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Extrapolate mic noise "raw score" from sens + self noise?
Old 1st December 2014
  #1
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szegedin's Avatar
Extrapolate mic noise "raw score" from sensitivity + self noise?

----
Oktava mk-012 : noise 19dba sens -35db
Earthworks M23 : noise 22dba sens -30
CAD e100s : noise 4 dba sens -30db
DPA 4041SP : noise 8dba sens -23db
----

I am not trying to get an exact noise figure per se. I am trying to get a relative noise raw score, so I can compare apples with apples. I understand that the self noise will be amplified along with the signal, to the extent the sensitivity requires amplification of the signal, to unity. Unless I am missing something egregious here.

Does it basically make sense to construct a raw score (crude as this may look) like this:

----
(Oktava) (19db of self-noise) + (35db of gain needed to unity) = 54
(Earthworks) 22db + 30db = 52
(CAD) 4db + 30db = 34
(DPA) 8db + 23db = 31
----

With a low score, obviously, meaning lower overall noise. Or am I missing something logarithmic in the math? As in, 22db is not ten percent more noise than 20db, and 30db of gain is not double 15db of gain? Therefore the "15db" in (30db vs 45db) not equal (15db vs 30db). so.....

If it is that simple, I don't know why this isn't used. Anyway, it's useful to me. If only all the world's mics were in a spreadsheet & I could apply this formula.
Old 2nd December 2014
  #2
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Found the 'correct answer' in this calculator

Megalithia: microphone and recorder noise calculator

Interesting because my ranking was wrong. So the CAD is quieter than the DPA even though, or because, the latter has the extremely high sensitivity of 70mv/Pa. The results are somewhat puzzling. I guess it's certainly not linear, and the high sensitivity of a noisy mic will bring up its own self-noise. So mic noise dominates over preamp noise at high gain. Better to have lower sensitivity given a noisy mic, given you have a quiet preamp.

More math and discussion here:

All Aspects of Neumann Products - Calculate mic noise into dBA from mic data


Apparently this is not a load of fun to talk about

/ - \
Old 3rd December 2014
  #3
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It gets a little complicated as it depends on where the dominant noise source is in the mic. But, high sensitivity (i.e. high mV/Pa, small negative dBs) usually means a better SNR overall. In a well designed mic, the dominant noise source is "after the gain" - it is mostly in the channel of the FET or in the Anode-Cathode path of the tube.

Going on the assumption above, the *Noise Floor* of the mics is as follows (a linear sum of logarithmic dB values):

*Noise Floor* = *Noise Figure* - 94 - sensitivity + 2.21

The 94 is dBSPL relative to 1 Pascal. The sensitivity figure is relative to 1V per Pascal. The 2.21 is to get you from dBV to dBu (and not strictly necessary just for comparisons)

So, if you do the math, the noise floor in the CAD is 11dB below the noise floor in the DPA.

The signal level will be proportional to the sensitivity. In your example figures, the CAD has 7dB lower sensitivity and thus 7dB less signal than the DPA for the same Sound Pressure Level.

So, overall, the CAD is +11 - 7 = 4dB better Signal to Noise Ratio than the DPA.

That is a little surprising, but it could well be true. It depends on whether everyone is using A-weighting and the same overall bandwidth for their measurements. Of course, there are other considerations such as linearity and headroom, and flatness of frequency and phase response (if that is a goal - it may or may not be, depending on application), THD (again, nice HD might be desirable depending on application) and things like off-axis response and fidelity of polar patterns across the full audio spectrum.
Old 3rd December 2014
  #4
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Furthermore, if the frequency response of the mic does deviate quite a bit from flat, the actual apparent sensitivity may be different to the spec figure. The spec figure is usually measured with a spot 1kHz tone. The figure measured by integrating a full frequency sweep would be more accurate with a non ruler-flat mic.
Old 3rd December 2014
  #5
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Quote:
Originally Posted by Matt Nolan View Post
It gets a little complicated as it depends on where the dominant noise source is in the mic. But, high sensitivity (i.e. high mV/Pa, small negative dBs) usually means a better SNR overall. In a well designed mic, the dominant noise source is "after the gain" - it is mostly in the channel of the FET or in the Anode-Cathode path of the tube.

Going on the assumption above, the *Noise Floor* of the mics is as follows (a linear sum of logarithmic dB values):

*Noise Floor* = *Noise Figure* - 94 - sensitivity + 2.21

The 94 is dBSPL relative to 1 Pascal. The sensitivity figure is relative to 1V per Pascal. The 2.21 is to get you from dBV to dBu (and not strictly necessary just for comparisons)

So, if you do the math, the noise floor in the CAD is 11dB below the noise floor in the DPA.

The signal level will be proportional to the sensitivity. In your example figures, the CAD has 7dB lower sensitivity and thus 7dB less signal than the DPA for the same Sound Pressure Level.

So, overall, the CAD is +11 - 7 = 4dB better Signal to Noise Ratio than the DPA.
Thanks much for explaining this. With your math I get numbers that are about the same as the calculator.

I'm more confused than ever, as to why higher sensitivity seems to worsen, not improve, signal to noise ratio. Or does it worsen the s/n of the mic, but improve the picture at the preamp stage, which compensates for it(?)

Take two mics:
1) 18db self noise, -35db sensitivity (17mv/pa) = -107.9
2) 18db self noise, -23db sensitivity (40mv/pa) = -96.8

What the heck? Maybe I did the math wrong here. Do I then correct for the difference in sensitivity such that:
35-23=12
-96.8+12= "108.8"
Mic 2, a lot more sensitive than mic 1, is only about 1db "quieter"(?)

I'm seriously concerned I'm about to buy the wrong mic.
Old 4th December 2014
  #6
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Quote:
Originally Posted by szegedin View Post
Take two mics:
1) 18db self noise, -35db sensitivity (17mv/pa) = -107.9
2) 18db self noise, -23db sensitivity (40mv/pa) = -96.8
17mV/Pa = -35dBv
40mV/Pa = -28dBV

So there's your first mistake (if I'm not mistaken myself!)

So the noise floors are -111dBv and -104dBv respectively (or -108.8dBu and 101.8dBu, still a 7dB difference). So, looking at noise floor alone, mic (1) is 7dB quieter than mic (2).

Quote:
Originally Posted by szegedin
What the heck? Maybe I did the math wrong here. Do I then correct for the difference in sensitivity such that:
35-23=12
-96.8+12= "108.8"
Mic 2, a lot more sensitive than mic 1, is only about 1db "quieter"(?)

I'm seriously concerned I'm about to buy the wrong mic.
Mic (1) is 7dB less sensitive. So, in this case, they have the same SNR.

And, you know what? I've just realised that I've over-thought and over-complicated this.

The difference in SNR is just the difference in Noise Figure. That's part of the point of why it is defined the way it is - to make it independent of sensitivity. Sorry for adding to your confusion.
Old 4th December 2014
  #7
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Quote:
Originally Posted by Matt Nolan View Post
17mV/Pa = -35dBv
40mV/Pa = -28dBV

So there's your first mistake (if I'm not mistaken myself!)
Yep you're right, my typo there.

Quote:
Originally Posted by Matt Nolan View Post
And, you know what? I've just realised that I've over-thought and over-complicated this.

The difference in SNR is just the difference in Noise Figure. That's part of the point of why it is defined the way it is - to make it independent of sensitivity. Sorry for adding to your confusion.
Well sure, you're just saying mic noise is mic noise and that's it. Well perhaps I overthought this in the first place, but mic sensitivity 'effects' overall noise you'll get from the mic. But I guess I'm talking about what effect this has upstream in terms of how much preamp gain you have to apply. And maybe that's, strictly speaking, a matter of preamp noise. You have to apply x% more gain to the less sensitive mic. So I'm no closer to a quantification of it.

In the original post I'm trying to get a way to compare mics in terms of noise with a quantitative ranking, given that they're going into the same preamp. Without complicating it by running the preamp's noise specs per se. The calculator I linked to does this, but I'm confused as to why a less sensitive mic, given the same 18db self-noise, results in a lower noise floor. I thought it would be the other way around.

It probably turns on some threshold of one of those specs, can't figure out which. 'Mo mics, 'mo math problems.
Old 4th December 2014
  #8
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We need someone to chime in who uses this stuff every day!

I think I've confused myself with Noise Figure, EIN and "Self Noise". I was thinking that Self Noise is the same as Noise Figure. Now I don't think it is.
Old 4th December 2014
  #9
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You should re-post your question in the geekslutz sub-forum
Old 4th December 2014
  #10
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szegedin's Avatar
Quote:
Originally Posted by Matt Nolan View Post
You should re-post your question in the geekslutz sub-forum
Appreciate your brainstorming, anyway

I better think about how to re-phrase this.
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