# From pressure to SPL : microphone calibration using sound level meter calibrator and sound level meter

I have a microphone + signal conditioner with adjustable gain and filter. I capture amplified signals using an oscilloscope. I'm using this signal to compute equivalent continuous sound level

With the signal conditioner, I set the needed gain and the A-weighted filter.

From oscilloscope signal $$V$$ I can get pressure $$p = \frac{V}{g \cdot s_{mic}}$$ where $$g$$ denotes the gain and $$s_{mic}$$ the microphone sensitivity.

We can suppose the A-weighted filter filters out frequency out of the audio range. So I can easily compute $$L_{eq} = 20 \log_{10} \left( \frac{ \tilde{p}_{a}}{p_{ref}} \right)$$, where $$\tilde{p}_{a}$$ is the time domain A-weighted pressure and $$p_{ref}$$ is the reference pressure $$= 20 \cdot 10^{-6} ~ Pa$$.

I used a sound level calibrator to check if it works. I get an $$L_{eq}$$ of $$\sim 94 ~ dB$$ and $$\sim 114 ~ dB$$ when applying $$94 ~ dB$$ and $$114 ~ dB$$ level with calibrator.

I also have a sound level meter. I also checked it with the sound level calibrator.

Now, in my room (some noise because of the oscilloscope...) with A filter it measures $$\sim 46 ~ dB_{A}$$. Now I put my microphone close to it, and with the microphone, I get an $$L_{eq}$$ of $$55 ~ dB$$. When changing the sound level meter filter from A to C results are better: the sound level meter measures $$\sim 56 ~ dB$$. I changed the microphone acquisition duration but $$L_{eq}$$ results are the same.

• How can we explain such $$L_{eq}$$ difference when the sound level meter and microphone measure $$dB_{A}$$?
• How can I calibrate my microphone with the sound level meter?
• is 55dB the noise floor of your system perhaps? Jul 2, 2019 at 10:45
• Can you tell us what kind of sound level calibrator you use? Or please explain in detail how the geometrical set-up changes when using the mic and the sound level meter. Aug 1, 2019 at 12:40

## 2 Answers

### Difference between A and C filters

Assuming all other parameters are equal (which is not necessarily a safe assumption as you don't provide much information on your setup), the fact that your measurements correspond better to each other with a C weighting filter compared to A, then I would come to believe that the noise you are measuring has frequencies well in the range of attenuation of the A filter.

If this is not the case then maybe the two filters are not equal. It is well known that the bilinear transformation used to convert the analogue A filter to a digital one is not perfect and can introduce some discrepancies. To be honest, I don't believe this would result in such huge differences if you are using MATLAB (which I assume you do from the links you provided) but I can't be sure about that either.

Furthermore, there may be some other issue with your implementation (bad code, bugs, forgotten variables or (un)commented code or a whole bunch of other problems). I would try to measure without any filters to make sure the two systems measure the same thing. You may have a faulty microphone (or Sound Level Meter [SLM]) whose frequency response is bad and attenuates, or exaggerates certain frequencies that happen to be included in your noise source (still the difference is quite large to justify such differences).

I would assume a worst-case scenario where all of the above are true and try to go one step at a time. If for example, you make sure that your linear (Z) measurements are within some reasonable tolerances you could narrow the problem down to the filter.

### Calibration

Using a calibrator is the "best" way to calibrate your system. You'll notice that calibrators most often than not, use a $$1 ~ kHz$$ tone which is left unchanged by all weighting filters (it is considered the reference in Fletcher-Munson curves for the definition of phon too). Thus, you can calibrate your system even if you have already applied a weighting filter.

To take it one step further, you could acquire the transfer function (frequency response) of both microphones and use them to "cancel" their effect on the measurements (deconvolve their response to get "flat" measurements). Caution is to be advised here as the frequency response of the microphone may correspond to its "on-axis" response, quite rarely to its power response (kind of an average over all the steradian angles) or its diffuse field response (most often equalised for a flat frequency response in a diffuse field at an angle of $$\sim 70^{0}$$ from the main axis). The idea is that measurement microphones are most often omnidirectional (they are designed like that and their polar pattern is not a product of summation of the signals from multiple capsules like in the case of various microphones used in studios) and thus it is assumed that their frequency response remains constant (to an adequate level) over all steradian angles.

In any general case though, where you do not have a transfer function to use, the use of a calibrator is all you can do to bring systems to "equal measures".

First, I would check the positioning of sound level meter and microphone. If you are putting them close to the oscilloscope a few centimeters of displacement may change the measured value dramatically. (6dB/doubling of distance)

Second, which microphone do you use? The link you provided leads to a preamplifier. The actual capsule can either be a free field or a pressure field one. A free field capsule should be facing the sound source directly, while a pressure field capsule should face it sideways.