I'm new to electronics tinkering and have recently started experimenting with the Arduino and electronic circuits in general. I'm thinking of buying a digital oscilloscope (probably one of the Chinese brands like Rigol or Instek in the 70-100MHz range) because I think it would help me understand what's really happening in my circuits (i.e., right now I'm convinced that smoothing capacitors are a hoax because I've never seen any repercussions from omitting them, but I know that's just my lack of experience and understanding.)
The scopes that I'm looking at come with 1x/10x passive probes, differential probes being sold separately and quite expensive. I understand that if I use regular probes, when I connect the probe's ground lead to my circuit's ground I'll actually be connecting my circuit to earth ground via the scope chassis (I understand that for this reason I should never use regular probes to measure mains). Is this a problem for my Arduino-related circuits, though? Should I be concerned about stray currents entering my circuit that way? Do I need differential probes, or is earth-grounding my circuit an acceptable thing to do? Does it matter what's powering the circuit (battery, USB into the Arduino, or a bench power supply)? Thanks for any advice.
when I connect the probe's ground lead to my circuit's ground I'll actually be connecting my circuit to earth ground via the scope chassis
Yes that is correct.
I understand that for this reason I should never use regular probes to measure mains
No you can measure mains with a regular probe, just don't try and measure across something, like a current sensing resistor in the high side of the mains.
Is this a problem for my Arduino-related circuits
Not usually.
Should I be concerned about stray currents entering my circuit that way?
No because the USB power will be grounded from your PC, or it will be floating if you have a laptop.
Do I need differential probes
No.
Does it matter what's powering the circuit (battery, USB into the Arduino, or a bench power supply)?
Your understanding of probe earth grounding is correct. It is not a problem for your Arduino-related circuits and will not induce any damaging currents into your circuit. In the case of powering from batteries or a bench power supply (which is most likely isolated) it simply forces the GND node of your entire circuit (including battery and/or power supply) to be at the same potential as earth ground. This is fine. Batteries don't care, and bench power supplies usually have the option to do this anyways by connecting the "black" output terminal to the "green" output terminal.
Powering from USB is when things might start to get wonky. Again, it's not going to hurt anything, but I've found that oscilloscopes sometimes give strange readings when probing USB-powered circuits coming from a laptop. Disconnecting the laptop from the mains (i.e., running off the laptop's battery) or switching to a bench supply/battery makes the "strange readings" go away. Laptops and their associated power supplies are just really noisy beasts, so it's not entirely unexpected.
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The Ruggeduino: compatible with Arduino UNO, 24V operation, all I/O's fused and protected
Thank you both for the very helpful and timely answers!
Grumpy_Mike, could I ask you to elaborate on why having a load between mains and the scope makes it dangerous while it otherwise wouldn't be? I have no intention of doing it in any case ("real" electricity gives me the heebie jeebies), but I thought that probes give you 1M ohm or 10M ohms (depending on whether the probe is 1x or 10x) of impedance anyway, and I thought that impedance looks like resistance that's impacted by the frequency of the signal. I would have figured (obviously incorrectly) that a resistor would only reduce the current that passes through the scope to ground. Thanks again for your help!
I think Grumpy_Mike was referring to the (common) misconception that you can use a scope to make a differential measurement across a resistor by just connecting the probe to one end, and the ground clip to the other end. Since the ground clip is at earth potential (and so is one side of the mains) you are essentially placing all of the mains voltage across the resistor, likely blowing it up.
This is why they have (expensive) differential probes.
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The Gadget Shield: accelerometer, RGB LED, IR transmit/receive, speaker, microphone, light sensor, potentiometer, pushbuttons
And when probing high speed logic its best to use the x10 setting on the probe to minimize the load on your signal, otherwise you risk interfering with the circuit's function due to reflections back along the probe's cable.
Of course the probe is really a divide-by-10, its the oscilloscope settings that you have to multiply by 10 to compensate.