#### omm0910

##### Member
How does SINAD chain? My DAC has a SINAD of 114 and my amp has a SINAD of 94. Here is the definition of SINAD https://en.wikipedia.org/wiki/SINAD. So should I upgrade the amp or the DAC? And could factor in cost somehow.

Should I just sum the SINAD and say that I have a net SINAD of the chained components of 114+94=208. If so then it’s cheapest to upgrade the DAC. From an m200 to an e50. From SINAD fo 114 to 121. And total net SINAD from 114+94=208 to 121+94=215.

Now, I've read here that changes in the high end of SINAD may not be audible. But how does this notion of "overall net SINAD of the whole chain of equipment" factor in. Maybe the formula is not to simply sum the SINADs. I suspect most people would advise me to spend \$1000 for a new Hypex MC500 amp or Purifi amp, rather than \$269 for a new e50 DAC, but does that hold up in terms of some net chain SINAD formula. And by implication, bang for the buck.

Can we extend the chain (and net SINAD formula) out further on either end. Is there a notion of the SINAD of a song that is "Ultra HD" (24 bit. / 96 kHz) on Amazon Music instead of just "HD" (16 bit / 44.1 kHz). Of transmitting that song over Bluetooth (and the different profiles within that) rather than USB. On the other end of the chain, is there a notion of the SINAD of a given speaker.

And how do we quantify Dirac in terms of net system-chain-wide SINAD? One of these months Dirac will release their “virtual sound card” version for Mac. That would be the most bang for the buck at \$350 but how do I quantify that? (And technically, the quality of the calibration mic becomes part of the chain too).

#### Blumlein 88

##### Grand Contributor
Forum Donor
Well you don't sum them no. The part of your chain with the least SINAD is the bottle neck which will set your system SINAD. Usually that will be the speaker and room noise.

For an extreme example you have all SOTA components, and live in an apartment next to a construction site where a jack hammer is running non-stop. What limits the level of detail you can hear in your music? The high noise of the jackhammer.

So in your example of a 114 db DAC and 94 db amp, the amp will set the result of those two at 94 db or slightly less.

Using SINAD this way is really a misuse of it. In general few speakers will do better than 60 db SINAD because distortion will be at least that high. As I say often, you really get further along to split up SINAD in to THD and noise separately. Doing that noise is likely to be limited by room noise and THD is likely limited to that of the speaker.

#### MakeMineVinyl

##### Major Contributor
Technical Expert
In any typical home or apartment, natural background noise is likely reducing the ultimate SINAD to something like -60dB, or as expressed so misleadingly around these parts "10 bits of resolution".

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#### abdo123

##### Master Contributor
Forum Donor
In any typical home or apartment, natural background noise is likely reducing the ultimate SINAD to something like -60dB.

at 50Hz maybe, but i pity the person who has natural background noise of -60dB in the 1Khz to 5Khz region.

#### DonH56

##### Master Contributor
Technical Expert
Forum Donor
SINAD = signal-to-noise-and-distortion ratio, often called THD+N in the audio world. You cannot really calculate the SINAD of a gain chain since it includes noise, which is usually uncorrelated and thus sums in root-sum-squared fashion (vn_total = sqrt(vn1^2 + vn2^2 + ...), and distortion, which may sum directly, but is typically shifted in phase through the signal chain so peak amplitude sums but not the RMS or average value. And in a signal chain you need to calculate the gain for each component at each stage, and for noise the noise bandwidth, so it can get complicated. There are programs and spreadsheets for RF systems but it is difficult to get all the needed information to apply them to audio systems. I have thought about running some examples now and then to at least illustrate the process but am afraid of where it might lead. E.g., "Oooh, that works for your example, but what if I have this preamp and that DAC and that power amp, what then?" Plus getting accurate noise a internal stage gain numbers from manufacturers is probably an exercise in futility.

It is one of those things much easier to measure than calculate, again mainly because it's hard if not impossible to get all the data needed, then you have to sweep over volume settings and all that jazz.

Blah. - Don

#### Blumlein 88

##### Grand Contributor
Forum Donor
SINAD = signal-to-noise-and-distortion ratio, often called THD+N in the audio world. You cannot really calculate the SINAD of a gain chain since it includes noise, which is usually uncorrelated and thus sums in root-sum-squared fashion (vn_total = sqrt(vn1^2 + vn2^2 + ...), and distortion, which may sum directly, but is typically shifted in phase through the signal chain so peak amplitude sums but not the RMS or average value. And in a signal chain you need to calculate the gain for each component at each stage, and for noise the noise bandwidth, so it can get complicated. There are programs and spreadsheets for RF systems but it is difficult to get all the needed information to apply them to audio systems. I have thought about running some examples now and then to at least illustrate the process but am afraid of where it might lead. E.g., "Oooh, that works for your example, but what if I have this preamp and that DAC and that power amp, what then?" Plus getting accurate noise a internal stage gain numbers from manufacturers is probably an exercise in futility.

It is one of those things much easier to measure than calculate, again mainly because it's hard if not impossible to get all the data needed, then you have to sweep over volume settings and all that jazz.

Blah. - Don
Yes, I left all that out of my answer, but for all those reasons the simplest thing is to measure SINAD at the speaker terminals. Yet even after all that the SINAD in room is going to be much less (or you have a pretty poor group of components feeding the speakers).

#### amirm

Staff Member
CFO (Chief Fun Officer)
How does SINAD chain? My DAC has a SINAD of 114 and my amp has a SINAD of 94. Here is the definition of SINAD https://en.wikipedia.org/wiki/SINAD. So should I upgrade the amp or the DAC? And could factor in cost somehow.
You need to use a dB calculator and use a negative sign. Doing that will give you a SINAD of -93.956. In other words, you always lose SINAD, never gain!

As a rule of thumb, if one device is 10 dB better than the other, you can ignore its effect. Using 104 and 94 will give you 93.56 so almost as good as 114 dB.

Note that this is brute force math. Actual make up of SINAD determines how the addition works from audibility point of view.

#### tuga

##### Major Contributor
Forum Donor
Using SINAD this way is really a misuse of it.

Anyway of using SINAD is misusing it...

OP
O

#### omm0910

##### Member
Thanks folks! Can I then say, that the plan should be, to first attack the weakest link in the chain, the component the lowest SINAD? And then can I further say that, if speakers are by far the weakest link in the chain, shouldn't we be testing speakers here instead of DACs?

I seem to recall reading that the Purifi dudes were also working on speaker drivers with less distortion.

#### amirm

Staff Member
CFO (Chief Fun Officer)
And then can I further say that, if speakers are by far the weakest link in the chain, shouldn't we be testing speakers here instead of DACs?
??? I am testing speakers here!

#### MakeMineVinyl

##### Major Contributor
Technical Expert
Thanks folks! Can I then say, that the plan should be, to first attack the weakest link in the chain, the component the lowest SINAD? And then can I further say that, if speakers are by far the weakest link in the chain, shouldn't we be testing speakers here instead of DACs?

I seem to recall reading that the Purifi dudes were also working on speaker drivers with less distortion.
The performance of speakers is orders of magnitude worse than even the crappiest DAC, not to mention your listening environment, or your ears for that matter. So yes, SINAD is meaningless in assembling a practical system (unless you just like 'buying by the numbers'). SINAD is great for the eggheads in lab coats, but for anybody else, there are far more useful metrics like for instance the features you want for the amount you want to pay. Reputable manufacturers on the whole rarely produce truly awful components.

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#### Beershaun

##### Major Contributor
Forum Donor
I am also curious about the OPs underlying question. How do we evaluate the effect of each component on whole system? Is there no fidelity improvement or additional musical information delivered through the speakers at all if the DAC or Amplifer SINAD is better than the rated distortion of the speakers? I expect that is an oversimplification. I really want to understand how to think about the complete system and how information is maintained or lost along the way and what actually makes it out of the speakers if we change a DAC or change an amplifier.

OP
O

#### MakeMineVinyl

##### Major Contributor
Technical Expert
I am also curious about the OPs underlying question. How do we evaluate the effect of each component on whole system? Is there no fidelity improvement or additional musical information delivered through the speakers at all if the DAC or Amplifer SINAD is less than the rated distortion of the speakers? I expect that is an oversimplification. I really want to understand how to think about the complete system and how information is maintained or lost along the way and what actually makes it out of the speakers if we change a DAC or change an amplifier.
I would say that generally everything which comes before the speakers is going to contribute an insignificant amount of harm to the signal. The distortions introduced by speakers generally goes by unnoticed unless there is a direct comparison to another speaker. Frequency response of speakers at the listening position is probably more of an issue.

#### farcurse

##### Member
Forum Donor
If you're interested in the decibel math, here's a python snippet that will do the computation (decibel is just a scaled log transform of a level):

Python:
``````from math import log10
def db(s):
return 10 * log10(s)
def inv_db(d):
return 10 ** (d / 10)``````

Code:
``````[ins] In [28]: db(inv_db(-114) + inv_db(-94))
Out[28]: -93.95678626217358``````

OP
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#### omm0910

##### Member
The performance of speakers is orders of magnitude worse than even the crappiest DAC, not to mention your listening environment, or your ears for that matter. So yes, SINAD is meaningless in assembling a practical system (unless you just like 'buying by the numbers'). SINAD is great for the eggheads in lab coats, but for anybody else, there are far more useful metrics like for instance the features you want for the amount you want to pay. Reputable manufacturers on the whole rarely produce truly awful components.

In my limited sample, “buying by the (SINAD) numbers” has produced marked audible improvements. Both in theory and in practice. [Have you heard the one about the French Academic, excitedly reporting “this is not only true in practice, its true in theory!”]

Though I agree that there’s one number that can always be measured very accurately, to two decimal points: the price, in dollars and cents!

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OP
O

#### omm0910

##### Member
Thanks Farcurse! Can I add 3 values like so? (Intending to include DAC, amp, and speaker in the chain)
Code:
``````db(inv_db(-114) + inv_db(-94) + inv_db(-60))
-59.99825410393011``````

If that is accurate, then it would be good to have SINAD for speakers, and in terms of the chained SINAD, the terrible SINAD of speakers completely dominates the net result.

However, in practice, well I should run the numbers, but does it explain why my swapping out the amp, then the DAC, from an old Denon AVR, with the -114 DAC and the -94 amp, each upgrade sounded markedly better. OK maybe it does, the DAC and the Amp in the Denon may also have had lousy SINAD closer to the speaker SINAD.

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#### farcurse

##### Member
Forum Donor
Thanks Farcurse! Can I add 3 values like so? (Intending to include DAC, amp, and speaker in the chain)
Code:
``````db(inv_db(-114) + inv_db(-94) + inv_db(-60))
-59.99825410393011``````

If that is accurate, then it would be good to have SINAD for speakers, and in terms of the chained SINAD, the terrible SINAD of speakers completely dominates the net result.

However, in practice, well I should run the numbers, but does it explain why my swapping out the amp, then the DAC, from an old Denon AVR, with the -114 DAC and the -94 amp, each upgrade sounded markedly better. OK maybe it does, the DAC and the Amp in the Denon may also have had lousy SINAD closer to the speaker SINAD.

Yeah, that's right. The intuition is that the lowest component SINEAD is going to dominate the chain. That's why some argue that if your room has significant background noise, really high SINEAD values don't matter much. I'll leave that debate to the experts.

#### Bear123

##### Addicted to Fun and Learning
Thanks folks! Can I then say, that the plan should be, to first attack the weakest link in the chain, the component the lowest SINAD? And then can I further say that, if speakers are by far the weakest link in the chain, shouldn't we be testing speakers here instead of DACs?

I seem to recall reading that the Purifi dudes were also working on speaker drivers with less distortion.
SINAD is like a grain of sand on the beach….good speakers, bass management, dual subs, and eq all make up the beach. If you are deficient in one of those areas, SINAD is nearly meaningless in comparison if you are trying to chase what matters in terms of sound quality. Even once those fundamentals are in place, whether your SINAD is -80 db or -120 dB is still nearly meaningless in most cases other than in ones imagination.

OP
O

#### omm0910

##### Member
Yeah, that's right. The intuition is that the lowest component SINEAD is going to dominate the chain. That's why some argue that if your room has significant background noise, really high SINEAD values don't matter much. I'll leave that debate to the experts.
Not to derail the thread, but my take is that we then need to bring in some psycho-acoustic considerations… that the brain is able to latch onto Miles Davis’ trumpet pouring out of the speakers and tune out background noise. And that then its still worth having the chain output the purest music possible, and not throw in the towel.

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