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I'm currently doing a lot of work in measuring transfer functions of circuits. One thing that crops up a lot is mains frequency noise:

enter image description here

As you can see there is a huge 11 dB leap at 50 Hz, followed by harmonics all the way up past the end of the amplitude response.

There also seem to be some side-bands around the 50 Hz. By this I mean observing the TF close to 10 Hz it is quite clean, but upon approaching 50 Hz there is an increase in noise. I don't have enough resolution to really see what this looks like properly but to me it seems like side-bands.

My question: what causes the distortion in the mains noise?

Is the power already heavily distorted when it reaches my sockets? Or is caused by the circuit? (Which for reference is a DAQ measuring an RC circuit). Is that intermodulation distortion around 50 Hz or just time-varying behaviour of the mains power?

EDIT:

To obtain the above figure, an RC circuit of 2 MΩ and 56 pF is being driven with a wide-band multi-sine signal of frequencies between 1 Hz - 192 kHz for 1 second. 100 seconds are concatenated which are then averaged for noise suppression. The FFT of the averaged output signal is then found, and divided by the FFT of the input signal (deconvolved). This results in the transfer function of the RC circuit.

However there is significant mains interference on the measured signal which has not been removed from averaging. This appears in the transfer function as a peak at 50 Hz and several harmonics. There is also disturbance around the 50 Hz peak.

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  • \$\begingroup\$ I'd be concerned with that spectral response if I saw it = 0 dBV at 10 Hz to 50 Hz = you've done something wrong. \$\endgroup\$ – Andy aka Apr 24 '18 at 13:19
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    \$\begingroup\$ It's your nickname - sorry had to get that off. \$\endgroup\$ – Arsenal Apr 24 '18 at 13:22
  • \$\begingroup\$ @Andyaka Not a spectral response, a transfer function. This is error caused by mains noise on the transfer function of an RC low pass. 0 dB means that there is no change in gain. \$\endgroup\$ – loudnoises Apr 24 '18 at 13:35
  • \$\begingroup\$ A TF doesn't have harmonics. Signals have harmonics. \$\endgroup\$ – Andy aka Apr 24 '18 at 13:38
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    \$\begingroup\$ @loudnoises If you can plot the current going in some of your consumers (charger, TV, PC, etc), you'll see just what it means -- the current will, most likely, not be a nice sine, or even in phase with the voltage (which, in some cases, may also be distorted due to weak grid, for example). This is the short version of John D's answer. The vast majority of today's poer consumers do nasty things to the current, and it will probably be quite an ugly revelation to see just how the cuurent looks like in some of them having incorporated PFC. Don't get me started on what waveforms are inside some... \$\endgroup\$ – a concerned citizen Apr 24 '18 at 15:55
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If the question is why do you see harmonics of the line frequency popping up as EMI in your measurements of a transfer function the the answer follows:

Harmonics on the AC line are generally caused by nonlinear loads. For example, a bridge rectifier followed by a capacitor filter will cause the following kind of current waveform, as current flows only when the line voltage exceeds the capacitor voltage:

enter image description here

In many parts of the world regulations require power factor correction, or more precisely harmonic elimination circuitry to mitigate (but not necessarily eliminate) the problem, but lower power (<75W for example) equipment is exempt. So in aggregate this equipment can still cause harmonic distortion on the lines.

The IEC standard that applies is IEC 61000-3-2, which specifies the maximum allowable value for harmonic currents from the second harmonic up to the 40th harmonic current.

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  • \$\begingroup\$ Thank you for your answer! Could you offer anything on the side-bands I have mentioned? \$\endgroup\$ – loudnoises Apr 24 '18 at 16:32
  • \$\begingroup\$ No, I can't comment on your specific case because there's not enough information, but a nonlinear load can cause intermodulation distortion (like a mixer generating sidebands) if there are load transients at a frequency near the mains fundamental. \$\endgroup\$ – John D Apr 24 '18 at 19:05

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