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About the folded back harmonics theorem

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twteng

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Hi All:
I am designing a delta-sigma modulator. In my spectrum result, I'll find out many high order harmonic tones in my concerned bandwidth, I think that is call "harmonics folded back", Could somebody tell me why the high order harmonic tones which will folded back into our designed bandwidth, please explain
as detail as possible.

Many thanks for all reply.

Eason
 

JoannesPaulus

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I doubt you see "folded" harmonics in your delta-sigma design. Harmonics fold back when they are above fs/2 and in a typical ds-adc, fs is several times the bandwidth of interest.
So, to answer your question, in a nyquist adc, for a sampling rate of 100MHz and an input frequency of 41MHz, you would see a folded 2nd harmonic at 18MHz, a folded 3rd harmonic at 23MHz.

I hope this helps!
 

twteng

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Thanks for JoannesPaulus's reply, as you say, If Fin is 41MHz, and then 2nd harmonic at 18MHz(abs(41M*2-100M)), a folded 3rd harmonic at 23MHz(41M*3-100M). That's just I would like to know what the theorem is?
Any materials or references could let me know that would be appreciated.
Thanks a lot.
 

JoannesPaulus

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It is the sampling theorem by Nyquist-Shannon, the fundamental paper on sampling theory.
 

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