Hello everyone,

I am currently involved in a project where I'm using two distinct types of microphones connected to an Audio Precision system, comprising an APx525 audio analyzer and an APx1701 transducer. The microphones in question are a digital MEMS model (SPH0641LU4H-1) and an analog model (GRAS_46BF-1). I aim to calibrate the digital MEMS microphone utilizing the analog microphone as a reference standard.

Both microphones have recorded background noise simultaneously within an acoustic box, and the output has been saved as WAV files. The measured signals appear to fluctuate around zero, which suggests that these are digital amplitude readings in millivolts. I'm looking for insights into how to proceed with the calibration accurately, based on a 30-minute recording of background noise captured by both devices.

**Calibration Issues and Queries:**

1. Using the MEMS Microphone's Data Sheet Response Curve: 

- Should the average amplitudes (in dB SPL) be computed over the 30-minute period?

- Should data be normalized at 1 kHz to a baseline of 0 dB for comparison with the digitized response curve from the MEMS microphone's data sheet? 

- The recorded signal for the MEMS microphone shows a local maximum around 25 kHz and after a local minimum at about 32 kHz, there is a linear increase in amplitude with frequency. What might explain this phenomenon?

2. Conversion Steps for Analog GRAS_46BF to dB SPL: 

- Calculate the absolute voltage value

- Compute the sound pressure level in Pascals (Pa) using the formula: 

p = |V| / S, with S (sensitivity) being 3.6 mV/Pa. - Convert to dB SPL using the equation: dB SPL = 20 x log10(p / pref), where pref is 20 x 10^-6 Pa

3. Conversion Steps for Digital SPH0641LU4H-1 Microphone to dB SPL: 

- Convert to dB Full Scale (FS) using: 20 x log10(p / pmax).

- Then, convert to dB SPL: dB SPL = 94 dB SPL + (value in dB FS + 26 dBFS), where 26 dBFS represents the sensitivity measured at 94 dB SPL at 1 kHz

**Procedure:**

2. Normalize using: Value_norm = 1 / sqrt(number of values per window) x current value. 

3. Follow the conversion steps detailed above. 

4. Calculate the calibration vector: c = MEMS mic dB SPL - Ref mic dB SPL. 

**Questions to the Community:**

- Does it matter if the "Conversion Steps" are applied to the signal in the time domain or the frequency domain?

- If it doesn't matter, what should be used for the \( p_{max} \) value during conversion from voltage to dB FS for the analog microphone?

- Am I correct in assuming that to calculate dB SPL for the analog microphone, one should convert the input voltage value to an RMS value, whereas for the digital microphone, use a peak-to-peak value?

- If the conversion steps can only be correctly applied in the time domain, how should I calculate the RMS value for the analog microphone if its signal resembles noise rather than a clear sinusoidal waveform?

**Further Considerations:**

- How should I account for the amplitude discrepancies across different frequencies when analyzing future MEMS microphone signals?

- What are the potential causes of the MEMS microphone's readings showing an increase in amplitude post-32 kHz?

I appreciate any guidance or suggestions from those with experience in audio system calibration and signal analysis.

Thank you for taking the time to read and respond to my queries.

Best regards,

Karoline

Two questions:

1.)  If you have an existing GRAS microphone, do you have a respective calibration device like the B&K Type 4231 Handheld calibrator?

2.)  The frequency response in the specification sheet for the MEMs microphone you've noted only goes up to 10 kHz (relatively flat response up to 10 kHz for the GRAS microphone too).  What is your desired upper frequency limit?

Thank's a lot for your answer. 

1.) We certainly don't have a handheld calibrator or anything like that. However, the GRAS microphone is calibrated.

2.)We would like to obtain the ultrasonic response curve and measure frequencies up to 90 kHz.

Any progress?

A quick look and MEMs microphones seem to not support frequencies beyond 10 kHz.

MEMS microphones are PDM encoded, in the case of the one you are using they appear to be noise shaping the coding to put the quantization noise at 25kHz. In nominal audio applications this would be fine as you're typically not interested in frequencies above 20 kHz but in the Ultrasonic case it is the reverse, so they still leave the quantization noise at 25kHz but the microphone is relatively flat from 38 - 68 kHz. With a 3.072 MHz source clock you're down to about 4.5 bits of effective resolution at 80 kHz. So you're not going to get a lot of detail.