Magnetoresistance: Better Than Hall-Effect Multipliers
April 6, 1964 Electronics Magazine

April 6, 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.

I'm having a hard time writing this with my eyes rolled back in my head. The last time I experienced this level of overwhelmedness was probably the third or fourth week of my feedback and control class at the University of Vermont (UVM). Even though electricity and magnetism shares many complimentary and parallel concepts, for some reason thinking in terms of magnetics when describing amplifiers, mixers, modulators, etc., has always caused brain freeze. Maybe it has to do with an ingrained bias due to my earliest dealings with circuits being from a technician background before earning an engineering degree. The equations of electric fields and magnetic fields are very similar so that helps lower the barrier a bit. An engineer I worked with once had the uncanny ability to comprehend time domain waveforms in the frequency domain, and vice versa, when viewing an o-scope or spectrum analyzer display. Sure, simple things like sine waves or square waves can be recognized by most people who have been in the field for a couple years, but this guy's ability went way beyond that.

Magnetoresistance: Better than Hall-Effect Multipliers

A new circuit makes this multiplier practical in many applications. It is more efficient than Hall-effect devices currently used in amplifiers and oscillators

By S.F. Sun

Institut fur Hochstfrequenztechnik, Stuttgart, Germany

Physicists have known for years that the magnetoresistive effect in semiconductors (the resistance of a material changes in a magnetic field) was theoretically more efficient for high (3000) gauss fields than the Hall effect where a semiconductor carrying a current generates a voltage at right angles to the current. The magnetoresistive effect could be especially useful in devices like a multiplier (two input voltages are multiplied to produce the output) but has been impractical because the magnetoresistive element always needed an extra-biasing magnetic field to improve its non-linear characteristics. This extra field posed additional problems. If the field was weak, it did not make the element sensitive enough or linear enough for large signal applications. To make a strong field, an engineer had to design a complex and impractical circuit.

The extra-biasing field is no longer needed, however, if a specially designed push-pull magnetoresistive circuit is used. This new circuit basically is a three-dimensional multiplier that can replace any Hall-effect device. It is more sensitive and more efficient than the widely used device. In addition, the magnetoresistive multiplier is easier to adjust than a Hall-effect device and can operate at room temperature.

Particularly in Europe, Hall voltage generators have been put to work in industry because they are simple, economical and reliable. The new magnetoresistive multiplier may well replace Hall devices in such applications as amplifiers, mixers, modulators and d-c transformers.

Theory

The increase in semiconductor resistance influenced by a weak magnetic field may be considered as following the square law, in relation to flux density. In terms of flux density B, the resistance R may be expressed as:

R = R₀ + mB²

where R₀ is the initial resistance at zero magnetic field and m in the equation is a proportionality constant.

A magnetoresistive unit consists of a semiconductor placed in the air gap of a magnetic core which has two excitation windings. If two semiconductors with identical properties are used, and are arranged in a bridge circuit (similar to a push-pull amplifier) the external resistance (R_ex) is much larger than that of the semiconductors. With one unit subjected to the influence of the sum of two variable magnetic fields, (B₁ + B₂), and the other subjected to their difference (B₁ - B₂), the resistance of the specimens R₁ and R₂ becomes:

R₁ = R₀ + m (B₁ + B₂)²

and

R₂ = R₀ + m (B₁ + B₂)²

respectively. Under conditions that the magnetic cores are well below saturation and the core reluctance is negligibly small in comparison with that in the air gap, inductions B₁ and B₂ may be considered as proportional to the excitation currents I₁ and I₂.

By passing a current of equal magnitude (I₃) through each unit, the voltage difference, V, between the terminals of R₁ and R₂ will be

V = I₃ (R₁ - R₂) = 4m B₁ B₂ I₃

or

V = K I₁ I₂ I₃

where K is a constant which includes the factor 4m and also takes care of the proportionality between the inducted and the exciting currents. The result is a three-dimensional electronic multiplier whose input currents represent three parameters and whose output voltage gives their product.

The 3-D multiplier may be reduced to a two-dimensional multiplier by keeping one of the parameters B₁, B₂ or I₃ constant. This parameter will then be used to adjust the sensitivity of the device or to improve the linearity of the composite characteristics. Some examples of practical circuits follow.

Analog Computing Element

Since the output voltage of the multiplier is proportional to the product of three currents, the output voltages of two multipliers, A and B, can be written as

V_A = K_A I₁ I₂ I₃, V_B = K_B I₄ I₅ I₆

respectively. If the outputs of multipliers A and B are connected to a difference amplifier, and V_A and V_B will be compared and, as a result, the amplifier will supply to unit B an output current corresponding to I. This current will become stable when V_A is equal to V_B; it gives the equations:

I₆ = (K_A/K_B) (I₁I₂I₃ /I₄I₅).

Polyphase Wattmeter

In electrical power system, the multiplier is modified by a permanent magnet inserted in the core of the magnetoresistive unit. This allows one of the variable magnetic fields to be kept constant. The voltage difference, V, will be reduced to

V = (4mB₁) B₂I₃ = K I₂I₃

If the excitation current I₂ of the variable field is made proportional to the instantaneous phase current, i, of an electrical power network, while the current I₃ through the semiconductor is proportional to the instantaneous phase voltage, so that

I₂ = k_i i = k_i I_m sim (ωt + θ)

and

I₃ = k_e = k_e E_m sim ωt

the output voltage of the multiplier will become V = KI₂I₃

V = K I₁I₂

= - 1/2 Kk_i k_e I_m E_m cos (2 ωt + θ) + 1/2 Kk_i k_e I_m E_m cos θ

which consists of an alternating-current and a direct-current component, the latter being in proportion to the power of the network. It is possible to construct a polyphase wattmeter with a single indication to show the total power consumed in a multiphase system. Take a three-phase network as example; the circuit arrangements are shown with those parts enclosed by the dotted lines as units of a single-phase wattmeter. Since the current in the semiconductor is drawn from the source through a voltage transformer, the output terminals of the units can be joined in series so that the output voltage will be added together and the sum can be indicated by a d-c voltmeter. Modifying the circuit produces polyphase power meters able to measure reactive power or apparent power.

Amplifiers and Oscillators

There are many ways to construct amplifiers and oscillators. One of them is to make two of the parameters of the three-dimensional multiplier mutually dependent, for example B₂ = k I₃ so that the voltage different may be rewritten as

V = 4mkB₁I₃² = KB₁I₃²

where the k's are a proportional constant. An amplifier circuit has the field winding of B₂ in series with the semiconductor and the input is applied to the field winding of B₁ which may have many turns. The amplitude of the output voltage will be controlled by current I₃ and is proportional to its square.

An amplifier is shown with a feedback winding that may produce an induction B, additive (or subtractive) to B₁. If the mmf (magnetomotive force) required by the magnetic path in the core is negligible, the value of B will be dependent on the air-gap length g, the permeability in the gap μ_a the resistance of the feedback winding r and the number of turns of the feedback winding N. The voltage difference becomes

V = K I₃² (β₁ VNμ_a/2gr

or

V = K I₃² β₁ / (1 - KNμ_a I₃²/2gr)

α = 1/(1 - KNμ_a I₃²/2gr)

This kind of amplifier with feedback arrangement is suitable only for d-c signals.

In the last voltage difference equation, if the feedback term

β = KNμ_a I₃²/2gr

is made equal to or larger than unity, the circuit becomes unstable and an oscillator can be obtained by simply connecting a capacitor between the two feedback windings and omitting the field winding of B₁. Frequency f will be determined by

f = 1/2π √(LC)

with L the total inductance of the windings and C the capacitance. Another example for an oscillator circuit is given in (D) where two capacitors complete the tank circuit.

Mixer, Modulator and Demodulator

Since all these devices are based upon a process by which the output frequency differs from the input signal, yet is controlled by it, the nonlinear elements, used to achieve this purpose, can be replaced by magnetostrictive elements capable of multiplication operation. Circuit (A) illustrates a three-dimensional multiplier as a mixer. Signals of different frequencies f₁ and f₂ are fed to any two inputs of the three parameters, while the last one supplied with d-c can be used as a means of regulating the amplitude of the output voltage consisting of the components of (f₁ + f₂) and (f₁ - f₂). Eventually the last parameter can also be used as the input of a third signal of frequency f₃ to mix three frequencies.

The principles of modulator and demodulator are similar and explained by an example of a demodulator. The semiconductors bridge circuit (B) receives a modulated signal from input terminals while one of the magnetic fields is tuned to the carrier frequency by means of a resonant circuit and a local oscillator. The third multiplier parameter is the amplitude control element. If the input modulated signal is

e₁ = E₁ (1 + M cos ω_Mt) cos ω_ct

and the local oscillator supplies to the field winding of a signal of

e₂ = E₂ cos ω_ct

the output voltage of the three dimensional multiplier is

V = e₁ e₂ = E₁ E₂ (1 + M cos ω_Mt) cos2 ω_ct

= 1/2 E₁ E₂ [1 + M cos ω_Mt + cos (2 ω_c + ω_M) t + cos (2 ω_c - ω_M) t]

The modulating term (M cos ω_Mt) can be filtered out by conventional techniques.

D-C Current Transformers

This device is suggested for measurement of very heavy direct current. Using the magnetic field of an U-shaped permanent-magnet as the constant bias field the magnetoresistive elements are placed on the pole faces and the whole unit is situated between the d-c bus-bars. With the bridge circuit drawing current from a d-c or a-c supply, the heavy d-c through the bus-bars will excite a magnetic field on the specimens and be measured with a d-c or a-c voltmeter.

If the d-c voltage of the bus-bar supplies current to the bridge, the voltage at the output will be proportional to the power through the bus-bar. However, by means of a quotient-measuring instrument having one pair of its terminals connected to the output of the multiplier, and the other pair connected across the bus-bar voltages the current in the bus-bar will be indicated by the deflection of the instrument ψ, which is

ψ = K V_dc I_dc/V_ac = K I_dc

This arrangement has the advantage that no extra supply for the bridge circuit is required. Also, the correct value of the direct current is always shown by the instrument without being affected by doc voltage fluctuations.

Experimental Result

The perfection of a three-dimensional multiplier depends mainly on its linearity and sensitivity. With InSB (Indium antimonide) of proper doping as the active element, it is possible to make magnetoresistive specimens with resistance equal to 100 ohms at zero flux density, and about seven times that amount at a flux density of 10 kilo gauss. The specimen is reproducible and almost temperature independent within the range of ordinary working temperatures. Characteristic curves of two such magnetoresistive specimens are shown to have identical form when the magnetic field is less than four kilogauss. The three-dimensional multiplier constructed with these elements will have a family of curves which are very linear when B₁ and B₂ are less than four kilo gauss but do not go exactly through the origin. This discrepancy can, however, be eliminated by introducing a potentiometer of low resistance between the magnetoresistive elements. If the external resistances Rex are connected together through a potentiometer, and the field circuit of the individual magnetoresistive unit is provided with tunable choke coils, the linearity and symmetry of the characteristic curves can be adjusted. Further adjustment is possible by varying the length of air gap in the magnetic core.

Using a control current I₃ = 10 ma and at B₁ = B₂ = 2 kilogauss, the experimental multiplier has an output voltage of 1.2 volts. Since the magnetic fields are low, the magnetic circuit can he constructed with small ferrite cores of very narrow air gap, and the indium antimonide which is in the form of a thin film may be deposited directly on the pole face. The multiplier unit can thus be made compact, shockproof and rugged.

Other advantages include lifetime of all parts in the multiplier is practically unlimited; the multiplier is also suitable for high frequency operation up to the megacycle range; and, the output of the multiplier can be used in regulation or telemetering applications.

The efficiency of the magneto resistive device is always better than that of a Hall effect device when the magnetic field is sufficiently large. To obtain higher efficiency, the magnetic core should be composed of a material other than a ferrite, so that larger flux densities can be applied to the specimen without approaching core saturation.

The author thanks Professor H. Welker and H. Weiss, Siemens-Schuckertwerke, Erlangen, Germany, for supplying the semiconducting materials used in construction of the above units.