with the assumption that they are not correlated
I may be wrong, but isn't this really just the equation for adding
non-correlated (random) noise figures? I wondered about this, and surely the problem is that harmonic distortion
is correlated, with the nonlinearity adding up at specific tones (2nd, 3rd, 4th harmonics, etc)?
The definition of THD is 100*(P2+P3+P4 ...)/P1, where P1 is the power of the fundamental and P2, etc are the powers of the harmonics. Using power rather than voltage makes the calculations easier. If device A has 0.3%THD, then its nonlinearities (P2+P3+P4 ...) = 0.003*P1. If device B has 0.03%THD then it adds nonlinearities that amount to 0.0003*P1 at the same tones as device A. So surely the THD of a system consisting of devices A+B should sum up all these tones: 100*(P2A+P3A+P4A ... +P2B+P3B+P4B ...)/P1.
But it doesn't end there. Device A is receiving a single tone, but device B is receiving a signal with multiple tones (the harmonics from device A), and each of these will produce additional nonlinearites which will all lie on the harmonics of the original tone. So you end up with a series like:
[P2A +P3A +P4A ...
+ P2B + P3B +P4B ...
+ (P2B)*(P2A + P3A +P4A ...)
+ (P3B)*(P2A + P3A +P4A ...)
... ]
/P1
So the end result will be slightly higher than simply adding the two distortion figures together.
But as I said, I might be wrong about this. I couldn't find an authoritative source on the question with a quick search.