# How to interpret the FFT of the mains voltage in this case?

I coupled the 230Vrms AC mains voltage to a scope channel through a 10Vpk-pk step-down transformer. I can imagine the transformer will already filter high freq. noise but I thought I can still see some spectrum for at least narrower bandwidth. So then I saved the time series data using the scope's SAVE function. The scope apparently sampled the input with 250kHz sampling rate.

Here is the time series data plotted in Python:

Here is the FFT:

And below is the zoomed view of the FFT where the horizontal axis is set to linear:

(left-click to zoom the view)

Regarding the last spectrum I have the following questions:

1. I marked the harmonics of the fundamental 50Hz in red color. As you see the highest harmonics are at 150Hz, 350Hz, 550Hz, 750Hz. These are the 3rd, 7th, 11th and 15th harmonics. Is that order of significant harmonics something common in the world or completely random?
2. I marked the highest non-harmonic FFT components after 50Hz in green. They are 60Hz, 70Hz, 80Hz so on. I'm confused here because I thought the real distortion in mains would come from the harmonics. But here there are 60Hz, 70Hz, 80Hz ect. whose amplitudes' are greater than the harmonics. What could these be? Am I interpreting something wrong here?
• Those non-harmonic components are just consequences of the measurement; they would go away if you were performing the FFT on an infinite dataset, but of course you can't do that. Basically, the shorter a time you sample the broader the peaks become; this is actually exactly what the Heisenberg uncertainty principle is, just applied to something other than what it is usually applied to. Sep 30, 2019 at 15:51
• Either run the FFT over a complete number of cycles, or apply "windowing" e.g. "Hamming window" before the FFT to smooth the discontinuities wher ethe data starts and stops.
– user16324
Sep 30, 2019 at 15:53
• @Hearth Does that mean if the data array was much more they would tend to diminish. But of course if I try to do that then the scope will lower its sampling rate:(
– cm64
Sep 30, 2019 at 15:53
• Yes, it would, but then you'd start to have sampling problems. There's a lot of literature about this, but generally the best thing for it is to just apply a window function and be aware of how that will distort your Fourier transform. You'll still have peaks in the same places, you'll just get bits of "slope" around each peak. Sep 30, 2019 at 15:55
• The FFT works with what information you provide, obediently performing honest correlation with its basis_functions, the sine and cosine, to extract magnitude and phase (sin and cos provide quadrature 4-quadrant sensing). To resolve at 1Hz frequency bins, your covered-time-series must be at least a second. Its your tradeoff on how you use the available scope sampling-depth memory. So alter your scope timebase, and experiment with the FFT bin-spacings. Have fun. Sep 30, 2019 at 15:58

I marked the harmonics of the fundamental 50Hz in red color. As you see the highest harmonics are at 150Hz, 350Hz, 550Hz, 750Hz. These are the 3rd, 7th, 11th and 15th harmonics. Is that order of significant harmonics something common in the world or completely random?

They are common and are generated from transformers and other components

Complex waveforms are generated by common electrical devices such as iron-cored inductors, switching transformers, electronic ballasts in fluorescent lights and other such heavily inductive loads as well as the output voltage and current waveforms of AC alternators, generators and other such electrical machines. The result is that the current waveform may not be sinusoidal even though the voltage waveform is Source: https://www.electronics-tutorials.ws/accircuits/harmonics.html

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I marked the highest non-harmonic FFT components after 50Hz in green. They are 60Hz, 70Hz, 80Hz so on. I'm confused here because I thought the real distortion in mains would come from the harmonics. But here there are 60Hz, 70Hz, 80Hz ect. whose amplitudes' are greater than the harmonics. What could these be? Am I interpreting something wrong here?

No, they are not really peaks, just part of the 50Hz signal with noise. In an ideal world, with perfect sine waves if we took the FFT it would look like a spike (or dirac delta function if you want to get technical). Because the real world is noisy, with phase and amplitude noise, when we observe noisy sine waves. The difference looks like this and is also common:

Is that order of significant harmonics?

Typical transformer response

What could these be? Am I interpreting something wrong here?

normal IF filter shape @ ? BW

BW or Q of IF filter limits steepness of filter vs noise floor , this is just tracing the filter response.

Other than first few odd harmonics, the rest of your results are:
- measurement errors and lack of experience on how this works.
- (search Spectrum Analyzer, theory of operation)

• When you say transformer response do you mean the transformer I used or all the transformers in the electic distribution system?
– cm64
Oct 1, 2019 at 8:25