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1. Introduction
   
   Hall effect is one of the the sensing elements that has been used in the design of many different sensors. I find this type of sensing interesting, and therefore, in this wiki page I will discuss briefly the physical principle of sensing based on Hall effect.

   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]

2. 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.

   Image Added                                                                     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.

3. 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.

   Four questions will be answered to explain how it is applied.

   The following shows the US1881 Hall effect sensor to give a feel how it looks like.
   Image Modified                                                                                                Figure

   2

   3. US1881 Hall effect sensor [3]
   

   The first question is if

   
   According to the physical principle of the Hall effect

   sensors convert the stimulus directly into electrical output

Add a new wiki page under the Physical principles of sensing and write about the physics behind the scene. You may try to find answers to the following questions:

• Does your sensor convert the stimulus directly into electric output?
• What steps are required to transform the signal into electric output?
• What types of physical effects and energies are involved in the sensing and in transformation?
• How the sensing and transformation can be modeled mathematically or physically?

After completing all this, click the Submission button below and write shortly:

• What have you done so far on this course?
• How much time have you spent?
• What have you learnt so far?
• What has been most difficult for you?

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1. 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.
   Image Added                                                                    

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

2. References

1. Bridgemen, P. W. (1939). Biographical Memoir of Edwin Herbert Hall. National Academy of Sciences.
2. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/hall.html
3. https://www.sparkfun.com/products/9312
4. Jacob Fraden. Handbook of Modern Sensors: Physics, Designs, and Applications (4th edition). Springer Publishing
5. http://farside.ph.utexas.edu/teaching/302l/lectures/node74.html
6. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/hall.html
7. http://sensing.honeywell.com/honeywell-sensing-sensors-magnetoresistive-hall-effect-applications-005715-2-en.pdf

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