90dBspl is an rms value in the acoustic domain.
The digital level of 2500 rms in a 16bit system is the same as approximately -22dB FS rms (actually -22.35), where 0dBFS rms is a full scale square wave. A full scale sinusoidal in such a system is 0dBFS peak and -3dB FS rms (reaching from -32768 to +32767).
A square wave of +/-2500 can be calculated as:
20 * log ( 2500/32767) = -22.35 dB FS rms
Please note that peaks of sinusoidals are always 3dB higher than the rms level. The only signal that has the same rms and peak level is the square wave.
Now, Android has a requirement of 30dB linearity around 90dBspl, but this linearity shall be +12dB above 90dBspl and -18dB below the same point. Outside this range there can be compression in different ways, depending on which phone model you test.
The guaranteed highest linear level inside an Android phone is -22dBFS +12dB = -10dBFS rms. Above this level it is uncertain. The most common scenario is that the last 7dB of peak headroom are still linear, leading to an acoustic maximum level of 90dBspl + (22-3 dB) = 109dB spl rms for a sinusoidal without clipping (or 112 dB spl peak).
In some phones you will find a peak limiter that reduces the gain above 102dBspl rms. The outcome of this is that you can still record up to the level of saturation for the microphone. This saturation level varies, but it is common to have like 2% distortion at 120dB spl. Above this level the microphone component starts to saturate and clip.
Looking at the other end of the scale:
Small phone microphones are in general noisy. The latest microphones can have a noise floor at -63dB below 0dBPa (94dBspl), but most microphones are between -58 and -60dB below 0dBPa.
How can this be calculated to dBFS rms ?
0dBPa rms is 94dB spl rms. From the statement above we know that 90dBspl rms acoustic level will be recorded at the digital level of -22dBFS rms in Android phones. -63dB below 90dBspl is the same as -22dBFSrms +4dB -63dB = -81dBFSrms. The absolute maximum range of dynamics in a 16 bit system can be approximated to 96dB (or 93dB depending how you see it), so the noise level is at least 12dB above the quantization noise in the digital file.
This is a very important finding for video recording mode. Unfortunately many video applications in Android tend to have too high microphone gain in the recording. This leads to clipping when recording loud music concerts and similar situations. We also know that the microphone itself is good up to at least 120dB. So it would be a good idea for any audio system engineer to make a video recording mode that actually used the whole dynamic range of the microphone. This means that the gain should be set at least 8dB lower. It is always possible to change the rms level afterwards in a video recording if the sound is too soft, but if it is clipped, then you have damaged the recording forever.
So, my message to you programmers is to implement a video recording mode where the acoustic level of 90dB spl rms is recorded at -30dBFSrms or slightly below that. Any maximization can be done afterwards. In this way we could record rock concerts with much better sound. Doing automatic gain control does not help the sound quality. The dynamic range is often too big to be controlled automatically. You get a lot of pumping in the sound. It is better to implement two different video recording modes: Concert mode and speech mode. In speech mode (optimized for a talking person at 1m distance) the recording gain could be even higher than -22dBFSrms for 90dBspl. I would say -12dBFS rms for 90dBspl would be a suitable recording level. (speech at 1m distance has an rms level of approximately 57dB spl and peaks 20-30dB higher).
Björn Gröhn
Audio system engineer at Sony mobile Lund, Sweden