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# How to determine the number of harmonic in a ADC FFT figure?

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#### urian

##### Full Member level 3
Hi,there
When we checking the SFDR of an ADC, we usually apply FFT to the result and locate the 3rd HD magtitude. But in my case, I find that the 3rd HD is not the largest harmonic, e.g. in my 8b 100M pipeline ADC with 41.4MHz input, the FFT shows that the 3rd HD(24.2MHz) is -67dBc, but the bin 17.3MHz is -57dBc, I dont know wether this is a HD and the number of it. How to calculate the HD number with FFT plot?

Regards
urian

Are you using an anti-aliasing filter? I think you are not and this is my reasoning. If your ADC is clocked at fs=100MHz, and you put in a tone at 41.4MHz, below Nyquist a good thing, your harmonics I think are aliasing down. So your HD2 is 82.8MHz, the alias would be 100MHz-82.8MHz=17.2MHz. If you have a HD3, this would be at 41.4MHz*3=124.2MHz, therefore, 200MHz-124.2MHz=75.8MHz, alias again, =>100MHz-75.8MHz=24.2MHz. Since it is a double aliasing of the HD3 thats why it is smaller. Does this make sense?

JGK

urian

### urian

Points: 2
Hi,jgk
There is no anti-aliasing filter in my design. For HD3, my calculation is 41.4MHz*3 -100 =24.2MHz. I wonder whether this way is wrong in concept comparing with your method. Should it be first subtracted from 200MHz and then calculate the alias again to get the 24.2MHz result? And if there is anti-aliasing filter, the HD will not fold back in the 1st nyquist zone?

Regards
urian

Hello Urian,

I am sure you can't just subtract 100 to get 24.2MHz. You have to always subtract which fs multiple first. since the third harmonic is above 100.. you have to look at 200 first. Just try this. Put in your input tone at 10MHz, you should have your HD2 at 20MHz and HD3 at 30MHz. Then put in another tone at 22MHz, HD2 will be at 44MHz and your HD3 will alias down since it will be at 66MHz, therefore in your band, you would see 100MHz-66MHz=34MHz.

Hope this helps
JGK

urian

### urian

Points: 2
Hi,jgk
I got it. I should always subtract HD from the multiple of fs instead of reverse order to get the aliasing HD. Thx

Regards
urian

Hi,jgk
I got it. I should always subtract HD from the multiple of fs instead of reverse order to get the aliasing HD. Thx

Regards
urian

This is correct imho too. For fft though, the bins will only go upto Fs/2, so you would have to 'fold' it into an Fs/2 multiple.
apologies for jumping in...

No problem for jumping in! So this is why I was saying you subtract off of fs, so if your at say 75MHz and your fs is 100MHz you get an alias (folding down) at 25MHz. Just like if you put something in at say 51MHz, you get the fold at 49MHz.

JGK

urian

Points: 2