Harmonic distortion phase and it's effects

[rockypunch]

For a given output voltage, let's say a DAC outputs a 2nd order harmonic -60 dB down from the fundamental. If that DAC is connected to an amplifier that also has 2nd order harmonic distortion at -60 dB, what is the result?

I'm guessing that if the 2nd order harmonic is of the same phase, the result is a 3 dB boost, so -57 dB 2nd order harmonic. It's also possible for the phase of the harmonic to be different though, right? If the phase of the harmonics differ by 180 degrees between the two devices, would they cancel each other out?

 

[DonH56]

The usual assumption for cascaded components is that signals are not completely in phase and thus the average levels RSS and max (peak) levels add. Thus the two terms would result in a -57 dB 2HD term as you said but that is assuming they are not in phase. If they were in phase, the result would be -54 dB, a 6 dB increase in 2HD.

Yes, if they were 180 degrees out of phase, and levels were matched, the distortion would cancel. That is what negative feedback does.

 

[Blumlein 88]

When I did 8 generations of AD to DA conversions I included a couple signals to check levels and such. In those the increase in distortion for each additional generation was right about 3 db. The first loop thru in the case of the gear on hand was distortion of -102 db. 7 more generations made it 81.4 db. 3 db per generation would have been 81 db. I would have thought perhaps using the same exact gear the distortion would have lined up and increased by 6 db per loop, but that didn't turn out to be the case. This was from a couple years ago.

I did the same thing with different AD and DA converters more recently. In this case 1 loop distortion was -107.1 db and 7 more generations was -87.4 db. Once again slightly less than, but very close to 3db per loop increase in distortion. So what Don is saying works out in actual practice.