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I was using one of the little XR2206 Function Generator kits with my analog oscilloscope. It displayed a sine wave no problem - but I noticed that as I connected the ground strap of my oscilloscope probe to the ground terminal on the XR2206 board - there was a little bit of sparking visible like when you short a 9V battery. I pulled out the multimeter to measure the voltage across the two grounds and it showed a reading of 4V DC between them and just under 21V AC.

I was powering the XR2206 with a 9V DC wall plug power supply, no ground pin.

Is there a simple explanation for what is likely taking place? Where would this voltage potential between the two grounds be coming from?

Thank you!

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The potential difference comes from capacitive coupling between mains voltage side and low voltage side inside the ungrounded power supply. Sometimes you can even feel it by touching only the 9VDC output, and the effect can be amplified if you touch scope ground at the same time. It kind of stings if the contact area to skin is small.

It is either due to pure stray capacitive coupling between the transformer primary and secodary sides, or intentional if there is a so called Y capacitor between primary and secondary sides to reduce electromagnetic interference.

When the power supply output capacitively floats like this, the output may be referenced to ground by few tens if not couple of hundred volts, so connecting it to scope ground will ground the floating output, and the capacitor discharges via oscilloscope ground lead. The spike is short but the current spike during discharge can be quite large. As the capacitor is usually in the order of 2.2 nF, the AC current through it should be below 200 microamps.

This is why many devices with two-prong power supplies say in their manuals that units must be disconnected from mains before connecting to other units.

Just imagine what happens, if you try connecting ground lead between two devices first, and then it happens to disconnect accidentally before you connect another wire between devices, like GPIO pins between two microcontrollers. They could take a couple of hits but get damaged eventually.

So I also suggest not connect powered devices together if they spark while connecting. Unplug them first.

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Lets suppose the power transformer has primary-secondary overlap area of 10cm * 10cm, and insulation thickness (between those windings) of 1mm. Assume the Er (relative permittivity) is 5. What is the capacitance?

C= E0 * Er * Area/distance

C = 9e-12 farad/meter * 5 * (0.1 meter * 0.1meter) / 0.001 meter

C = 45e-12 * 10 = 450 pF = 0.45 nanoFarad

What is the peak current (displacement current) from primary to secondary, assuming 200 volts peak?

I = V/Z

What is the Z of 0.450 nanoFarad at 60Hz (we'll ignore any spikes)

Z = 1/(2 * PI * F * C) = 0.159/(60 * 0.45e-9)

Z = 0.159/27e-9 = 0.159/0.027e-6 ~~~ 5 * 1Million = 5,000,000 ohms reactive

I = 200 volts / 5,000,000 ohms = 0.04 milliAmps = 40 microAmps

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