# Gas station without pumps

## 2013 July 31

### Microphone sensitivity exercise

Filed under: Circuits course — gasstationwithoutpumps @ 13:46
Tags: , , , ,

I’ve been thinking a bit about improving the microphone lab for the Applied Circuits course.  Last year, I had the students measure DC current vs. voltage for an electret microphone and then look at the microphone outputs on the oscilloscope (see Mic modeling lab rethought).  I still want to do those parts, but I’d like to add some more reading of the datasheet, so that students have a better understanding of how they will compute gain later in the quarter.

The idea for the change in this lab occurred to me after discussing the loudness detector that my son wanted for his summer engineering project.  He needed to determine what gain to use to connect a silicon MEMS microphone (SPQ2410HR5H-PD) to an analog input pin of a KL25 chip.  He wanted to use the full 16-bit range of the A-to-D, without much clipping at the highest sound levels. Each bit provides an extra 6.021dB of range, so the 16-bit ADC should have a 96.3dB dynamic range.  The sound levels he is interested in are about 24dB to 120dB, so the gain needs to be set so that a 120dB sound pressure level corresponds to a full-scale signal.

He is running a 3.3v board, so his full-scale is 3.3v peak-to-peak, or 1.17v RMS (for a sine wave).  That conversion relies on understanding the difference between RMS voltage and amplitude of a sine wave, and between amplitude and peak-to-peak voltage. The full-scale voltage is 20 log10(1.17), or about 1.3dB(V).

Microphone sensitivity is usually specified in dB (V/Pa), which is 20 log10 (RMS voltage) with a 1 pascal RMS pressure wave (usually at 1kHz).  The microphone he plans to use is specified at –42±3dB (V/Pa), which is fairly typical of both silicon MEMS and electret microphones.The conversion between sound pressure levels and pascals is fairly simple: at 1kHz a 1Pa RMS pressure wave is a sound pressure level of about 94dB.

Scaling amplitude is equivalent to adding in the logarithmic scale of decibels, so for a sound pressure level of 120dB, the microphone output would be about 120–94–42±3=–16±3dB(V), but we want 1.3dB, so we need a gain of about 17.3dB, which would be about 7.4×. Using 10× (20dB gain) would limit his top sound pressure level to 117dB, and using 5× would allow him to go to 123dB.

One can do similar analysis to figure out how big a signal to expect at ordinary conversational sound pressure levels (around 60dB):  60–94–42=–76db(V).  That corresponds to about a 160µV RMS or 450µV peak-to-peak signal.

I tried checking this with my electret mic, which is spec’ed at –44±2dB, so I should expect 60–94–44±2=–78±2dB, or 125µV RMS and 350µV peak-to-peak. Note that the spec sheet measures the sensitivity with a 2.2kΩ load and 3v power supply, but we can increase the sensitivity by increasing the load resistance.  I’m seeing about a 1mV signal on my scope, so (given that I’m not measuring the loudness of my voice), that seems about right.

I’ll have to have students read about sound pressure level, loudness, and decibels for them to be able to understand how to read the spec sheet, so these calculations should be put between the microphone lab and the first amplifier lab.  I’ll have them measure peak-to-peak amplitude for speech, and we’ll compare it (after the lab) with the spec sheet.  This could be introduced as part of a bigger lesson on reading spec sheets—particularly how reading and understanding specs can save a lot of empirical testing.