# Understanding digital MEMS microphone sensitivity and obtained bits for a given input SPL

I'm trying to understand /simulate the communication between 2 smartphones by means of ultrasounds. As this is a general study I'm considering that the smartphones are equipped with the "typical" most common kind of transducers. One of them is broadcasting a sound and the other recording it. I would like to know under what conditions is the transmitted sound properly recorded. The first thing I did was trying to understand how directivity at this frequency affected the transmission. You can see that analysis here .

Now I'm trying to understand the technical parameters in the MEMS digital microphone and microspeaker (the kind of sound transducers most commonly used in smartphones). I'll assume that the transmitting smartphone is equipped with a speaker of this type and that the receiver is equipped with a microphone of this type.

In the speaker specification I can see :

Rated Input Power : 0.5W(2.0Vrms)

S.P.L : 83±3dB/0.1m/0.1W at 0.8,1.0,1.2,1.5KHz average

The speaker frequency response is:

In the microphone specification I can see :

Sensitivity : 94 dB SPL at 1 kHz : -26 dBFS

The microphone frequency response is:

My questions are:

1. Is the sensitivity the difference between maximum acoustic signal (maximum SPL) at the mic input (which causes full-scale digital word, 16 bits? ) and the 94 dB SPL reference? So, if the mic sensitivity is –26 dBFS at 94 dBSPL, is maximum SPL 120 dBSPL? (–26 dBFS = 94 dBSPL – 120 dBSPL) Is it alright to mix dBFS and dBSPL ?

2. This is a PDM smartphone so it's output is only 1 bit. But if we assume that after proper conversion we obtain a 16 bit when the maximum acoustic signal (120 dBSPL) is being received, at 94 dBSPL will its output be about 11 bits?

3. Assuming that we are working at 1 kHz if the speaker generates 83±3 dBSPL at 10 cm and we place the microphone at this distance, how many useful bits will it output?

4. What can I do to find out the speaker generated SPL when it is supplied with 0.5W (instead of 0.1 W which is the only data given)?

5. What can I do to find out the speaker generated SPL and microphone sensitivity at, lets say, 18 kHz?

6. If mic SNR is 64.5 dB. How many useful bits above the noise floor can it work with?

1. The mems microphone produces a digital signal and when the incident RMS pressure is 94 dB SPL, the digital signal has an RMS level of -26 dBFS. If the positive full scale is (say) $2^{15}$ or 32,768 then the digital RMS level is 26 dB down on this at 1,642. This will be at 1 kHz.
2. 1,642 is an RMS number so the full peak-to peak value (for a sinewave) is 4644 LSbs. This cannot be represented by signed number less than 12 bits (13 bits including sign).
3. 83 dB SPL is 11 dB down on 94 dB SPL hence the RMS digital signal level will be 11 dB down on 1,642 i.e. 463. Because you are using a sine wave this translates to a peak-to-peak reading in digital counts of 2.828x higher or 1309 counts p-p.
4. 0.5 watts is 5 times more power than 0.1 watts or an increase of 3.16 dB and, accordingly, the SPL will be 3.16 dB higher and ditto the digital signal produced.
5. I have no clue on this because I don't know the frequency responses of either speaker or microphone nor the ambient acoustics.
6. This is tricky to predict because if the equivalent noise is 100 counts RMS (gaussian) then there will be a 99.9% probability it will be within a digital level of 660 digital counts p-p (see below). What is an acceptable level only you can decide.

Gaussian noise and probability: -

• Thank you very much for your answer! I have some doubts. In 1) You don't mention anything about maximum acoustic signal. If at 94 dB SPL the digital signal has an RMS level of -26 dBFS at 120 SPL it has an RMS level of 0 dBFS, that means the full scale has already been reached and since it is RMS then the maximum is clipping!!! The sensitivity and output level of digital microphones are given as peak levels because they are referred to the full-scale digital word, which is a peak value. See analog.com/en/analog-dialogue/articles/… – VMMF Aug 24 '17 at 19:24
• I've edited my question to add the microphone and speaker frequency responses, assume we are working on an anechoic chamber. Can I just add and subtract the increment in sensitivity and decrement in sound pressure level of respective mic and spk when they work around 18 kHz? – VMMF Aug 24 '17 at 19:59
• The single line that specifies sensitivity is clear; in the absence of any statement to the contrary RMS values must be assumed. If they are peak values then the gain does not change. Don't make a meal of this please. If it clips at 120 dB SPL and this is a problem then find a better one. – Andy aka Aug 24 '17 at 20:13
• Regards the frequency response, yes – Andy aka Aug 24 '17 at 20:13

A communication link's success depends on SNR. Narrowband links can greatly improve the SNR. Simple on-off modulation needs SNR of 10dB for 0.1% bit error rate (depends on bandwidth, but good rule-of-thumb); thus 2 bits or 3 bits will suffice for OOK.

For 16_QAM, with 4 bits per symbol, where a settled-amplitude is needed, you need more accuracy and more time to settle to recognizable point in the constellation.

Regarding your question, if the receiver microphone digitizer has a fixed floor, then dropping the power 6dB (2*2, at 3dB per power ratio of 2) produces 6dB worse SNR (lower SNR).

From your question, if 16 bits at 120dBSPL, then 26 dB lower at 94dB would cost 4+ bits.

Yes----dbFullScale are dB/dB comparable to dBSPL.

• Thank you very much for your answer. From the first part of it I guess you didn't understand my question very well. I'm not interested in identifying a digital modulation scheme. Although its nice to know that dbFS is dB/dB comparable to dBSPL! Would you mind improving your answer? Could you answer it in the enumerated order? – VMMF Aug 24 '17 at 20:07