# Science and Math for Audio Humans – Putting It Together: Microphones

by Danny Maland

This disclaimer continues its epic, multi-month run:

Everything that I set before you should be read with the idea that “this is how I've come to understand it.” If somebody catches something that's flat-out wrong, or if you just think that an idea is debatable, please take the time to start a discussion via the comments.

Now that I've talked your ears off with all of these conceptual bits, let's see how some of them integrate when we deal with a couple of microphones. Microphone one will be a dynamic moving-coil type, and microphone two will be a condenser.

Microphone one works by way of electromagnetic induction. It has a diaphragm that's connected to a wire coil. The wire coil is suspended in a magnetic field. When the diaphragm moves, the coil also moves through the magnetic field. This generates an electrical current which is analogous to the sonic event at the diaphragm.

Microphone two uses the principles of capacitance to operate. It also uses a diaphragm, but the diaphragm does not have a coil attached. Instead, the diaphragm is some distance away from a non-moving backplate. The whole assembly has a bias voltage applied so that the diaphragm and backplate become charged plates with an insulator between them – the insulator being air. At rest, the assemblage has a certain capacitance, or ability to hold a charge. When exposed to sound pressure waves, the diaphragm moves in relationship to the backplate, and the system capacitance changes as a result. If the diaphragm moves toward the backplate the capacitance drops, which means that the system must release charge. The reverse is true if the diaphragm moves away from the backplate. This release and taking up of charge naturally results in current flow which is analogous to the sonic event at the diaphragm.

Figure 1 shows some simplified cutaways of these microphone designs.

• Our microphones are set up side by side in an anechoic chamber so that acoustical reflections can be effectively ignored. Each microphone's element is precisely 2 meters from a sound source. The sound source is producing a 1 kHz tone at 100 dB SPL, unweighted, averaged over 1 second, measured at 1 meter from the source.
• Question: What is the SPL at the microphone elements?
• Since our chamber is anechoic, we don't have to account for reflected sound. That being the case, we can simply assume that the basic inverse square law is in effect. If the distance to the source is doubled, the observed intensity should only be one quarter of that experienced at the closer distance. One quarter intensity is 6 dB down from the original intensity – we use the “10 log” formula because we are concerned with power (intensity being power divided by area).

So, the SPL at the microphones is 94 dB SPL, unweighted, averaged over 1 second. (I wanted this number specifically. The reason is that microphone sensitivity is most often expressed in terms of a decibel output relative to 94 dB SPL at 1 kHz.)

Microphone one has a sensitivity of -55 dBV at 1 Pascal/ 94 dB SPL. Microphone two has a sensitivity of -50 dBV at 1 PA/ 94 dB SPL.

Question: What might account for the higher sensitivity of microphone two?

Remember that microphone two is a condenser microphone. The mass of its moving part, which is just a diaphragm, can be much smaller than the mass of the dynamic mic's moving part, which is a diaphragm and a wire coil. For the same amount of force on each mic's diaphragm, the diaphragm of mic two will have substantially greater acceleration. What may be surprising is that the sensitivity of microphone two is not enormously greater than that of mic one.

I don't have a definitive explanation for this, but I can say that – as I have come to understand it – you have to be holistic about the sensitivity issue. Yes, the diaphragm of the condenser moves much more readily for a given sound pressure event, but that's not all there is to consider. For instance, condenser mics require impedance changing amplifiers to be integrated into their design for them to work well with downstream equipment. It's possible that this extra circuitry could be “dialed up” such that a condenser mic would have a very large output relative to other mics, but this could cause some problems. For instance, applying appropriate preamp gain to the mic would be wildly different from what would be required for other mics. There might be significant noise issues as well.

Question: What is the voltage output of each mic in this situation?

Since the sensitivity measurements given to us are in dBV, we know that the reference point involved is 1 volt. We're working in volts and not power, so the multiplier we'll need to use is 20, instead of 10. For microphone one, then:

Thus, the voltage output of microphone one is 0.001778 volts. Using the same method, we can find that the output of mic two is 0.003162 volts.

This illustrates an adage that was handed down to me when I was in school: “The mic pre is the highest gain stage in the chain.” Whether or not you're into all the nuances of different microphone preamps, the fact remains that the 50+ dB they have to add to a signal to get it up to “nominal” level in a professional system is a lot of work to do. That work has to be done cleanly and accurately (or somewhat inaccurately in a pleasing sort of way). Even large power amplifiers don't have to apply with that kind of voltage gain.