THD and SINAD Correlative Math Equation?

[confucius_zero]

Remind me how THD relates to SINAD again? how do you translate it?

(THD+N ?%)*equation = SINAD ?DB

Thank you

 

[DonH56]

SINAD ~ 20*log10(THD+N%/100)

 

[March Audio]

Or be lazy like me

http://www.sengpielaudio.com/calculator-thd.htm

 

[confucius_zero]

Or be lazy like me

http://www.sengpielaudio.com/calculator-thd.htm

So "distortion attenuation" is sinad?

 

[flipflop]

So "distortion attenuation" is sinad?

No, it's the dB equivalent to the THD%. 0.1% = -60 dB.
SINAD is the signal without distortion (and noise). Remove the minus sign and you get SINAD: 60 dB.

 

[Killingbeans]

SINAD = (Signal+THD+N)/(THD+N)

THD+N is not a factor but a term, so it's not signal without distortion and noise.

 

[DonH56]

SINAD = (Signal+THD+N)/(THD+N)

THD+N is not a factor but a term, so it's not signal without distortion and noise.

Depends on what standard you follow... For ADCs and DACs, it is defined as:

Signal to noise and distortion = signal / (noise + distortion)

In this definition the numerator only includes the signal. It is used this way to calculate the effective number of bits, ENOB, and often used in communication systems (digital or analog, at least in the courses and work I have had). Ref IEEE Standards 1241, 1057, O&S, etc. Since my career focused on data converters that is the definition I have (almost) always used. The definition you provided is used more in the RF world and guarantees SINAD can never fall below 1 (so the log never goes negative). My comm theory book defines both but uses the IEEE definition, while my microwave radio book uses "your" definition. Most of the grad classes I took long ago also used the IEEE definition so we got to talk about how our circuits could recover the signal even with "negative" SNR.

Lovely the way we can complicate everything...

 

[Another Bob]

I have noticed that in a majority of the product measurements here, that the SINAD number is within a few dB of the highest (non-signal) point on the FFT spectrum graph. In today's Hegel HD12 review, however, these differ by about 20 dB. The text says this is due to noise, but the noise floor is pretty low (about -125 dB) and flat. I feel like I'm missing something. Is the noise causing the SINAD degradation above 20kHz?

 

[DonH56]

If you look at a field and add up all the leaves of grass they may total more in height than the tree standing in the field, especially if it is a small (short) tree. Not quite the way it works, but that's the general idea. Broadband noise power may be more than the power in a single small'ish spur. If the noise floor is a little higher for one component than another then the former will have lower SINAD even if they have the same distortion spurs.

Or there may be a mistake somewhere...

There is some handwaving and examples here: https://www.audiosciencereview.com/...ital-audio-converters-dacs-fundamentals.1927/

HTH - Don

 

[Another Bob]

Thanks. I understand the "grass and tree" analogy, and I understand that the analyzer may pick up things that are hidden by the limited resolution of the spectrum display, but I'm still troubled by the visual inconsistency. Look at the Audio Research D300 review: lots of spikes (distortion, PS artifacts, etc.) in addition to broadband noise at about -135 dB, yet the SINAD pretty much exactly matches the value of the H2 peak. The Hegel's spectrum is much cleaner (again, visually), but the SINAD value is getting "penalized" for something I can't see. Looking at the past 20 or so reviews, I've noticed this spectrum/SINAD mismatch happens more frequently with DACs than amps, although the Nord Three SE 1ET400A was an exception to this trend.

 

[Schackmannen]

Thanks. I understand the "grass and tree" analogy, and I understand that the analyzer may pick up things that are hidden by the limited resolution of the spectrum display, but I'm still troubled by the visual inconsistency. Look at the Audio Research D300 review: lots of spikes (distortion, PS artifacts, etc.) in addition to broadband noise at about -135 dB, yet the SINAD pretty much exactly matches the value of the H2 peak. The Hegel's spectrum is much cleaner (again, visually), but the SINAD value is getting "penalized" for something I can't see. Looking at the past 20 or so reviews, I've noticed this spectrum/SINAD mismatch happens more frequently with DACs than amps, although the Nord Three SE 1ET400A was an exception to this trend.

My knowledge of this is very limited, but the noise floor you see in an FFT is not what the actual noise floor looks like, instead it's much lower due to something called processing gain (I believe, correct me if I'm wrong) that happens when you take the FFT of a signal. The processing gain can be calculated by the formula 10*log10(N/2) where N is the length of the FFT. The FFT length of Amir's dashboard is 32k (32768) so the processing gain is 10*log10(32768/2)=42 dB which means that the actual noise floor of the device is 42 dB higher than what it appears to be in the FFT. So in the case of the Hegel amp the noise floor in the FFT looks to be a bit lower than -130 dB, add roughly 40 dB to that and you essentially get the same as the SINAD value. Again, my knowledge of this is very limited so if I'm way of the mark please correct me

 

[RayDunzl]

The processing gain can be calculated by the formula 10*log10(N/2) where N is the length of the FFT. The FFT length of Amir's dashboard is 32k (32768) so the processing gain is 10*log10(32768/2)=42 dB which means that the actual noise floor of the device is 42 dB higher than what it appears to be in the FFT.

If the "noise" here were 42dB higher than then 32k FFT reading, I should think I would hear it.

(I get to be wrong, so... 2 cents)

Seems to me if you increase the FFT gain, the spectral components of the noise would emerge from the new floor... So, ???

Sorry... I don't know how to quantify noise except to cock an ear and say something like "Dang, that's noisy!"

 

[Schackmannen]

If the "noise" here were 42dB higher than then 32k FFT reading, I should think I would hear it.

(I get to be wrong, so... 2 cents)

This is from Amir's old guide on audio measurements and here we can see that increasing the FFT length from 256 points (that has 21 dB processing gain) to 32k points seems to lower the noise floor by about 20 dB which seems to match the calculations that a 32k point FFT has 21 dB (42-21) more processing gain than a 256 point FFT. As for audibility, I think people just overestimate the capability of their ears. -90 dB relative to 2.5 V is still only 79 uV, which would produce about 21 dB SPL in a pair of HD 650 (if I did the math correct using a sensitivity of 103 dB/V) which most likely is not audible considering the background noise is usually 15-20 dB higher in a normal room. Again, I might be completely wrong, but that's my understanding of it from trying to learn from all the knowledgeable people here, which is my reason for sticking around in the first place

 

[RayDunzl]

Ok, so, time for an experiment:

Using 8k, 128k, and 1M for the FFT length and an RTA window:

Whoa.

Surprise.

No change in "level" a little more detail.

---

And with Spectrum display:

Using 8k, 128k, and 1M for the FFT length and an Spectrum window:

So, where's the "real" noise floor again?

 

[Blumlein 88]

Ok, so, time for an experiment:

Using 8k, 128k, and 1M for the FFT length and an RTA window:

View attachment 41075

Whoa.

Surprise.

No change in "level" a little more detail.

---

And with Spectrum display:

Using 8k, 128k, and 1M for the FFT length and an Spectrum window:

View attachment 41076

So, where's the "real" noise floor again?

The spectrum view looks like you'd expect from different sized FFTs. I've never used the RTA octave setting. Looks like it might take whatever FFT values you have and put them in octave amounts which would make you get nearly the same value with any FFT size. Looks like the noise level over the 24 khz band is around 56 dbc either way. Mostly set by the lowest frequencies.

 

[JohnYang1997]

distortion can go over 100%. harmonic distortion is comparing to the fundamental. So basically SINAD is 1/(THD+N) in dB scale.
SINAD has noise contribution. And the noise component increases as the bandwidth increases. The noise is calculated in RMS.

 

[JohnYang1997]

Ok, so, time for an experiment:

Using 8k, 128k, and 1M for the FFT length and an RTA window:

View attachment 41075

Whoa.

Surprise.

No change in "level" a little more detail.

---

And with Spectrum display:

Using 8k, 128k, and 1M for the FFT length and an Spectrum window:

View attachment 41076

So, where's the "real" noise floor again?

That depends on how you define the "noise floor". If noise floor means the graphical "floor" of the noise, then there is no real noise floor. However FFT size means the amount of points in the FFT, so if you do the integration of noise (accumulation or RMS) the result is roughly the same. Higher FFT size gives you better resolution and gives you the ability to see below the noise floor with lower FFT size.

 

[DonH56]

The ARC D300 has a very large distortion spike that is far above the noise floor (and above most other spikes) so dominates the SINAD measurement. The Hegel has much smaller spikes closer to the noise floor and increasing noise at higher frequencies. The ARC's spike is large enough to "swamp" the noise, while the Hegel's small spikes do not and so noise tends to set the SINAD rather than distortion.

Going back to my (admittedly weak) field analogy, in a large wheat field a small bush or two poking just above the grass does not impact the noise floor much. Stick a redwood tree in there, and it dominates the scene.

HTH - Don

 

[Bob8701]

My company make analog Audio analyzer, it measures SINAD by measure test signal first then turn off the signal, by compare the level amp on both measurement to determine the sinad, the limiting is 120db due to AGC of the detect circuit. The THD test is using notch filter to filter out test signal, and measure the left over signal, the result is heavily dependent on detector filter setting.

 

[pozz]

My company make analog Audio analyzer, it measures SINAD by measure test signal first then turn off the signal, by compare the level amp on both measurement to determine the sinad, the limiting is 120db due to AGC of the detect circuit. The THD test is using notch filter to filter out test signal, and measure the left over signal, the result is heavily dependent on detector filter setting.

Do you mind saying which company do you work for?