Combined Noise + Distortion

[Yorkshire Mouth]

I’ve enjoyed reading a lot of the reviews and measurements of DACs and headphone amps, and it’s particularly pleasing to see so many of them being effectively transparent, in regards to noise and distortion.

But what happens when you combine them?

Do you effectively add (for example) the noise from both together? Or does the noise from the ‘noisier’ item effectively ‘drown out’ that from the quieter (even though neither can be heard)?

Many thanks.

 

[Vini darko]

Yes sinad ratings are the sum of noise and distortion. I prefer to look at them separately as noise is more of a concern to me. Harmonic distortion at least to my ear is much less of a problem. However having less of both is nice.

 

[DonH56]

Audio reviews typically post SINAD which includes noise and distortion (signal-to-noise-and-distortion ratio). That means each distortion component also includes a little bit of noise at the same frequency. At higher signal levels the noise is low enough that it does not matter, but at low levels distortion gets very small and noise starts to dominate, thus you end up with a SINAD curve that rises at low amplitudes.

But I think what you are asking is what happens if you cascade two (or more) components? It can get complicated since how they combine depends upon phase and bandwidth among other things, but the usual rule of thumb for a quick calculation is to root-sum-square (RSS) them assuming they are uncorrelated (unrelated). You do need to convert to absolute numbers to do this...

For two voltage sources: RSS = sqrt(V1^2 + V2^2)

If you have dB, then you need to convert to absolute numbers, typically doing the inverse log. For voltages, say given SINAD (or SNR or THD, take your pick): X dB = 20*log10(V2/V1) and when the ratio is normalized you can calculate for SNR: Vsnr = 10^(SNRdB/20). For power, change "20" to "10". But often you are comparing two different levels so this might not work, and for THD it may be off because different components may emphasize different harmonics. The gain of each stage also matters. It's complicated.

In practice, referencing the lower number for SNR or THD, a 10 dB difference will only change the result by about 1 dB, and two equal sources will degrade the result about 3 dB. That is, if you have one component that has 90 dB SNR and another 100 dB, then the resultant SNR will be about 89 dB (1 dB worse than the 90 dB component alone). If you have two components, each having 100 dB SNR, then combined you'll get about 97 dB SNR.

With a bunch of caveats about equal reference levels, bandwidths, etc. But the idea is they do not just "add up" (linear addition) in general.

HTH - Don

 

[Yorkshire Mouth]

Audio reviews typically post SINAD which includes noise and distortion (signal-to-noise-and-distortion ratio). That means each distortion component also includes a little bit of noise at the same frequency. At higher signal levels the noise is low enough that it does not matter, but at low levels distortion gets very small and noise starts to dominate, thus you end up with a SINAD curve that rises at low amplitudes.

But I think what you are asking is what happens if you cascade two (or more) components? It can get complicated since how they combine depends upon phase and bandwidth among other things, but the usual rule of thumb for a quick calculation is to root-sum-square (RSS) them assuming they are uncorrelated (unrelated). You do need to convert to absolute numbers to do this...

For two voltage sources: RSS = sqrt(V1^2 + V2^2)

If you have dB, then you need to convert to absolute numbers, typically doing the inverse log. For voltages, say given SINAD (or SNR or THD, take your pick): X dB = 20*log10(V2/V1) and when the ratio is normalized you can calculate for SNR: Vsnr = 10^(SNRdB/20). For power, change "20" to "10". But often you are comparing two different levels so this might not work, and for THD it may be off because different components may emphasize different harmonics. The gain of each stage also matters. It's complicated.

In practice, referencing the lower number for SNR or THD, a 10 dB difference will only change the result by about 1 dB, and two equal sources will degrade the result about 3 dB. That is, if you have one component that has 90 dB SNR and another 100 dB, then the resultant SNR will be about 89 dB (1 dB worse than the 90 dB component alone). If you have two components, each having 100 dB SNR, then combined you'll get about 97 dB SNR.

With a bunch of caveats about equal reference levels, bandwidths, etc. But the idea is they do not just "add up" (linear addition) in general.

HTH - Don

Cheers, that makes a lot of sense.