Help converting mic sensitivity references

[cashhewn]

Hi,

I’m hoping that a real engineer might be able to kindly help me understand the math and theory behind converting a mic sensitivity listed as “-54 dBv re: 1V/Pa” into simply mV/Pa?

And if it’s not asking too much while we’re at it, how about a mic sensitivity that’s listed as “-80dB re: 1V/dyne/cm2” into mV/Pa?

Many thanks!

[Wonks]

mV/Pa isn't a particularly good unit for mic sensitivity. dBV re:1V/Pa is a much better one, especially if you want to compare relative audible volumes. That's why all the figures use dB, even if referenced to some now very obscure units.

Any decibel level for voltages is 20xLog10 of the difference, so divide the dB value by 20 and then take the antilog of that and there you go.

So -54dBv is antilog (-54/20) = antilog of -2.7 = 0.00199. So say 2mV.

1 Dyne/cm2 equates to 0.1Pa, so a value that will be ten times bigger if there was 1Pa rather than 0.1Pa present.

So -80dB of the dyne reference level is (antilog-80/20)x10 in mV/Pa, or (antilog-4) x 10 = 1mV/Pa

To convert the mV figure to dBv, then 0.001v/1v = 0.001 (as you need the ratio compared to a 1V signal. Then Log10 of 0.001 is -3. Multiply that by 20 (for your 20 log10 of the ratio) and you find that converts to -60dBv re 1V/Pa

[Hugh Robjohns]

I’m hoping that a real engineer might be able to kindly help me understand the math and theory behind converting a mic sensitivity listed as “-54 dBv re: 1V/Pa” into simply mV/Pa?

There's a good explanation of the maths here, complete with converters for the legacy standards.

https://sengpielaudio.com/calculator-transferfactor.htm

A sensitivity of -54dB re 1V/Pa equates to 1.99mV/Pa.

...how about a mic sensitivity that’s listed as “-80dB re: 1V/dyne/cm2” into mV/Pa?

Equates to 1mV/Pa.

(10 dyne/cm^2 = 10ųbar = 1 Pascal = 94dB SPL)

I dont know the origins for this, but European manufacturers tend to use mV/Pa for their sensitivity specs, and American manufacturers tend to use dB re 1V/Pa.

And I agree with Wonks that the dB re 1V/Pa figures are more useful, more relevant, and easier to compare for the end user. ... but conversion to/from mV/Pa is straightforward.

Dynes/cm^2 and ųbar are both legacy pressure units which are only found on mic specs dating before the 1970s.

[ef37a]

Cashhewn I don't know where your numbers came from but if you are comparing the sensitivities of older microphones be aware that there was at least one SPL standard different from today?

Modern usage is the Pa, equal to about 94dB SPL IIRC. Older mics used 75dB SPL for sensitivity and thus will seem very low compared to today's products.
They weren't really and dynamic mics over the last 80 years or so seem to be in the -55dB to -57dB/Pa range, about 2mV to 1.5mV. There are of course a few weak sisters like the SM7b. You must also take rated impedance into account. Modern dynamics are 150 Ohms or 200 Ohms as a rule but some really old stuff was 30 Ohms. I have little Geloso mic that is 16 Ohms!

Nod to speedy Hugh!

Dave.

[Hugh Robjohns]

Cashhewn I don't know where your numbers came from but if you are comparing the sensitivities of older microphones be aware that there was at least one SPL standard different from today?

True! Today we use the Pascal as the reference pressure, which is 94dB SPL. Way back when they used 74dBSPL which is 20dB lower.

Older mics used 75dB SPL for sensitivity and thus will seem very low compared to today's products.

It was 74dB SPL, and while the raw sensitivity numbers might seem low, that difference is completely taken into account in the pressure units: ubar or dynes/cm^2 which are a factor of 10 smaller too:

As noted above, 1PA = 10ubar or 10dynes/cm^2.

And as we know, 20*Log10 = 20dB.

You must also take rated impedance into account. Modern dynamics are 150 Ohms or 200 Ohms as a rule but some really old stuff was 30 Ohms

The rated output impedance doesn't affect the sensitivity figures if used within a voltage-matched interface (as all modern mic preamps do).

[ef37a]

"The rated output impedance doesn't affect the sensitivity figures if used within a voltage-matched interface (as all modern mic preamps do)."

Not sure I understand that Hugh? Some of our old valve PA amps use 1:100 input transformers. A 30 Ohm mic was way less sensitive than say a later 200 Ohm Grampian DP4, so beloved of the itinerant reporter.

Then, when very early mono cassette machines arrived they had a mic wound to around 600 Ohms to get a few more mV into the rubbish electronics. A lot of karaoke mics are 600R, I use them in my garden. N.B. none of those cheap 600R mics used transformers and most were made of plastic.

Dave.

[cashhewn]

mV/Pa isn't a particularly good unit for mic sensitivity. dBV re:1V/Pa is a much better one, especially if you want to compare relative audible volumes. That's why all the figures use dB, even if referenced to some now very obscure units...To convert the mV figure to dBv, then 0.001v/1v = 0.001 (as you need the ratio compared to a 1V signal. Then Log10 of 0.001 is -3. Multiply that by 20 (for your 20 log10 of the ratio) and you find that converts to -60dBv re 1V/Pa

Wonks, that is so helpful! I can simply convert and compare dB differences in sensitivity between mics. Thank you!

There's a good explanation of the maths here, complete with converters for the legacy standards.

https://sengpielaudio.com/calculator-transferfactor.htm

...And I agree with Wonks that the dB re 1V/Pa figures are more useful, more relevant, and easier to compare for the end user. ... but conversion to/from mV/Pa is straightforward.

Dynes/cm^2 and ųbar are both legacy pressure units which are only found on mic specs dating before the 1970s.

Hugh, also so helpful, thank you.

Cashhewn I don't know where your numbers came from but if you are comparing the sensitivities of older microphones be aware that there was at least one SPL standard different from today?

Dave, I'm compiling a quick comparison chart for my mic locker, some of the mics are quite old, yes. Very good point on the older SPL standard, thanks for mentioning that.