Having no prior experience with scopes, it seems strange to me that when the probe is not measuring anything (~ not connected to a circuit) it measures a small 50Hz (~ my mains are running at 230V 50Hz) signal instead of some random noise. Is this normal behaviour (my scope is a Rigol DS1052E)?
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7No that's not normal ... 60Hz is normal ;-) – Tut Aug 14 '13 at 10:39
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4@Tut nonsense. [25Hz is normal](http://en.wikipedia.org/wiki/Utility_frequency#25_Hz_origins). – Phil Frost Aug 14 '13 at 10:52
2 Answers
Yes, that's normal. Due to its high impedance the probe acts as an antenna for the 50Hz field from the mains which fills the space surrounding the wiring (i.e. any room in your house). You'll notice that touching the probe will even show a stronger signal, indicating that your body is even a better antenna.

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1Thank you, isn't this mains signal interfering with the signal being measured when the probe is actually connected to a circuit being measured? – damd Aug 14 '13 at 10:10
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6@damd: good question. Most of the time the signal source will have a low impedance, and then the energy of the 50Hz field is too low to create a voltage. Only when measuring at very high impedances you may see the 50Hz – Johan.A Aug 14 '13 at 10:14
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1@damd: The probe is designed so that the voltage at the tip may be influenced very easily. This is generally a good thing because it means that a circuit to which the probe is connected won't have to divert much of its effort toward driving the probe. If the circuit being measured is being driven with any significant amount of "oomf", that drive will totally dominate the weak effects of the power-line-generated ambient field. The only time the probe pickup is apt to be a problem is either when measuring a circuit which is driven exceptionally weakly, and which... – supercat Aug 14 '13 at 14:59
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1...is better shielded than the probe (if the circuit isn't better shielded than the probe, it would be picking up the line-frequency interference whether the probe was there or not), or when measuring a circuit without a ground reference (in that case, if there were no connection between the circuit and anything tied to scope ground, the two grounds would likely vary 50 times per second relative to each other, but nothing would care about it). – supercat Aug 14 '13 at 15:02
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Any contribution to the noise amplitude from incandescent/fluorescent lighting? – Sparkler May 29 '16 at 15:13
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"oomf" would be measured in Coulombs (s*A), Amperes (A) and/or seconds per Amperes (s/A) for defeating parasitic serial resistance, parallel capacitance and serial inductance?? – Oskar Skog Feb 07 '17 at 16:17
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Yes it's normal.
You're seeing a capacitive divider effect. One capacitor is within the scope-probe and essentially is connected between the probe-tip to the scope ground. The other, much smaller capacitance is across empty space: from the probe tip to any distant 220vac wires in the walls. The empty space around the probe is the dielectric of this capacitor.
Wave your scope probe around and try to find the location of the strongest 50Hz signal. For me it was the metal arm of the spring-arm magnifier lamp on my test bench. (Here in USA it's not 50, it's Nikola Tesla's 60Hz, because everything MUST be evenly divisible by three, as was his hotel room number and the number of laps he'd swim each morning in the public pool!)
Note that the (usually 10Megs) probe impedance is loading down this parasitic capacitive-divider circuit. Try connecting a 1meg reistor between probe tip and ground, and you'll see the 50Hz signal diminish significantly. Ok, now try a 10K resistor. See what's happening? Most circuitry with its well-under-1Meg impedance will short out this 50Hz signal. This signal will rear its head where high-megs impedances are present: e.g. the dangling test leads of your DMM when set to AC volts and sensitive ranges. Or a dangling unused input on a CMOS logic gate will sometimes inject unexpected 50Hz pulses into your system. And the loud 50Hz buzz in an audio amp with faulty microphone grounding is exactly due to this same signal.

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Would a decoupling capacitor (say 0.1uF) be able to filter out this 50Hz/60Hz noise? – Sparkler May 29 '16 at 15:10
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(say 0.1uF) Actually you'd need a low-pass filter. You don't want to be connecting a capacitor in parallel to anything the scope is measuring. Or, again: *wave your scope probe around and try to find the location of the strongest 50Hz signal.* Find and eliminate the problem? Move your whole test bench away from strong 50Hz fields. Also: if the 3-pin power cord on your scope is faulty, or plugged into a faulty plug-strip, then the ungrounded scope will itself become a source of 50Hz AC from its own power line. – wbeaty May 30 '16 at 08:42
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Any contribution to the noise amplitude from incandescent/fluorescent lighting? – Sparkler May 30 '16 at 11:24
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1Yes, sometimes Fluorescent or LED circuitry. To detect sources, turn them off or unplug them, see if the problem vanishes from the scope. That, or wave the scope probe around while watching the size of the wave on the screen, see if the wave becomes huge when near certain devices or near their power cords. Or, plug the scope into a long extension, and carry it around to find a "quiet zone" with low 50Hz noise. – wbeaty May 31 '16 at 05:28
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I could be wrong, but it seems to me that this is not really a capacitive divider. The scope probe acts like a 1 Mohm resistor in *parallel* with, say, a 20 pF capacitor. So at 60 Hz, the probe is acting like a resistor, not a capacitor. – May 25 '20 at 22:11
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@BenCrowell The Thevenin Equiv of the capacitive divider is 20pF in series with distant 220VAC source, all in parallel with 10Megs as you say ...AS WELL AS THE DIVIDER EFFECT. Perform calcs for three components. Suppose there is 0.01pF between the distant 220VAC line and the probe tip. That gives a 1/2000 divider effect, in addition to a highpass-filter attenuation of 1:15.9 at 50Hz. (In other words, what's the Thevenin equiv. for a capacitive divider using 0.01pF and 20pF? Then place 10Meg on its output, to create a hipass.) Apply 220VAC, and the scope w/floating probe will measure 6.9mV – wbeaty May 26 '20 at 02:20
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@wbeaty: I'm confused by your comment and want to make sure I understand this correctly, so I've created a separate question: https://electronics.stackexchange.com/questions/502014/quantitative-analysis-of-capacitive-pickup-of-60-hz-by-an-oscilloscope-probe – May 26 '20 at 13:09