THD+N, SINAD and an amateur's struggle to understand what these things mean

[50°F=Hellfire]

I just spent approximately two hours browsing the internet in pursuit of information regarding the specifications Amir measures. As I am not an electrical engineer and most of the sources I found seemed to be aimed at people in that field or a similar one, I had some trouble interpreting my findings/translating them to words I am (semi-) capable of understanding. I guess my intentions mostly boil down to verifying and, if need be, correcting my interpretations.
1) Ostensibly, THD+N is equivalent to SINAD if measured under the same conditions. Is that true?
2) SINAD/THD+N is, in layman's terms, the ratio of the signal itself to all "undesirable" parts/factors.
I guess the way my questions are written shows how uneducated I am on this particular topic (I'm a high school senior who hasn't had physics classes for approximately five years). Thus, I would greatly appreciate answers formulated in a comparably simplistic manner, if at all possible.

 

[vitalii427]

1) It’s not equivalent. It’s the same thing but expressed differently. THD+N usually expressed in percentage, SINAD in dB. For example: 1% (THD+N) = 40 dB (SINAD)

Actually, SINAD is a reverse expression of THD+N:
SINAD = 1/(THD+N)

And both can be expressed in dB and %.

https://en.m.wikipedia.org/wiki/Decibel

I think the only reason why Amir uses SINAD is that it is easier to compare.
100 dB (SINAD) = 0.001% (THD+N)
101 dB (SINAD) = 0.0008913% (THD+N)

I hate to count those zeros.

 

[dc655321]

Although yes, it is also aimed at an EE/physics audience, this paper contains your answers.
In particular the first 5 pages and figures are quite good. Or maybe not? You judge...
It's a good reference, regardless.

Quotes from the paper to (hopefully?) answer your questions:
1)

SINAD is equal to THD + N, provided the bandwidth for the noise measurement is the same for both (the Nyquist bandwidth).

2)

Signal-to-Noise-and-Distortion (SINAD, or S/(N + D) is the ratio of the rms signal amplitude to the mean value of the root-sum-square (rss) of all other spectral components, including harmonics, but excluding dc.

 

[pozz]

To add to the above.

• Noise is hash across the entire frequency range. There are many causes.
• What is usually called "distortion" are the tones added by the playback equipment to the input signal. You can think of "distortion" like the electrical version of resonance in a mechanical system.
• SINAD expresses the dynamic range of the measured unit untouched by either distortion or noise over a certain bandwidth.
• THD+N is the inverse of SINAD in that it is the sum of all spectral components of the test tone (excluding the test tone itself) over a certain bandwidth.
• The voltage and level of the test tone and a greater or narrower bandwith (e.g., 4V, -3dBFS, 20Hz—20kHz) will affect the results.

This might be better https://www.ranecommercial.com/legacy/note145.html for beginners.

Edit: Updated link.

 

[q3cpma]

Would be nice to have a weighted THD+N considering masking and audibility of distorsion by frequency. The equivalent of C or A weighting for SPL calculation, basically.

 

[50°F=Hellfire]

Would be nice to have a weighted THD+N considering masking and audibility of distorsion by frequency. The equivalent of C or A weighting for SPL calculation, basically.

Lotoo included that in the spec sheet of a device I intend to buy.

 

[pozz]

Lotoo included that in the spec sheet of a device I intend to buy.

Hi @50°F=Hellfire

A dB is a ratio which depends on a reference, so for SPL that reference is variation in barometric pressure to which your ear responds. dB SPL cannot be directly compared to referenceless dB given in the specs you posted, or to the dBFS scale used in ASR's reviews.

What @q3cpma is talking about is a psychoacoustic model, which isn't easy to calculate in a straightforward manner. However, in your case it's not necessary. Added spectral content ("distortion") will generally not be audible. What will audibly affect a headphone amplifier is power output (should be high) and output impedance (should be low). If you are using IEMs, which are very sensitive relative to headphone, you may hear hiss, so what is desirable in this case would be a high SNR.

Unfortunately the spec sheet uses A-weighting, which makes its numbers not comparable to ASR's measurements. Second, the distortion, noise and output power specs don't reference which gain (high/low).

What this all means is that manufacturer has provided incomplete information, so buying would be like rolling the dice.

 

[thomasjast]

Of all the graphs presented on this site, I find the channel imbalance one the most confusing. I can't make heads of tails of it. At best, all of them look really bad.

 

[pozz]

Of all the graphs presented on this site, I find the channel imbalance one the most confusing. I can't make heads of tails of it. At best, all of them look really bad.

Time in seconds on the x axis. Level on y left (red), amount of variation when comparing two channels on y right (blue). Ideal is a flat blue line. The more peaks/valleys, the less useable a headphone will be, and high efficiency headphones will be affected more than others.

 

[MRC01]

... (I'm a high school senior who hasn't had physics classes for approximately five years). Thus, I would greatly appreciate answers formulated in a comparably simplistic manner, if at all possible.

Here's an introduction to what is a dB and how to convert back and forth to percentages: http://www.mclements.net/Mike/mrc-blog/blog-140310.html

 

[thomasjast]

Time in seconds on the x axis. Level on y left (red), amount of variation when comparing two channels on y right (blue). Ideal is a flat blue line. The more peaks/valleys, the less useable a headphone will be, and high efficiency headphones will be affected more than others.

What's the relevance of time in seconds? I assumed it was more like clock coordinates of the dial, actually. That would make sense to me.

 

[pozz]

What's the relevance of time in seconds? I assumed it was more like clock coordinates of the dial, actually. That would make sense to me.

Lol it's a scale of how long it takes Amir to physically twist the volume knob. The slope of the red line corresponds to how fast the level drops.

 

[pozz]

1) It’s not equivalent. It’s the same thing but expressed differently. THD+N usually expressed in percentage, SINAD in dB. For example: 1% (THD+N) = 20 dB (SINAD)

Actually, SINAD is a reverse expression of THD+N:
SINAD = 1/(THD+N)

And both can be expressed in dB and %.

20 dB = 100 = 1/(1/100) = 1/0.01 = 1/(1%)

https://en.m.wikipedia.org/wiki/Decibel

I think the only reason why Amir uses SINAD is that it is easier to compare.
100 dB (SINAD) = 0.001% (THD+N)
101 dB (SINAD) = 0.0008913% (THD+N)

I hate to count those zeros.

Easy conversion:

• 100%=0dB
• 10%=20dB
• 1%=40dB
• 0.1%=60dB
• 0.01%=80dB
• 0.001%=100dB
• 0.0001%=120dB

Etc.

 

[MRC01]

More generally, for voltage, dB = 20 * log(V1 / V2)
So every time the ratio of V1/V2 changes by a factor of 10, that's 20 dB.
For power, it's 10 * log(P1/P2), so each factor of 10 is 10 dB.

 

[pts]

....
This might be better https://www.rane.com/note145.html for beginners.

Results in Page not found, what was the title ?

Is it https://www.ranecommercial.com/legacy/note145.html Audio Specifications

 

[Blumlein 88]

Results in Page not found, what was the title ?

Is it https://www.ranecommercial.com/legacy/note145.html Audio Specifications

That is the correct link. One of the best condensed explanations of specs.

 

[taisho]

For THD+N% equal 0.001%, in Excel you type 0.001 in cell A1 and use this formula to convert:
=20*LOG10(A1/100)

 

[Music1969]

Actually, SINAD is a reverse expression of THD+N:
SINAD = 1/(THD+N)

And both can be expressed in dB and %.

Are these dB values (right column) comparable to Amir's SINAD values? These are at high voltage output of course, so would be lower at lower voltage.

 

[VintageFlanker]

Are these dB values (right column) comparable to Amir's SINAD values?

At 1Khz, yes.

These are at high voltage output of course, so would be lower at lower voltage.

Yep. 18dBu equals 6.15V. But SINAD not always goes down with voltage.

 

[Trouble Maker]

These are at high voltage output of course, so would be lower at lower voltage.

This is just my best intuition of what is happening, would love for someone to confirm or refute/correct.

I imagine the noise floor as long as you are in the linear/regular operation of the device is pretty constant e.g. even without a signal present, the same amount of noise is there, probably about the same as if a signal were there. But, the distortion components will scale with signal. So, if the noise is constant and your signal/distortion decrease, noise will start to become a large percentage of the final output as signal decreases. Since SINAD is a comparision of signal to noise, your signal is going down but the noise is not. SINAD get's worse as signal goes down.

It seems like most devices have the worst SINAD at the lowest end, go down to a through but then as they get towards the non-linear operating range e.g. clipping they start to rise again. I also guess that at this point distortion is starting to go up as the devices starts to get to some power/voltage/current limit of some part of the device, which causes the rise in SINAD. Maybe noise is still constant or at least not rising like distortion

For example.
https://www.audiosciencereview.com/...ents-of-new-jds-labs-atom-headphone-amp.5262/