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How to interpret SINAD numbers of separate DAC + Amp combos

Roen

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Let's say I have a SINAD of a DAC and a SINAD of an Amp.

When comparing combos, should I look at Avg(SINAD_1, SINAD_2) or Min(SINAD_1, SINAD_2) as a more representative number of the performance of the combination?
 

amirm

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The distortions add linearly. Noise doesn't quite. So it is not a very simple thing. If you just care about the distortion part, easiest thing is to use the calculator at the bottom of this page: http://www.sengpielaudio.com/calculator-thd.htm

Make sure to use negative values for SINAD:

1543004873127.png


Note that per above example, if the SINAD of one device is much better than the other, its effect is negligible. This is why it pays to use a very transparent amp after a DAC even if the DAC can't rise up to its level. You minimize the additional distortion.
 
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Roen

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Wow this is helpful!

Now time to compare D50 + O2 (99.914), Tone Board + Atom (108.128) and D1 + 789 (111.527) configurations!

I imagine all are quite inaudibly different from each other at this combined SINAD level.

Though, 10 dB down seems to be the price of portability.
 
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DonH56

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That calculator, like many others, uses the root-sum-square (RSS) method. That is pretty standard though certain phase relationships can impact the result. Convert each number in dB to a voltage, square it, add it to the other number(s), take the square root of the resultant sum, and then convert back to dB, e.g. 20*log10(sqrt{[10^(-100/20)]^2 + [10^(-80/20)]^2)}) = -79.9567862... dB. Distortion 10 dB or so lower adds less than 1 dB to the result, e.g. -100 dB and -90 dB results in about -89.5 dB net SINAD. Two equal terms degrade the result by about 3 dB, e.g. -100 dB combined with another product also -100 dB results in total SINAD ~ -97 dB.

HTH - Don
 
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Roen

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That calculator, like many others, uses the root-sum-square (RSS) method. That is pretty standard though certain phase relationships can impact the result. Convert each number in dB to a voltage, square it, add it to the other number(s), take the square root of the resultant sum, and then convert back to dB, e.g. 20*log10(sqrt{[10^(-100/20)]^2 + [10^(-80/20)]^2)}) = -79.9567862... dB. Distortion 10 dB or so lower adds less than 1 dB to the result, e.g. -100 dB and -90 dB results in about -89.5 dB net SINAD. Two equal terms degrade the result by about 3 dB, e.g. -100 dB combined with another product also -100 dB results in total SINAD ~ -97 dB.

HTH - Don

Makes sense, thanks for the explanation!
 

Krunok

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The distortions add linearly. Noise doesn't quite.

How is it with noise? Does noise add up at all or is noise level always equal to the level of noisest device in chain? :)
 

amirm

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How is it with noise? Does noise add up at all or is noise level always equal to the level of noisest device in chain? :)
No, you always get higher noise level. If they have same spectrum and level, then you get 3 dB more noise. The issue is that they may not have the same spectrum or statistical qualities.
 

HeadphoneFan

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The distortions add linearly. Noise doesn't quite. So it is not a very simple thing. If you just care about the distortion part, easiest thing is to use the calculator at the bottom of this page: http://www.sengpielaudio.com/calculator-thd.htm

Make sure to use negative values for SINAD:

View attachment 17904

Note that per above example, if the SINAD of one device is much better than the other, its effect is negligible. This is why it pays to use a very transparent amp after a DAC even if the DAC can't rise up to its level. You minimize the additional distortion.

Yikes. Now I have to spend more money. I hope that NX5 deal will last for a while longer.
 

DonH56

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How is it with noise? Does noise add up at all or is noise level always equal to the level of noisest device in chain? :)

What Amir said. Assuming the noise is not correlated it will RSS.
 

Krunok

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If they have same spectrum and level, then you get 3 dB more noise. The issue is that they may not have the same spectrum or statistical qualities.

I would imagine inherent noise in DACs (random noise all over freq range )to have same spectrum and statistical quaities as in amps, correct?

Btw, what kind of noise is that, is it "pink"? Which parameter in your measurements is noise component of SINAD?
 

Blumlein 88

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I would imagine inherent noise in DACs (random noise all over freq range )to have same spectrum and statistical quaities as in amps, correct?

Btw, what kind of noise is that, is it "pink"? Which parameter in your measurements is noise component of SINAD?

SINAD signal to noise and distortion ratio.

Power of the signal, power of the noise and power of the distortion divided by the power of noise and power of distortion.

It's the obverse of THD+N.

So noise isn't separated out from other components directly.

You could have a component with a very low noise floor and moderate distortion levels so the residual after notching out the test signal is mostly distortion. You could have another component with distortion products pretty much buried in a moderate noise floor and after notching out the signal is mostly noise. Both could even have the same SINAD number, but noise and distortion levels would be rather different.

The idea is if you get SINAD down to very, very low levels, it doesn't matter how you mix or match noise and distortion, all of it is low enough to be inaudible.

As for noise spectrums, they usually are something like pink or between pink or brown assuming they aren't polluted with 60 hz hum, or other garbage.
 

Krunok

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SINAD signal to noise and distortion ratio.

Power of the signal, power of the noise and power of the distortion divided by the power of noise and power of distortion.

It's the obverse of THD+N.

So noise isn't separated out from other components directly.

You could have a component with a very low noise floor and moderate distortion levels so the residual after notching out the test signal is mostly distortion. You could have another component with distortion products pretty much buried in a moderate noise floor and after notching out the signal is mostly noise. Both could even have the same SINAD number, but noise and distortion levels would be rather different.

The idea is if you get SINAD down to very, very low levels, it doesn't matter how you mix or match noise and distortion, all of it is low enough to be inaudible.

As for noise spectrums, they usually are something like pink or between pink or brown assuming they aren't polluted with 60 hz hum, or other garbage.

I know what SINAD is, I was wondering how comes noise is not measured separately as THD is? Is it because THD is dominant component fo SINAD?
 

amirm

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I would imagine inherent noise in DACs (random noise all over freq range )to have same spectrum and statistical quaities as in amps, correct?
No, I see fair bit of variation. Many times it has a slope or hump in certain region.
 

Blumlein 88

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I know what SINAD is, I was wondering how comes noise is not measured separately as THD is? Is it because THD is dominant component fo SINAD?

Okay, I wasn't sure the way you worded it. So my bad interpretation.
 

Krunok

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No, I see fair bit of variation. Many times it has a slope or hump in certain region.

So, in order to get a "true" picture, shouldn't you measure SINAD in the whole audible freq range as both, THD and noise change with freqs?
 

amirm

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So, in order to get a "true" picture, shouldn't you measure SINAD in the whole audible freq range?
I measure it across 22.5 kHz of bandwidth. You can see that in green at the bottom of the dashboard. Using wider bandwidth would naturally lower SINAD (sometimes by a ton).
 

Krunok

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I measure it across 22.5 kHz of bandwidth. You can see that in green at the bottom of the dashboard. Using wider bandwidth would naturally lower SINAD (sometimes by a ton).

So the value you get is average SINAD vaue within that range, or..?
 

JohnPM

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SINAD isn't a function of frequency in that way, it is a ratio of powers within a measurement bandwidth as stated above. The stimulus when a single figure is stated usually a 1 kHz (or sometimes 997 Hz) sine wave. It could be plotted for different stimulus frequencies in the same way as THD+N can be plotted vs frequency but since SINAD is just the reciprocal of THD+N it wouldn't really add much to plot it.
 

BurritoJustice

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The distortions add linearly. Noise doesn't quite. So it is not a very simple thing. If you just care about the distortion part, easiest thing is to use the calculator at the bottom of this page: http://www.sengpielaudio.com/calculator-thd.htm

Make sure to use negative values for SINAD:

View attachment 17904

Note that per above example, if the SINAD of one device is much better than the other, its effect is negligible. This is why it pays to use a very transparent amp after a DAC even if the DAC can't rise up to its level. You minimize the additional distortion.

Hey Amir, this just reminded me of a discussion I had with @andreasmaaan a while ago about using a THX AAA amp with an RME ADI2 and whether that would result in an increase in SINAD for headphones or whether the combination of added components makes it a wash. I assumed it would at the time but given the high SNR rating of the headphone outs of the ADI2 relative to the main I might be incorrect?

Given that you have a 789 on hand an are likely getting an ADI2 again soon it might be worth testing. Could be with any of the high end DACs really (I'm thinking Benchmark DAC3 with HPA2 internal vs HPA4 external), to answer the question of if it is worth adding a TOTL amp to a TOTL DAC/Amp combo.
 
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