A quick THD+N question

[SamM]

Hi All,

If two stages of an audio system were connected together and the THD+N for both stages were known, how would you go about calculating the total THD+N for the entire system?

For example, if a preamp had a THD+N of say.. -95dB and a power amp had THD+N of -90dB (obviously assuming they were both measured at the same fq, and appropriate amplitude), then what would be the resultant THD+N of both?
Sorry if this has already been covered in another post, i've had a search through the forums but not managed to find anything.

Cheers,
Sam.

[BrianL]

You do not have enough information to calculate anything.

You need to know the amplitudes of the individual harmonics
in each device's spectrum and the relative phases of each
of these device's corresponding harmonics..
Then you must sum each harmonic individually.

Noise is even trickier as you don't know spectral densities, etc. .

One could possibly make some educated guesses (assuming
one is educated). For example, if one of the units has
significantly better THD+N than the other one can assume
that the resultant won't be much worse than the worst
of the two devices. If the two had relatively equal THD+N
readings, one could assume that the resultant might be 3 dB
worse than the worst of the two. Even this is all a guess as
a THD+N number doesn't really tell you how much distortion
you have vs. noise.

In fact, the THD+N "number" is a relatively useless commodity
as (1) it doesn't separate distortion from noise and (2) it
doesn't tell you about the relative amplitudes of the distortion
components.

And your reason for wanting to do this calculation?

[Geek]

I'd like to add a number 3): THD caveats.....10% THD of odd harmonics is intolrable trash, while many can easily put up with 10% THD in even harmonics. So while amplitudes are important, quantity of even/odd is even more so I think.

If on a FFT spectrometer (lotsa freeware PC proggies for these), if you have one big THD spike and it's harmonic #2, even though it's large, it might go unnoticed by a listener. Odd harmonics usually appear a little spikes at 3, 5, 7, etc. and even though they may all add up to very little, most everyone will hear it.

But yeah, I agree that THD+N is pretty useless at quantifying performance - it's a marketing gimmick.

[SamM]

Thanks for the replies.

After reading them i now see that it was actually pretty obvioius all along that it's almost impossible to calculate it.

The reason i asked was that recently a friened asked me about the possiblilites of using analogue test gear to measure the THD+N of an ADC - DAC setup, then calcualting the THD+N of just the DAC if the THD+N of the ADC was known.
It just got me curious.

Cheers,
Sam.

[Havoc]

Difficult job. In order to get some meaningful results, your test gear needs to be at least 10dB better than the DUT. If however you have analog gear to put at the output of the DA, then by using a digital source with a known signal can give you a good indication of the performance of the DA.