not have a d-c output level between pulses.

Oscilloscope photographs of the output waveforms of the modulator are shown and also the unit packaged as a plug-in module.

In a variation of the device, a pulse repetition rate higher than the audio frequency was used. Output characteristics are similar to those of the preceding modulator. If a number of pulses per cycle of audio are desired, the audio range is restricted by the pulse requirements. For example, at one ampere peak pulse current, if the pulse width is 10 microseconds and the duty cycle is 0.1, the maximum prf is 10 kilocycles. For ten pulses or more per cycle of audio under these conditions, the maximum audio frequency is one kilocycle. By reducing the peak pulse amplitude, a higher duty cycle could be employed, thereby allowing higher audio frequencies.

A possible application for this mode of operation is the detection of low-frequency magnetic fields. The physical construction previously described could not be used; instead, the magnetic field would be applied to the semiconductor element with flux collectors or magnetic antennas.

Other modulator applications covering a wide range of frequencies have been described in the literature.^{5, 6, 7} The potentially rugged simplicity, low cost, and wide dynamic range of the Hall-effect modulator make it ideal for a wide range of applications where a true-product, suppressed-carrier device is required.

References

(1)W. A. Scanga, A. R. Hilbinger, and C. M. Barrack, Hall Effect Multipliers, Electronics, July 15, 1960, p 64.

(2) G. L. Keister, A Compact Multiplier Puts The Hall Effect to Work, Control Engineering, Nov., 1955, P 94.

(3) R. P. Chasmar and E. Cohen, An Electrical Multiplier Utilizing The Hall Effect in Indium Arsenide, Electrical Engineering, Nov., 1958, p 661.

(4) G. S. Glinski and T. P. Landolt, Theory and Practice of Hall Effect Multipliers, 1961 TRE International Convention Record, Part II.

(5) Armour Research Foundation of Illinois Inst. of Technology, "Instrumentation and Measurement Techniques Study", Signal Corps Contract No. DA 36-039 SC-78269, Quarterly Progress Report Nos. 2, 3, 4, 6, 7 and 8.

(6) E. Cohen, Hall Effect Multiplier for Use at Radio Fre-quencies, Eleotronic Engineering, 32 p 558, 1960.

(7) E. Cohen, An Improved Radio Frequency Hall Effect Modulator, Electronic Engineering, 34 p 316, 1962.

Posted September 25, 2018