# Hall effect device for circa 1 tesla gaussmeter

I'm thinking about building an unsophisticated bench instrument for measuring magnetic field density, just to support my learning about electromagnetism and building magnetics for power electronics applications.

I'm thinking I'll want something that can measure up to about 1 tesla (T) and was generally thinking that using a linear Hall effect sensor of some description was the way to go.

There are a number of such projects out there on the web, but they all seem to have a substantially lower operating range, which I understand is perfectly useful for a variety of other applications.

The linear Hall effect sensor devices I've been able to find all seem to top out at much lower flux densities, like 600 gauss (G), which is 0.06 T.

So I'm wondering, are there any Hall effect sensors that can operate at the flux densities I'm designing for? Or is it perhaps silly to be looking for something in that range? I figured line transformer iron can operate at between 1 and 2 T before saturation, so I'd be in the right ballpark.

• Where do you plan on finding a 1T field? Dec 21 '15 at 5:27
• Be careful your sensor doesn't damage the 1T magnet when you accidentaly drop it and it gets drawn into the magnet. A well known problem with MRI scanners. And once a piece of metal is stuck to such a magnet, the only way to remove it is to power off the magnet which is not particularly straightforward (nor quick) procedure with a superconducting inductor with some serious current flowing in it. Dec 21 '15 at 5:51
• How about trying for .06 T first? You can measure that directly, after all. Then it's just a matter of scaling it up, right? "First the bucket, then the pail, then the laboratory scale. Ever bigger, ever faster; faster, faster, then - disaster." Dec 21 '15 at 5:55
• Gaussmeters or Magnetometers can often measure 20 or 30 kGauss, DC to a few kHz. I've used them to measure gapped NeFeBo magnetic structures in the past. Sometimes they're called Teslameters too. So, the sensors are out there. Dec 21 '15 at 6:02
• @MadHatter : You can easily find a field around 1.1 to 1.2T, in the gap of a large (hi-fi or PA) loudspeaker magnet, having pulled the speaker apart. But you'll need a pretty thin sensor (<1mm ) to fit in there. And take care not to get fingers trapped between these magnets! Dec 21 '15 at 10:49

It seems most sensors on the market are made for very low to medium ranges up to 300mT, as you already observed.
Hall elements themselves usually allow field strengths in the order of a few Tesla, but the range is then limited by the electronics.

Some sensors allow to apply an offset voltage, which is applied to the signal before further processing. For example, I had students which tried to measure fields up to 1.2T in their setup consisting of 4 neodymium magnets and an iron yoke:

They used the "CASSY system", one of these ready-to-measure systems used at schools and universities for experiments. It had a probe with a hall element and was able to measure +/-1T (more precisely: -1.024...+1.023, you see it?). The system could be "calibrated" by defining the current reading as 0T. So, they put the sensor somewhere with -0.4T, "calibrated" it and were the able to measure more than 1T. The data looked fine, but we didn't check for linearity in that range.

So, it may be worth looking for pure hall elements without further electronics, which are a little difficult to find.

I found hallsensors.de which offer for example the CYAJ166A for fields up to 3T.

Another distributor is AKM.

However, these hall elements have a large part spread, so you have to calibrate your sensors. You can use a "reference magnet" which you measure with one of these 300mT sensors to get a precise value and calibrate your sensor against it.

There are a number of options. Whether any of them are practical will depend on physically what situation you want to measure.

It's true that most commercial Hall effect sensors use low fields. I haven't been able to find any high field ones with a quick google, which isn't to say they don't exist, just aren't offered to hobby users.

High field won't damage a Hall sensor, so you could attempt to calibrate the saturation region. I would expect that drift uncertainty would degrade any remaining sense of accuracy, but it may be worth a try, if you can figure out a trustworthy method of getting a strong, known, field.

If you knew the field direction, then using a sensor off axis would result in a smaller on axis (measured) component. Using two sensors on slightly different axes, and rotating the assembly until they both gave the same magnitude output, would line up the strong field between their axes, so automatically ensure that the field to sensor axis was at an angle of half of the sensors' mutual angle.

The Old Skool way of doing this depends on movement, the Integrating Fluxmeter. A coil is placed in the part of the field that needs to be measured, and is then removed to a large distance, where the flux is negligible. The voltage that the coil generates is integrated during the removal process by a 'capacitor wrapped round an op-amp' integrator. The voltage on the output of the op-amp represents the change of flux at any time. The coil removal does not have to be done at any speed, as long as it is fast enough for the integrator. With a low input bias op-amp, TL071 for instance, you should be able to use many seconds.

While the movement may seen to be a disadvantage, if you have a bench-top instrument with a probe, there are times when you'd want to put the probe into this gap, or that gap, employing the very movement you would need to make the measurement. How do you find a zero flux region? Turn the probe over and watch the integration output, it if changes, there is significant flux, and you need to go further away from your magnets.

The calibration of an integrating fluxmeter depends on the coil area, the number of turns, and the value of the capacitor used in the integrator. You could work it out from first principles, or calibrate it against a Hall sensor. Ideally, you'd do both and compare them.

While it's true that wrapping the sensor in ferrite or iron would reduce the field it sees, I can't think of any practical way to make such an arrangement remotely calibratable or linear.

• Good description of integrating fluxmeter, you can make the coil as thin as you like. If you know of an example, with circuit, that would be a valuable addition to the answer. Dec 21 '15 at 10:54

Disclosure: I work for this company.

It just so happens that the company I work for produces Hall effect sensors that are calibrated up to 3.5 Tesla.

Lake Shore Hall Sensors

May not make sense for a casual setup, but I mention it just to show the existence of such sensor elements.

Alternating magnetic fields can induce voltage in a coil of wire, so if you were just interested in alternating magnetic fields, you could use a coil. Simply note the number of turns and the radius of the coil. Then, employ Faraday's law: \begin{align} V(t) &= -NA\frac{dB}{dt}\\ B(t) &= -\frac{1}{NA}\int_{-\infty}^{\infty}V(t)dt \end{align}

Thus, all you have to do is measure the voltage across the coil when the flux through it is changing, and use either an active integrator circuit (e.g. with an op-amp) or integrate the signal numerically. Numerical integration typically results in drift since it's an approximation, so adjust the signal by high pass filtering. Here's some Matlab code you might use to perform this integration:

% V is the measured voltage across the coil
% N is the number of turns
% A is the cross sectional area of the core
% t are time points of acqusition / integration
% f_cutoff is the cutoff frequency of the high-pass filter (below the
%   frequency that you expect to measure but higher than the frequency of
%   drift)
% rate is the sampling rate

dB = -V/(N*A);
B = cumtrapz(t, dB);

[d, c] = butter(2, f_cutoff/rate, 'high');
Bfilt = filter(d, c, B);


Such a sensor could be designed to handle up to 2 T of magnetic flux.