Summary
A laboratory instrumentational amplifier has been described that can measure µV DC voltages, which will be useful for a range of interesting physics and engineering experiments (e.g. Hall effect, potentials, photo current effects etc.). The 'flying capacitor' (switched capacitor) input stage provides a true differential input, minimising input offsets and earth loops, that can cause errors when measuring small signals. etc. The electronics is made from easily obtained components and can be constructed fairly cheaply.
On this page we describe a set of experiments that can be used to test the amplifier, as well as some details about investigating the Hall effect with copper (pcbs) foils.
click here for the instrumentational amplifier
Test 1 - mV and μV test signals from a potential divider
In this test a variable power supply (vpsu) was connected across a two-resistor potential divider (R1 and R2), the smaller resistor (R1) of which will create mV, sub mV and μV signals to use as a test signal into the input of the amplifier. These tests were not performed in a screened metal box, instead with wire leads from the amplifier to the resistors and power supply. So, these are a potentially noisy set-up to test how rugged our amplifier is.
R2 = 1M and R1 = 100 R i.e. divide by 10,000: 1mV & 100μV tests
I set the vpsu to 10V into the potential divider to produce a 1mV test signal across the 100 ohm resistor which was then connected to the amplifier. On the x1000 setting this gave 1V o/p expected. Changing the vpsu to 1V gave a 100μV test signal and this gave 0.1V o/p on the x 1000 setting, as expected.
R2 = 10M and R1 = 100R i.e. divide by 100,000: 10μV test
I set the vpsu to 1V into the potential divider to produce a 10µV test signal across the 100 ohm resistor. This gave 0.01 V o/p on the x1000, 0.1 V on x10,000 and 1V on x100,000 ranges. As the o/p scaled as expected when the gain was increased, it shows that all the stages of the amplifier are working properly for these small inputs.
R2 = 10M and R1 = 10R i.e. divide by a million: 1μV test
Finally, I set the vpsu to 1V into the potential divider to produce a 1μV test signal across the 10 ohm resistor. This is getting to the limit of the amplifier and was noisy. It produced ca. 0.001 - 0.002V on x1000, ca. 0.01 - 0.02V on x10,000 and ca. 0.1 - 0.2V on x100,000 ranges.
With this 1μV input the output was noisy and varying as expected given the 'birds-nest' style croc-clip arrangement with no screening. Overall, though I was encouraged by these very simple tests and shows that ca. 1μV signals can be detected by the amplifier.
The voltage pulse we should expect will be about V = π x (0.15/2)2 x 1 x 0.1 ca. = 0.002 V = 2 mV pulse
Setting the extra gain unit to x1, the instrumentation amplifier will have a total gain of x1000 which, with this Faraday induction signal should create an output of ca. 0.002 x 1000 = 2 V
I brought a rare earth magnet near to the loop (thereby increasing the magnetic field strength the coil experiences i.e. dB/dt positive) and a large pulse was seen on the 1-volt scale. This dropped to zero when the magnet was stationary, but when the magnet was removed (dB/dt negative) I got an equally strong, but negative going pulse, as expected. This simple Faraday induction experiment was impressive considering it's only a very small single turn loop.
If you pass a DC current through a thin foil of copper, you will get a very slight voltage drop due to the resistance of the foil. This voltage drop is proportional to the current and the resistance of the foil. The copper foil on a standard printed circuit board is around 35μm (0.035 mm) thick. For example, I passed 200 mA through a 1 x 2 cm piece of pcb foil which produced a voltage drop of about 40 µV across the foil (points A and B) see conductvity measurements above.
Ignoring this voltage drop due to the foil resistance for a moment, there is another voltage that can appear if there is a magnetic field present. If the magnetic field is applied side on to the foil (see diagram) a force appears (Lorentz force) which causes the current to try to flow in a circular path. This results in a voltage appearing across the foil (C and D), perpendicular to the magnetic field - this is the Hall voltage.
For a foil thickness t (meters), current I (amps), magnet field B (Tesla) and the number of charge carries (n x e), The Hall voltage is given by:
V(Hall) = I x B / (n x e x t)
The number of charge carriers is dependent on the material (in this case copper) which is represented by the Hall coefficient Rh = 1/(n x e), which gives:
V(Hall) = I x B x Rh / t
The Hall voltage is dependant on the Hall coefficient and proportional to the current flowing in the foil, the magnetic field and inversely proportional to the foil thickness. You can make a magnetic field sensor using the Hall effect but as Rh is usually very small for metal films (for Cu Rh = ca. -0.55 x 10-10 m3 C-1), you need very thin films to get a strong enough signal to measure – even with a sensitive lab amplifier like this one.
Measuring the Hall effect
In the diagram you will notice a potentiometer RV1 going to two points either side of C (opposite D) on the foil. I used a 10 turn 1k pot but as the internal resistance of the foil is very low, almost any value linear pot will do. This is used to null out any voltage drop due to the resistance of the foil that we mentioned earlier, which we don't want to confuse with the Hall effect voltage. When a current is passing through the foil you simply adjust RV1 so the instrumentational amplifier reads zero when no magnetic field is present (ignore the Earth's magnetic field, as it will be too weak to pick up in these very simple copper foil experiments).
My first attempt at measuring the Hall effect using a strong rare earth magnet about 3cm diameter 6mm thick (ca. 0.5 Tesla surface field) using 1 amp current and the copper foil (35μm) on a standard pcb failed. If you put these numbers into the formula we can see why, as we get a magnitude of Hall voltage of less than 1μV:
V(hall) = 1 x 0.5 x 0.55 x 10-10 / (35 x 10-6) = 0.8 μV
The magnetic field from the magnet may actually be smaller than my estimate, which would result in an even lower Hall voltage. Signals less than 1μV are at the limit that can be measured with this amplifier and of course a very small voltage to measure!
Etching the foils
As the Hall voltage is inversely proportional to the foil thickness, I needed to make my films thinner if I was to have any chance of measuring the Hall effect for copper. The obvious thing was to etch the foils in exactly the way you do when you make a pcb. My etch tank is a commercially made heated Ferric Chloride device with the option of having air agitation bubbles to speed up the etch and make it more uniform.
I made up 6 identical pcbs samples (ca. 3 x 6 cm), cleaned them and etched them for 1, 2, 3, 4 and 5 minutes to see if I could make a thin enough film. 5 min in my etch tank was just too much and the foil was too patchy to use. There was enough of the 4 min etched foil left to try a measurement. Note: the etched foils need to be cleaned again back to bright copper, before making Hall effect measurements.
I devised a simple 3D printed holder with spring loaded pins to make reliable and repeatable probe measurements on the foils, see photo. The etched pcbs lie copper side down on the device. A plastic lid forces the copper foil onto four spring loaded pins which make a good electrical contact with the copper foil.
The 3D printed device to hold the spring-pins and pcb board.
Top left is the zero setting pot, top right is the mutiway plug / socket to go to the instrumentation amplifier.
The bottom feed throuigh connections go to a power suply to set the current (I) that flows through the foil.
click here for details of the apparatus on my 3D printer page
Using the 4 min etched foil with ca. 1.3 amp, I was able to measure ca. 100mV = 0.1 V signal when the magnet was brought near to the foil.
This was on a total gain of x100,000, now 0.1 / 100,000 = 1μV = Hall effect voltage for the etched copper foils - really tiny, but really there!
As expected, for a magnetic field sensor, the Hall voltage reversed when the magnet was turned around 180 degrees i.e. with the other pole of the magnet facing the foil.
Estimating the foil thickness change after etching
We can make conductivity measurements i.e. measure the change in the voltage drop (due to the foil resistance changes) to estimate the change in foil thickness when we etched the foils. I set up the 3D printed holder (see conductvity experiments section above) to measure the voltage drop across the identical sized etched pcbs, this time with no magnetic field. The voltage droped across the foil was measured in the two middle pins (see diagram above) for ca. 200mA current. I reversed the current and repeated the measurements just to make sure there were no unwanted offsets, but got similar results, see table below.
click here for details of the apparatus on my 3D printer page
| foil type |
voltage (x10,000 gain) mV |
actual voltage μV |
| unetched | 400 mV | 40 μV |
| 1 min etch | 500 | 50 |
| 2 min etch | 700 | 70 |
| 3 min etch | 850 | 85 |
| 4 min etch | 1250 | 125 |
A micro volt world is opening up ! .....
click here for the instrumentational amplifier
click below for 3D printed devices and higher resolution images:
3D printed conductivity holder
3D printed Hall effect holder
click below for Hall effect related links
Hall effect wiki page
Hall effect handbook
Hall effect measurement appendix
Jonathan Hare, Feb. 2025
THE CREATIVE SCIENCE CENTRE
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