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The following phenomenon is understood as the Hall effect (E. Hall, 1879).

When a current

I = b·d·n·e·v,

b,d - Width and thickness of the Hall lamina, n - Concentration of the conducting electrons e, v - drift speed of the electrons,

flows through a conducting lamina a Lorentz force is produced at right angles to the current I, providing the magnetic field B passes vertically through the lamina.

E = v·B

Diagram 6.6: Principle of a Hall-Effect Sensor

The open circuit Hall voltage can be obtained from the two equations

In the case where B is not perpendicular to the lamina but at an angle a to the normal then :

B·I

(2) U_H = R_H· · cos α. d

The concentration of conducting electrons by the various materials used is heavily temperature dependent and for pure metals R_H is too small to be used for measuring purposes. The semiconductors GaAs, InSb, InAsP and InAs are preferred for Hall Laminae.

Hall effect sensors made from GaAs or Si are becoming of increasing importance, due to advances in planar technology it is possible to integrate other functions such as current source, temperature compensation and output amplifier with the Hall-effect

element. In the data sheet the so called open circuit sensitivity K_H is given instead of the Hall coefficient R

H, this can easily be obtained from equation (1):

1 U_H

(3) K_H= = . n·e·d B·I

In the equivalent circuit of a Hall-effect sensor given in diagram 6.6 the following dimensions can be recognised:

R₁ - Bulk resistance in the current path, R2 - Internal resistance of the Hall generator, UH - Open circuit voltage of the Hall generator, U_R - DC voltage of the Hall electrodes when B=0.

all these parameters are temperature dependent. The numerical value of individual parameters can vary greatly between sensor type to sensor type; this may be due to the material, method of manufacture or the geometry (e.g. thickness d).

Magnetic field dependent resistances are capable of fulfilling the same functions as Hall-effect sensors, because of this they are mainly found in the automation sector as

proximity switches or position sensors.

Frequently semiconductor materials are used for magnetoresistance sensors. The ground material is for instance InSb. Conducting needle shaped inclusions of NiSb are embedded in the semicon-ductor, at right angles to the current flow (Dia-gram 6.7).

When no magnetic field is present the current takes the shortest path through the semiconduc-tor. As in the case of Hall-effect sensors, with a magnetic field present the current is laterally deflected, which increases the length of the current path and a greater resistance has to be overcome. The needles of NiSb have a very high conductivity compared to the base material InSb and therefore function as short circuits; this results in an almost homo-geneous electrical field within the semiconductor and a homohomo-geneous distribution of charge carriers is achieved.

The current paths run in a zig-zag form through the semiconductor. For low values of magnetic field the resistance increases in proportion to the square of the flux density.

The active material is arranged in a twisted form, in order to achieve a resistance of a few hundred ohms (thickness approx. 25µm). The sensors produced are also known as

magnetoresistors.

Various firms use the ferromagnetic material Permalloy (80% Fe, 20% Ni) for their magnetic sensors. This material is treated during manufacture so that the elementary magnets are mainly in the direction of the thin sensor strip ( x axis in diagram 6.8 ).

The maximum strip resistance (R=R_o) is obtained when no external field is present. The value of the resistance decreases in the presence of a magnetic field, that is proportional to the square of the field. By careful construction of the sensor strip the characteristic can be symmetrically linearised about the point B = 0.

For both the sensor types described above care is taken to ensure that effective

magne-Diagram 6.8: A magnetoresistance sensor made from ferromagnetic permalloy (The maximum value of R is dependent on B, for the illustrated direction of the field)

Diagram 6.7: A magnetoresistance sensor made from InSb semiconductor material (for the field direction illustrated the maximum R is dependent on B)

6.3.1 Construction and method of operation

Instruments for the measurement of magnetic fields, which use saturated core probes, are widely used where weak magnetic fields have to be measured. For example in geophysics for the exact measurement of the earths magnetic field and in space. These have been known, for a long time, under the name Forster Probe or

flux-gate-magnetometer method, utilise the non-linearity of the magnetisation curve of high permeability of soft magnetic materials. Here the probe consists of a high permeability rod or ring core (Diagram 6.9).

Diagram 6.9: Principle of the saturated core probe

The core material is periodically saturated by means of an alternating current i in the magnetising winding. This induces a voltage u in the sensing winding. Diagram 6.10 illustrates the relationship for the ideal case for a magnetisation curve constructed from the three linear portions.

The flux Φ in the core is proportional to the field strength H, and therefore to the current i and the permeability of the core. In saturation Φ is almost independent of i. The induced voltage u in the sensing winding is proportional to the rate of change of flux Φ with time.

In the absence of an external magnetic field the changes in H, therefore Φ, are

symmetrical about zero. Φ and u contain therefore only the fundamental frequency and odd harmonics. If the probe is placed in an external magnetic field the curve of the field strength is displaced ( dotted line). The flux Φ and the induced voltage u are no longer symmetrical and now contain even harmonics, the amplitudes of which are almost pro-portional to the DC field.

Magnetising winding Sensing Winding Core

A resolution of up to 10^-6 A/cm can be achieved with saturated core magnetometers. This is approximately onehundredthousandth of the earths magnetic field strength. These sensors were for a long time limited to expensive measuring instruments, because of their complicated construction extensive evaluation electronic. Advances in electronic integration and most important the development of high permeability materials have made this principle of interest to the automation industry.

Diagram 6.10: Function of a saturated core probe

1) The magnetising force H produced by the current i

in the magnetising winding (superimposed the DC magnetising force H₀ shown dotted) 2) Magnetising curve of the core

3) Variation of magnetic flux in the core 4) Induced voltage u in the sensing winding

6.3.2 Function and Measuring circuit

New saturated core probes use a amorphous metal as the core material, which has a number of advantages over the conventional crystallised alloys. Amorphous metals are characterised by a high permeability (up to 500000), small coercive field strength, as well as low eddy current and hysteresis losses. They are manufactured as thin strip (20-50 µm thick), they are very elastic and therefore insensitive to mechanical wear and tear.

Diagram 6.11 illustrates the construction principle of a magnetic position sensor. It consists of a strip of amorphous metal encapsulated together with a single coil in a plastic housing.

Diagram 6.11: Principle of a Magnetic Sensor

6.3.2.1 Measurements using an oscillator

When a saturated core coil is a frequency determining component of a circuit, similar to an inductive sensor, then the oscillating frequency, that is the change in the amplitude of the LC oscillations is evaluated. The approach of a magnet increases the magnetic field which in turn causes a change in the coil impedance and a change in the Q-factor of the oscillator.

Connecting cable

Housing

Amorphous metal Coil

6.3.2.2 Measurements using pulsed current

In this simple evaluation the core is driven into saturation by a pulsed current ( e.g.

100kHz) (diagram 6.12).

Diagram 6.12: Basic circuit for pulsed current operation

At each edge of the current pulse a voltage pulse is produced in the coil, the height of which depends on the stored magnetic energy, which in turn depends on the value and direction of the magnetic field to be measured. The induced voltage is rectified and passed through a low pass filter. The signal u which is produced is, to a close approximation, proportional to the magnetic field, providing the sensor core is not already saturated by the external magnetic field. Typical data for these sensors are:

measuring range 0.5mT, sensitivity 10V/mT, linearity 1% , frequency limit > 20kHz.

6.3.2.3 Evaluation by impedance measurement

A further possible method of evaluation lies in the measurement of the inductance or the Q- factor of the sensor coil. The coil inductance is dependent on the reverse permeability of the core material. This is the alternating field permeability for a small modulation

change dH and superimposed ∆C field H₀: 1 ∆B

µ_rev = · für ∆H → 0.

µ_o ∆H

Sensor element

Diagram 6.14: The reversible permeability of an amorphous metal Diagram 6.13: Definition of the reversible permeability

For a small change ∆H the hysteresis loop is lancet shaped and with a superimposed DC field moves along the magnetisation curve (Diagram 6.13). The tilt of the lancet axis corresponds to the reversible permeability.

Diagram 6.14 Illustrates the relationship between the reversible permeability and the DC field H_O.

The dependence of the resulting coil Q-Factor on the flux density B is shown in diagram 6.15.

A simple evaluation method is to measure the coil impedance; this decreases with increasing field strength as the inductance and the Q-Factor fall in value. When the sensor coil is supplied with an alterating current i, of constant amplitude, the resulting voltage u is a measurement of the field strength (diagram 6.16).

Diagram 6.15: Variation of the coil Q-Factor with changes in flux density, for the magnetic sensor shown in diagram 6.11

6.4 Applications

By using amorphous soft magnetic alloys and further development in control technology the saturated core probe principle can find new applications particularly in automation and the automotive industry. Compared to Hall-effect sensors and magnetoresistance elements they are an order of magnitude more sensitive. In comparison to inductive sensors the greater sensing range, with a smaller physical size and the possibility of totally encapsulating the sensor in a metal housing stand out.

Interesting applications could be:

- distance and position sensors,

- speed of ratation and angle of rotation sensors, - Current sensors,

- Sensors for traffic and vehicle counting,

- Navigation and earths magnetic field measurements.