1. HALL EFFECT TRANSDUCERS As already explained in- Art 14.12 page 562, when a conductor is kept perpendicular to the magnetic field and a direct current is passed through it, it results in an electric field perpendicular to the directions of both the magnetic field and current with a magnitude proportional to, the product of the magnetic field strength and current. The voltage so developed is very small and it is difficult to detect it. But in some semiconductors such as germanium, this voltage is enough for measurement with a sensitive moving coil instrument. This phenomenon is called the Hall effect and is explained below. Let us consider a slab of conducting material connected to a battery so that a current I flows through the slab in the manner shown in fig. The electrons constituting the flow of current I actually flow in the direction opposite to that of conventional current. Now no potential difference exists between the top and bottom of the slab, as shown in fig. (12), because no transverse magnetic field passes through the slab.

2. Fig (12) Hall Effect

3. When the magnetic field is applied so that it is perpendicular to the slab of Hall crystal, the electrons are acted on by a force because of magnetic field. The force acts in a vertical direction, and the electrons are forced toward the top of the slab. This results in an excess of electrons near the top of the slab and a deficiency of electrons near the bottom. Thus a potential difference is created between the top and bottom of the slab. The magnitude of this voltage is proportional to the product of strength of the magnetic field and current flowing through the slab and is given by the expression

4. where I is the current flowing through the slab in amperes, B is the flux density of the magnetic field applied in wb/m2, t is the thickness of slab in metre, and kH is the Hall effect coefficient and is inversely proportional to the carrier density in the solid. So the Hall effect is much more pronounced in semiconductors than in metals. Thus the voltage reading across the device can be calibrated to give the magnetic field strength directly in case the current glowing through the conducting slab is known. Hall-effective transducers can be built to be sensitive enough to detect very small magnetic fields.

5. Commercial Hall-effect transducers are made from germanium or other semiconductor materials. They find application in instruments that measure magnetic field with small flux densities. Hall effect element can be used for measurement of current by the magnetic field produced due to flow of current. Hall effect element may be used for measuring a linear displacement or location of a structural element in cases where it is possible to change the magnetic field strength by variation in the geometry of a magnetic structure. For example, an arrangement illustrated in fig. (13).

6. Fig (13) Hall Effect Displacement Transducer

7. The Hall effect element is located in the gap, adjacent to the permanent magnet and the field strength produced in the gap, due to the permanent magnet, is changed by changing the position of the ferromagnetic plate. The voltage output of the Hall effect element is proportional to the field strength of the gap which is a function of the position of ferromagnetic plate with respect to the structure. Thus displacement can be measured by the Hall effect transducer. Very small displacements (as small as 0.025 mm) can be measured by this method.

8. The arrangement for measuring small rotary shaft displacements with the use of Hall effect element is illustrated in fig. (14). The Hall effect element is rigidly suspended between the poles of a permanent magnet fixed to the shaft, as illustrated in fig. The element remains stationary when the shaft rotates. With a constant current I supplied to the element, the voltage output (Hall voltage VH) across the element is directly proportional to the sine of angular displacement of the shaft and for smaller angular displacements (say t 5° of rotation) the output voltage will be directly proportional to the angular displacement, there­by giving linear scale. The main advantage of Hall effect transducers is that they are non- contact devices with small site and high resolution. The main drawbacks of these transducers are high sensitivity to temperature changes and variation of Hall coefficient from plate to plate, thereby requiring individual calibration in each case.

9. Fig (14 ) Hall Effect Angular Displacement Transducer

10. Example. An Hall effect element used for measuring a magnetic field strength gives on output voltage of 10.5 mV. The element is made of silicon and is 2.5 mm thick and carries a current of 4 A. The Hall coefficient for is 4.1 x 10-6 Vm/A-wb/m2.

11. Solution: Hall effect element thickness, t = 2.5mm = 2.5 x 10-3m Output voltage, VH = 10.5 mV= 10.5 x 10-3 V Current, I = 4 A Hall coefficient, kH = 4.1 x 10-6 Vm/A-wb/m2

12. Magnetic field strength, B