How to convert from datasheet dB value to pressure per volt?

Question

I am trying to measure sound waves using a raspberry pi pico ADC pin but am having trouble converting the sensitivity value on my data sheet into pressure units per volt.

I have read a many articles and posts online but have not been able to follow any of them through all of their steps.

The datasheet of the electret I am using is here:

https://kitronik.co.uk/products/3310-microphone-insert-pcb-mount-pack-of-5?_pos=1&_sid=3e44071e0&_ss=r

I found the following equation for converting dBV to mV/Pa online:

S1 = 20 x log( S2/R )

Where:

• S1 is sensitivity in dBV
• S2 is sensitivity in mV/Pa
• R is labelled as output_AREF

Im thinking the value S2 is the sensitivity provided in the datasheet. To ensure the units in the logarithm cancel, Im thinking the value R is given by "0dB=1V/ubar" in the datasheet under sensitivity.

Rearranging the above equation for S2 gives:

S2 = (R)*10^(S1/20)

I'm thinking, keeping R in Volts per micro bar, then S1, given in the datasheet, is -54dB and R is 1V per ubar. So, the resulting value for S2 will be x amount in volts per microbar.

If all this is correct, then I'm thinking the output from the electret will have a certain DC offset with an AC component. The AC component will be proportional to the pressure. I can then convert this AC component into pressure (in micro bars) using the equation above:

Pressure = V*(R)*10^(S1/20)

Where V is the AC component of the electret output.

I then use this theory to come to a voltage I would expect for loud human voice - 110Pa from https://en.m.wikipedia.org/wiki/Sound_pressure

Using the equation for S2 above this gives:

S2 = 0.002mV/ubar = 2V/bar

Converting to Pa using ((bar/Pa)=10^5):

S2 = 2x10^5 V/Pa

So, loud voice, at 110 Pa, would give a voltage of 2.2 mega Volts. Definetely something wrong.

So, where is the error in my understanding ?

Notes of where I am going wrong in my thinking, with an explanation, would be appreciated.

Note on amplification

Im planning to build an amplification stage after first understanding the conversion from pressure to voltage. I'm expecting the output straight from the electret to be quite small, maybe in the range of micro Volts.

Answer 1

If the 0dB reference is 1V per 1 ubar, and the sensitivity is -54 dB compared to the reference, it means at 1 ubar you get -54 dB compared to 1V, or, you need +54 dB more microbars to get 1V. As 54 dB is a factor of about 500, you get 20mV at 1 ubar, or you need 500 ubar for 1V.

Now, 500 ubar is ear-deafening 128 dB SPL required for 1V and thus 54 dB less is of course 1 ubar which is 74 dB SPL required for 20mV.

Yes, electret capsules need amplification to be useful, approximately 40dB or a factor of 100 should be a good initial value, but it depends how large or small sound pressures you want to measure with a 3.3V ADC, a whisper across the room or a jackhammer right next to you.