Hall effect sensing principle

The Hall effect was discovered in 1879 by Dr. Edwin Herbert Hall while he was at Johns Hopkins University in Baltimore. While trying to verify electron flow theory proposed by Kelvin, he found that when a magnet was placed with its fields being perpendicular to one face of a thin rectangle of gold which current was flowing through, a potential difference appeared at the opposite edges. What he found is that this voltage is proportional to the current flowing through the conductor, and the flux density or magnetic induction perpendicular to the conductor. He experiments were successful and well received at the time. [1]

Theory of the Hall effect

The Hall effect is based on the interaction between moving electric carriers and an external magnetic field. If an electric current flows through a conductor in an external magnetic field, then a transverse force call Lorentz force caused by the magnetic field will exert on the moving charge carriers, which pushes these carriers to one side of the conductor. A buildup of charges at the sides of the conductors will balance this magnetic influence, producing a measure voltage between the two sides of the conductor. The presence of this voltage is called the Hall effect, and this voltage is the Hall voltage. [3,103-105]


                                                                             Figure 1. Hall effect principle with magnetic field present [2]

Figure 1 shows the principle of Hall effect with the direction of current being the conventional current. The magnetic field is perpendicular to both the direction of the current and the Lorentz force. The magnetic forceis given by

whereis an electronic charge, is the speed of an electron, and is the magnetic field. If the Hall voltage is, and the width of the conductor is, then the magnitude of the electric field is given by

Now the electric force on a charge is

The electric force acts in opposition to the magnetic force. In a steady state, the two forces are equal

Suppose the thickness of the conductor in figure 1 is, the length of the conductor is and that it containsmobile charge carriers per unit volume. It follows that the total current flowing through the conductor can be written as

Because all mobile charges contained in a rectangular volume of length, width, and thickness, flow past a given point in the conductor in one second. Combining equations (1) and (2) yields

From equation (3), we come to a conclusion that Hall voltage is proportional to the current flowing through the conductor, and the magnetic field strength, and is inversely proportional to the number density of mobile charges and the thickness of the conductor. This has important meanings in practice. In order to build a sensitive Hall probe, we need to take a thin conductor of some material which possesses very few mobile charges per unit volume (e.g, semiconductor), and then run large current through it.

                                                                     Figure 2. Magnetic field vector across the plate at an angle of α [4]

Another important point worthing pointing out is that very often the angle between the magnetic field vector and the current vector is not always perpendicular. At a fixed temperature the Hall voltage is given by

where α is the angle betwwen the magnetic field vector and the Hall plate, and h is the coeffient of overall sensitivity whose value depends on the plate material, its geometry, and its temperature.[4,104] Normally, the coefficient of overall sensitivity will be given in the datasheet of a particular sensor.

Hall effect accelerometers

Until now the physical principle of Hall effect sensing element has been studied. This section will try to find out how this sensing element is used in Hall effect sensor.The following shows the US1881 Hall effect sensor to give a feel how it looks like.
                                                                                                Figure 3. US1881 Hall effect sensor [3]

According to the physical principle of the Hall effect studied above, the Hall effect is converted directly from the stimulus which is the external magnetic field. However, typically this Hall voltage is relatively small. To make the output usable for most applications a signal conditioning circuit is required. The signal conditioning electronics needed are an amplifier stage and temperature compensation. Voltage regulation is needed also as part of the signal conditioning circuit when operating from an unregulated power supply. The signal conditioning circuit acts as a step to transform the raw signal (Hall voltage) into electrical output. In Hall effect sensors, energy from the external magnetic field and from the internal conductor are involved to make the output Hall voltage.
Mathematically, a transfer function can be used to describe the relationship between the sensor output and input. For analog output Hall effect sensors, the transfer function expresses the relationship between a magnetic field input and a voltage output. For a typical analog output sensor, the transfer function can be expressed as follows [5,6]

For digital output sensors, the transfer function can be expressed in the following graph.
                                                                    

                                                                          Figure 4. Transfer function out digital output Hall effect sensors [5,7]