Posted on 17 September 2013

Hall Effect Sensors


Hall effect

If we place a current carrying conductor or semiconductor in a perpendicular magnetic field B (fig. 1) then an electric field arises perpendicular to the I-B surface. This effect is known as the Hall-effect. This effect was discovered in 1879 by the American physicist Edwin Herbert Hall.

Hall effect

Figure 1. Hall effect

Consider a current composed of holes (I ) flowing in the positive x-direction. Due to the magnetic field the holes are forced towards the lower surface (2). Side 2 of the conductor is positive relative to surface 1, in other words an electric field E exists in the positive y-direction, and therefore perpendicular to the x-z surface (I-B surface).

A Hall voltage is generated, V_H = E\cdot d, between the electrodes 1 and 2.

In equilibrium the electric field will exercise a force (with opposite polarity) equal to the force of the magnetic field on the flowing charge carriers:

q\cdot E = B\cdot q\cdot v

with q = charge and v = drift velocity. From this it follows:

E = B\cdot v\mspace{15mu} \text{and}\mspace{15mu} V_H = E\cdot d = B\cdot v\cdot d

If there are n holes per m3 then the charge density is:

\rho = n\cdot q\mspace{10mu} (C/m^3)

If this charge is displaced with a drift velocity v (m/s) then the current density is:

J = n\cdot q\cdot v = \rho \cdot v\mspace{10mu} (A/m^2)

The current density may also be written as: J = \frac{I}{d\cdot b} , so that:

V_H = B\cdot v\cdot d = B\cdot \frac{J}{\rho}\cdot d = \frac{B\cdot I}{\rho \cdot b}

With the Hall constant of the material, R_H = 1/\rho, this becomes:

V_H = R_H\cdot \frac{B\cdot I}{b} = k\cdot I\cdot B

Hall constant of different materials

Table 1. Hall constants

In contrast to metals some semiconductors (e.g. indium based) have an important RH value (see table 1).

From V_H = k\cdot I\cdot B\; the possible applications follow.


  1. With a constant current a magnetic field can be measured: V_H = k_1\cdot B
  2. With constant magnetic field, e.g. from a permanent magnet, it is possible to measure currents: V_H = k_2\cdot I
  3. If I  is made proportional to the first input signal (V1) and B  is proportional to a second input signal (V2), then V_H = k_3\cdot V_1\cdot V_2 and we have a Hall-effect multiplier. In this way we can measure power:

    [V_1 =f_1(v)\mspace{15mu} \text{and}\mspace{15mu} V_2 = f_2(i)]

Technical implementation

A thin layer of a few μm of semiconductor material placed on a ceramic substrate is sufficient to make a sensor for detecting magnetic fields.

The semiconductor can be InSb (= indiumantimonide). A constant current is caused to flow through the semiconductor. If a perpendicular magnetic field is present at the sensor, then there is an output voltage (VH).

In practical sensors this voltage is 0.2 to 1V/T , hereby: 1 T ( Tesla ) = 1Wb/m2.

A differential amplifier is usually integrated into the sensor to produce a useful output voltage.


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- who has written 7 posts on PowerGuru – Power Electronics Information Portal.

Professor Dr. Jean Pollefliet is the author of several best-selling textbooks in Flanders and the Netherlands

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