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I am calibrating my microphone system consisting of a microphine whose signal is amplified and then converted from analog to digital with an ADC. The ADC converts the data to a 16-bit integer.

The calibration microphone produces 94 dBSPL at 1 kHz. I am sampling with 192 kHz, then plotting the FFT of that signal to find the given dBV at 1kHz.

First, converting the unit-free signal to V using:

calibration_94dB_1kHz = signal * (1 / 32768)

Then applying a window:

N = len(calibration_94dB_1kHz)
s = signal.windows.flattop(N) * calibration_94dB_1kHz

Then calculating the one-sided FFT with:

X = 2 * np.abs(np.fft.rfft(s))/N  # normalize the fft by the window-length and multiply by 2 since we are discarding the negative frequencies of the FFT
X_freq = np.fft.rfftfreq(N, 1.0 / 192000)

The data needs then to be plotted logarithmic so:

X_dbV = 20*np.log10(X)  # get fft in dBV

When plotting the data with:

axs[1, 0].clear()
axs[1, 0].semilogx(X_freq, X_dbV, color=colors[1], label='Frequency response |S(jw)| detrended and windowed')
axs[1, 0].grid(True)
axs[1, 0].legend(loc='upper left')

I get a peak at approximately 1 kHz that is -48.3 dBV. How can I convert this value to dBSPL if the mic has a sensitivity of -38 dBV +- 1, which is tested from the manufacturer with 1 kHz at 94 dBSPL?

enter image description here

EDIT: Here is the updated code:

calibration_94dB_1kHz_detrended = signal.detrend(data=calibration_94dB_1kHz, type='constant')
s = calibration_94dB_1kHz_detrended
Gain = 1 + 100 / 4.7
calibration_in_rms_Vpp = s / (2*np.sqrt(2))  # assuming p-p sinusoidal waveform
sensitivity = -38  # dBV

# Apply window
N = len(calibration_in_rms_Vpp)
s = signal.windows.flattop(N) * calibration_in_rms_Vpp
X = 2 * np.abs(np.fft.rfft(s))/N  # normalize the fft by the window-length and multiply by 2 since we are discarding the negative frequencies of the FFT
X_freq = np.fft.rfftfreq(N, 1.0 / 192000)
X_dbV = 20*np.log10(X)  # dBVrms
X_dbSPL = X_dbV - Gain - sensitivity + 94  # dBSPL
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  • \$\begingroup\$ This is already extensively discussed at dsp.se. And there are similar questions here. The manufacturer data sheet clearly says 94 dB(SPL) equals -38 dB(V), so there is an offset of 132. Now, for some reason, you assume 32768 is 1V, which may or may not be true. Just because an ST employee said so on a support forum (and was wrong on other points before that as well) it might not be true. \$\endgroup\$
    – Justme
    Nov 22, 2023 at 17:57
  • \$\begingroup\$ Lets assume 32768 actually equals 1V. Furthermore, i have calculated the gain of the opamp to be $1+\frac{R_f}{R_in}=1+100/4.7=21.27$. Yes, the sensitivity is -38 dBV. How can i then get the dBSPL? \$\endgroup\$
    – Tom
    Nov 27, 2023 at 16:18
  • \$\begingroup\$ It has been said many times now that mic data sheet says -38 dB(V) equals 94 dB(SPL), but I don't know why you are unable to make that connection. \$\endgroup\$
    – Justme
    Nov 27, 2023 at 16:22
  • \$\begingroup\$ I dont want to convert just -38 dBV to dBSPL. That is pointless at this point. I want to convert ALL values to dBSPL. After researching on this topic i have found, that i need to calculate with the gain, sensitivity and dBSPL like this: X_dbSPL = X_dbV - Gain - sensitivity + 94 # dBSPL. I have included the code above. \$\endgroup\$
    – Tom
    Nov 27, 2023 at 16:31
  • \$\begingroup\$ 1V is also, by definition, 0dBV. And then you know everything in both dBV and dB SPL, because you know the relation of 32768 to 1V, 1V to 0 dBV, and dBV to dB SPL. Sorry but I don't understand which part of the puzzle you think you are missing. \$\endgroup\$
    – Justme
    Nov 27, 2023 at 16:47

1 Answer 1

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I'm not sure what to make of "The calibration microphone produces 94 dBSPL at 1 kHz." The microphone is not being used as a projector, thus it will produce some sort of voltage output, not a sound pressure output as a projector would.

Sound-Pressure Level (SPL) in air, is normally given in \$dB \; re \; 20\; \mu Pa\$, also written as \$dB/\!\!/20\; \mu Pa\$ in some literature.

Microphone sensitivity is normally given in \$ dB \; re \; 1V/20 \mu Pa \$, also can be written as \$ dBV \; re \;20 \mu Pa\$. The sensitivity number will look something like -45 dBV re 20 µPa (note: the sensitivity number is normally a negative number).

The 94 dB thing you refer to relates SPL to \$ 1 \; Pa \$, i.e. \$ 93.98 = {20 log({1 \over 20e-6})} \$.
You do not need to include the number 94 in your calculations unless you're trying to redefine SPL relative to one Pascal.

When measuring SPL at a single frequency it is customary to use \$V_{rms}\$.

$$ (SPL\_in\_dB/\!\!/20 \mu Pa) = \\ {(Output\_Voltage\_in\_dBV) - (Amplifier\_Gain\_in\_dB) - (microphone\_sensitivity\_in\_dBV/\!\!/20 \mu Pa)} $$

When measuring the dB value in the FFT, verify the reported number by inputting a reference signal at a known amplitude (rms value) and see that the FFT reports the voltage you expect, i.e., just do a simple amplitude measurement.

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  • \$\begingroup\$ on dsp.se, it was apparent that there is a calibration sound source emitting 94dB at 1 kHz, and it was used incorrectly the last time I checked dsp.se so it is anyone's guess if the sound pressure ever was 94 dB at the microphone or not, and there is some weird belief that +/- 32767 equals +/- 1 volts but that info also came from ST forum person who was known to be wrong by saying the sampled values are in decibels, so not very trustworthy source. \$\endgroup\$
    – Justme
    Nov 27, 2023 at 21:26
  • \$\begingroup\$ I have successfully determined the gain of the opamp (13 dB) using an oscilloscope. Furthermore, if i compute the overall $V_{rms}$ of the calibration signal i get -45.81 dBVrms. Now, if i take the sensitivity, output rms voltage in dBV and the gain i get -38 dBV + (-45.81 dBVrms) - 13 dB = -94.5 dBSPL. Shouldnt dBSPL be a positive number? \$\endgroup\$
    – Tom
    Nov 30, 2023 at 13:22
  • \$\begingroup\$ @Tom Excuse me for giving you the wrong equation! I should have started from basics. I have corrected it in the post. Yes, the SPL should normally be a positive number. If not, then the SPL is below hearing threshold for the "average" human. What model microphone are you using? \$\endgroup\$
    – qrk
    Dec 1, 2023 at 1:28
  • \$\begingroup\$ The IMP23ABSU MEMS Microphone. If i use your new formula i get -45.81 dBVrms - 13 dB - (-38 dBV) = -20.81 dBSPL. This also seems not right. Should i add +94 dBSPL as offset? \$\endgroup\$
    – Tom
    Dec 1, 2023 at 8:29
  • \$\begingroup\$ @Tom The sensitivity in the data sheet is given as -38dBV with a 94 dBSPL applied which means the sensitivity is -38 dBV re 1 Pa. The sensitivity in customary units for audio mics is -132 dBv re 20 uPa. So, yes, add 94 dB to your result. \$\endgroup\$
    – qrk
    Dec 1, 2023 at 18:01

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