# Calculating noise in dB produced by microphone pre-amplifiers

I need to know whether my pre-amplifier or my microphone is limiting the sound quality (in terms of noise) of my recording setup.

The sound recorder (SM2Bat+, Wildlife Acoustics) has a specified equivalent input noise (EIN) value of -115 dBV at 44.1 kHz sampling frequency (and -105 dBV at 384 kHz). It is set to apply 36 dB of amplification to my microphone.

The microphone (ICS-40720, Invensense) has a signal-to-noise ratio of 70 dBA, an EIN of 24 dBA SPL (though according to @Mark this does not make much sense), and a sensitivity of -32 dBV.

How much noise (in dBA) is contributed by the pre-amplifier to the overall noise in a recording resulting from this setup?

• Is someone copying threads from homerecording.com ???????????? Commented Nov 23, 2019 at 20:42

The EIN specs of the microphone don't really make much sense as this parameter usually only refers to a preamplifier and is measured by grounding a 150 ohm resistor across the input.

Additionally, dBA is an acoustic measurement not an electrical one so again this doesn't make much sense when used in an electrical context unless you are picking up the microphone and holding it next to your ear to see how much noise it's making.

No, don't do that. It's silly. But unfortunately that's what specifying dBA for an EIN value is equivalent to.

Whoever wrote the Invensense specs for this mic probably needs a little talking to.

The answer to your question is actually contained in the question. The EIN of the recorder preamp is the noise level that is contributed to the recording by the preamp. (-115dBV).

Also note that the SM2BAT+ (according to the specs) records at 384kHz which means that the mics you use will need to have a much wider frequency response than the ICS40720 can deliver (according to the specs it rolls off at 20Khz). Being a bat detector, most bats work on ultrasonic frequencies so I guess this makes sense.

• I am not sure whether I understand. dBV is an electrical measurement, dB an acoustic one, got that. So either we cannot find out how many dB of noise are contributed by the pre-amp? Or are you saying that it is contributing -115 dB, just like its dBV figure? Commented Nov 17, 2019 at 9:34
• The SM2Bat+ can record at multiple sampling frequencies, it is not specialised for bats. I also wanted to calculate the noise for ultrasonic recordings but mentioned standard sampling frequencies here. The ICS40720 is well usable for recording bats, actually, despite the slight roll-off. Commented Nov 17, 2019 at 9:34
• dB is not an acoustic measurement or an electrical measurement. It is neither. What I said was that dBV is an electrical measurement and dBA is an acoustic measurement. When you are using the term 'dB' you are only referring to a relative measurement with no reference level.
– Mark
Commented Nov 17, 2019 at 23:41
• This is a useful reference if you havn't seen it already. wildcare.co.uk/media/wysiwyg/pdfs/UltrasonicMicrophones.pdf
– Mark
Commented Nov 17, 2019 at 23:43
• Thank you mark, yes I knew about that document. I adapted the question to be more accurate and correct. I still seems unanswered... Commented Nov 18, 2019 at 15:05

Microphones are linear. By subtracting their signal-to-noise ratio (in dB SPL) from their sensitivity (in dBV), we obtain the electrical noise floor of the microphone (in dBV). That value can be compared to the equivalent input noise (i.e. noise floor, in dBV) of the amplifier to find out how much noise is contributed by the amplifier. In this case, the amplifier contributes 13 dBA less noise than the microphone.

Explanation:

I provided an alternative answer to my own question after trying to wrap my head around it for some time. Thanks to Mark for improving my question, but I can understand it better like that. I hope it is correct...

The key here is that across most of their range, microphones (or at least all those whose spec sheets were detailed enough for me to check) are linear transducers of sound pressure into voltage. Not only that, but the increase in voltage is 1:1 with the increase in sound pressure. You can see that in linearity graphs in microphone specification sheets. Only above a certain threshold (roughly corresponding to the acoustic overload point), and also below the noise floor, this linear relationship flattens off.

As a consequence, specifying noise floors, equivalent noise (whether it should be called "input noise" for microphones can be a matter of debate, but technically, the microphone inputs voltage into the electrical circuit), signal-to-noise ratio, or sensitivity in dBV or dBA (only at 1 kHz) or dB SPL is equivalent. I am not saying that this is particularly straightforward or helpful, though.

In the end, the signal-to-noise value can be used to obtain electrical noise floors (using the sensitivity value) or acoustic noise floors (using the 94 dB SPL reference value). The latter can easily be compared to the equivalent input noise of amplifiers to answer the question.

Example with the ICS-40720 microphone mentioned above:

The microphone has a signal-to-noise ratio of 70 dB (for SPL, but actually it does not matter). By definition and by that standard, that signal is a 94 dB SPL tone at 1 kHz, thus the acoustic noise floor (which is constant) is 70 dB lower, at 94-70 = 24 dB SPL (in a calibrated audio recording).

This is the same as the equivalent (input) noise figure in the specifications, albeit that it is written in dBV.

The microphone has a sensitivity of -32 dBV. Since it is linear, with a 70 dB signal-to-noise ratio, it would mean that the electrical noise floor would be at -32-70 = -102 dBV. Turns out, this is actually the figure stated in the specification sheet.

When we compare it against the -115 dBV value for the equivalent input noise of the amplifier, we find that the latter contributes 13 dB less noise than the microphone.

• "Example with the ICS-40720 microphone mentioned above: The microphone has a signal-to-noise ratio of 70 dB (SPL, but actually it does not matter). So when picking up a 94 dB SPL 1 kHz tone, the acoustic noise floor is at 94-70 = 24 dB SPL (in a calibrated audio recording)." No, this is not how Signal-To-Noise ratio or acoustic noise floors work. The acoustic noise floor is not a dependent factor.
– Mark
Commented Nov 23, 2019 at 0:37
• thanks, corrected. Indeed I was uncertain about how to formulate that one. Commented Nov 23, 2019 at 9:29
• I don't think it is really meaningful to reference a varying noise floor based on signal-to-noise ratio. S2N is only meaningful in the context of electrical or preamp noise or when considering the maximum signal strength that can be detected. Acoustic noise floor is never the result of a mathematical calculation based on Signal to Noise. The answer would be improved with this paragraph removed.
– Mark
Commented Nov 23, 2019 at 9:38
• Previously, I wrote that the noise floor is constant. In the updated paragraph, I made a few more clarifications. The standard SNR SPL value, as it is defined, is just used to derive the noise floors, but is necessary for the argumentation and to obtain the solution. Specifically, I don't see how I could delete that (which?) paragraph. Commented Nov 23, 2019 at 22:12
• If that is the case, the solution falls over. Signal to Noise Ratio has nothing to do with SPL. Noise floors are related only to the electrical components - the microphone and the preamp - in that the electrical components and circuitry introduce noise. There is no such behaviour in the context of an acoustic noise source.
– Mark
Commented Nov 24, 2019 at 0:05