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# Making Sense of the Hall Sense

The Physics Behind The Hall Effect Sensor

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While I was at work the other day, I was doing some analysis on some Hall sensor circuitry and I thought, I should check to see how many different flavors of Hall sensors exist. FYI, Hall effect sensors are used widely in position sensing systems for motors, since they are usually tiny and can operate well enough in different environmental conditions compared to mechanical position switches. If you search for Hall sensors, you'll be granted by many different types to choose from, but all generally fall into 1 of 2 categories: discrete or linear. All differences aside, they are all driven by a Hall sensing element. But how does it work?

We are going to answer this question and plan to build a prototype of a hall element, as long as it won't break my wallet :(. The intro to this project will be somewhat physics based, but I'll do my best to break down the concepts.

Let's get started!

## Project Goal

Determine the constraints to be able to observe (measure) the Hall voltage in a conductor.  We would like to use a PCB as a prototype Hall element.  Specific constraints to determine are:

1. Magnetic field limitations; how big can we go??? (constrained by \$\$\$)
2. Electric current limitations
3. Dimensions of hall element; in this case I would like to use a thin conductor, like PCB or metal tape (dimensions constrained by 2)
4. Instrumentation & Error Budget (what levels of hall voltage can be attained, how do we plan to measure the hall voltage, and do it somewhat accurately?)

Once we figure out the above, we'll get the materials and test.

## Hall Voltage TL;DR

V= -(1  ⁄  nq) * I * B  ⁄  t

The 3 factors which influence Hall voltage magnitude:

1. The longitudinal current in a material (conductor or semi-conductor).
2. The magnetic field component cutting through the material, perpendicular to the direction of current
3. The material itself where (1 / nq) is known as the Hall coefficient for conductors and t is the thickness

Note:  The Hall coefficient (1 / nq from above) becomes a bit more complex when you start using materials that have more than one type of charge carrier (e.g. semi-conductors).  However, the concept is the same.

## Design of Experiment

Now to the fun part:  if we are intending to see what magnitude of current and magnetic field we will need to measure Hall voltage, we know we can't apply an infinite amount of either...we obviously have some constraints :).

Coming Soon

# Background Info

## What Is the Hall Effect?

The hall effect is the phenomena of a voltage (known as Hall voltage) formed due to the presence of:

1. current flowing in a material
2. magnetic field which is perpendicular to the current

where the Hall voltage:

1. appears in the plane which is perpendicular to both the current and magnetic fields, and
2. whose polarity is determined by the polarity of charge carriers and the directions of both the current and magnetic field.

## The Hall Voltage:  A Closer Look

When we talk about electric current, we're talking about moving charges.  When these moving charges cut through a perpendicular external magnetic field, a force is exerted upon these charges: the Lorentz force.  The same phenomena that accelerates projectiles beyond the speed of sound (aka the Railgun) is the same force responsible for Hall Effect.

Notice how I said "moving" charges above.  This means that if I take an otherwise non-magnetic (or weak magnetic) material (say copper), put an electric current through it, then place it in a magnetic field, the moving charges will start responding to the magnetic field.  Again, this response depends upon the magnitude of the current (moving charges) and magnetic field (in addition to some material properties).  Pretty sweet, right?

Here's the mathematical formula (don't be scared, use the google or the references):

### Hall_Voltage_Calculator.xls

ms-excel - 14.00 kB - 01/22/2019 at 06:34

• ### 02/10/2019: Making the Mag Field with Permanent Magnets

To generate a steady B-field for our experiment, we have two options to choose from:

1. Permanent Magnets
2. Electromagnets

Before I choose a path, I'd like to do a quick study to determine the cost of building a magnet with a 1 Tesla flux density through a 1" x 1" area.  If more than 1 Tesla is needed, we can approximate the cost as a linear function of flux density.

Using Permanent Magnets:

Benefits of using permanent magnets are:

1. Different sizes, shapes, and strengths readily available
2. Stacking smaller magnets is equivalent to a single magnet of the same thickness
1. Flux density (B) dependent on the magnet's dimension in the direction of the magnetic field's axis
3. Setup would require a simple mounting fixture

Some cons:

1. If using multiple small magnets, the B-field will not be uniform in certain places (compared to a larger permanent magnet or electromagnet) due to the gaps between the magnets.  (Not a show stopper)
2. Can get expensive as the number of magnets needed is increased to increase the B-field.

Example Jig set up:

• Using the B884-N52 rectangular magnets stacked in two rows, we can get a B-Field of ~ 1 Tesla (0.99 Tesla)
• Total cost would be ~\$30.  The jig would be made from scrap wood I have laying around.

Analysis using an electromagnet coming in the next log...

• ### 01/21/2019: Hall Voltage Calculator

Added the Hall voltage calculator.  Right now I only have copper in there, but feel free to use.  The process will be the same for different materials, just plug in the correct values.

• ### 01/21/2019: Deviating from the Original Experiment

There are going to be some differences between my experiment and the original:

1. use copper, or some other metal clad board/insulator (price is king) for the hall element, not gold leaf
2. use copper wires, not brass because why brass when there is plenty of copper wire in my lab stock?
3. wires will be soldered directly to the element which should provide less terminal resistance than using highly polished brass contacts
4. use an electro-magnet to generate the B-field with a split-core to place the hall element where the magnet shall have: a) a high permeability core, and b) a small split in the core as thick as the hall element +/- 2mm to minimize reluctance (and loss of flux) in the magnetic
5. use a better power source, Brunsen cells are somewhat out-of-date
6. to measure the hall voltage, I'll potentially need a high-precision amplifier and a current sense resistor to make my own galvanometer.

For the Hall element, I'd like to use either 1 oz or 0.5 oz copper clad board since minimizing thickness is key.  In Hall's paper, he stated that even using a strip of copper that 9cm x 2cm x 250um (that's micrometers, 10-6  meters) would fail to yield a detectable transverse voltage.  However, this could have been due to the limitations of the equipment he was using at the time.

I'll  have to do some more research as to the reason for this, but it may still be worth a shot to try the 1oz or 0.5oz copper since their thickness is significantly less than 250um, 30um down to ~17um respective to the copper clad weight.

• ### 01/20/2019: The Original Hall Experiment

Doing some more research, I found that I'm basically re-creating the 1879 E. Hall experiment.  It's a very interesting read, and relatively easy one too due to it being written in the first-person narrative.  Papers these days are so dry and boring :).

Hall stated the strength of the magnetic field he used was 20,000 times the strength of the "horizontal intensity of the earth's magnetism."  According to Wikipedia, Earth's magnetic field at the surface ranges from 25 to 65 microTeslas.  So let's see what it would take to generate 0.5 to 1.3 Tesla.

Another thing to notice about the original Hall experiment is the magnitude of input current that was put through the gold leaf.  From the looks of the data, the current put through the gold leaf was less than 100mA.  The test data Hall had collected did not have clearly defined units in the table, see below:

Hall goes on to postulate that the E-field generated is related to the momentum of the charge carriers (mass x velocity of charge carriers), with the velocity of electrons being equivocated to "C/s."  However, "C/s" in his paper means the ratio of input current to cross-sectional area of the hall element (which is actually current density).

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