Can I directly measure 220V AC with a oscilloscope?

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Are you sure that the speed controller is insulated from ac mains? If this is not true, you are in danger of electrocution by touching the scope. Your ac protection (differential switch) could trip. Do't know in Hk, but ac mains in Europe can be up to 252V rms (230 + 20%), thus the peak to peak value will be up to 726 Volts.
To display this on your scope you'll need a 10X probe, that must be rated for this voltage (752 V) dc+peak ac, and most aren't.
A solution could be to use an insulation transformer, with primary (220) connected to the motor, and the secondary (low voltage, e.g. 12 or 24 V) connected to the scope.
With a normal 10:1 probe, the 220 VAC is only 22 VAC and that should be well within the input range of any scope ever made. 22 VAC is safe. Also the 9 MOhm impedance of the probe will mean that not enough current could possibly* travel up the probe lead to harm anyone (But you must make sure that your probe can handle the voltage. If you don't have specs or a manual for your probe, forget it). Combine that with the fact that all bench-top scopes are grounded, and there is little safety risk. When probing, make sure you are not in contact with anything metal (including the scope) and keep your other hand in your pocket or behind your back. That's just in case you slip and contact something live with your probe-operating hand.

You probably don't need to connect the ground since the AC in the wall is already referenced to ground. If you see a lot of high frequency hash though, you could try grounding it. If you do, don't take for granted that the plug is wired correctly. Measure with your DMM first to make sure there is no AC or DC potential between your probe ground and the ground point you intend to use.

I am not saying "don't think twice, just do it". You need to think twice. And at least one more time. Make sure you are not going to electrocute yourself by touching something live or connecting the instrument wrongly. But if you can connect it properly, and are careful, you can safely probe the AC line.

Someone else mentioned the probe voltage rating in DC+Peak AC volts. "Peak AC" in this case is not the Peak-to-peak AC voltage (220 * Sqrt(2) * 2) but just the peak voltage WRT ground. for 220 VAC this is 311 volt. There should be no DC offset on the line.
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I used a EI transformer and did the reading. The voltage has a fluctuation of 0.3% at 235V while the frequency various at 0.04% for both 33rpm and 45rpm. The scope displays a normal sine wave that I don't think the speed controller is having trouble. Yet, there is some strange observation.

I disconnected the motor from the platter by taking away the silicon belts and I observed when I choose 33 rpm from idle, the motor starts turning but if I choose 45 rpm from idle, the motor does not turn by itself, I have to slightly turn the spindle before it starts turning. Why could this happen? Could this be the reason of producing hum?
I'm not sure what is the issue. If you can you hear hum pick-up (like through the speakers), then easy to explore situation by turning things on and off and conventional detective work.

I rather like my freeware computer real-time spectrum analyzer. If you are picking up a noise signal, then it will tell you the frequency and that often helps a lot. A scope with a sweep set or triggered to mains frequency can do the same sort of analysis.

Assuming of course, you respect the cautions about shock posted above.
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