How is microphone's frequency response determined

It seems this is the chicken and egg problem. To be able to determine the frequency response of a microphone one needs a speaker that has a known response. To be able to know the response of a speaker one needs a mic with a flat response.

Is there some trick used or some device(essentially a microphone) that is "provably" to have a known frequency response?

I know there are reference microphones that supposedly have a flat frequency response BUT the question is, how did they get to that point in the first place.

• This problem is not isolated to microphones. EVERY SINGLE meter in the world has to be calibrated to some standards. How did the come about? How did we end up with a 0.0001% resistance standard, for instance? It's all inter-dependent. The official unit definitions came about only after we created more and more accurate instruments. – Jonny B Good Jan 1 '13 at 20:24
• I think the best you can do is have a look at chapter 12 part XXIX "Reciprocity Calibration of Transducers" of "Acoustics" from Leo L. Beranek (page 377). There you can find a fair explanation for self-reciprocity and auxiliary-transducer methods for free field calibration. – Pep Aug 2 '18 at 13:05

Reciprocity calibration is the technique used to calibrate a microphone without the need for any calibrated sources. It relies on the basic physics of transducers that show that the ratio of the receiving response to transmitting response of most transducers (designated as reciprocal transducers) is independent of their construction and depends only on easily measured parameters such as frequency, air density and sound speed. General Radio used to make a reciprocity calibrator that included all of the necessary equipment including a cavity to hold the microphone under calibration. The process requires a reciprocal microphone. A series of electrical measurements are made while using the reciprocal microphone as both a transmitter and receiver. These measurements are combined to yield the sensitivity of the microphone under test. By varying the test frequency, a complete frequency response can be obtained. Once that is done, the test microphone is calibrated and can be used to calibrate other hydrophones by using comparison measurements. Details of reciprocity calibration can be found in any acoustic textbook as well as Wikipedia and other on-line sources. Accuracy of reciprocity calibrations is very high because all of the required measurements are electrical and, with the proper procedures, only ratios of measurements are required so a calibrated meter is not even needed (but it must be linear).

• Thanks. It looks like what I was looking for. Strange that a mic will be used as a speaker as I would imagine this would not be very good for the mic but I guess one can used specialized mic's to create a base reference mic. – Archival Jan 1 '13 at 15:44

One way is to use an event with a mathematically predictable frequency response. A spark of known short duration (i.e. much shorter than the shortest time of interest - 1 to 5 us for audio) in an acoustic free field, would do.

The support structure for microphone and spark gap, and the "free field" get in the way of perfection, but you do the best you can. If you can reproduce the results sufficiently closely in an anechoic chamber, you use that in future...

It's still so expensive to do this properly, that having calibrated one microphone this way, you compare others to it - so everyone else finds it cheaper to use reference microphones (even at Bruel & Kjaer prices) instead...

• Do you have any reference material where this method is explained or presented ? – Blup1980 Jan 1 '13 at 10:59
• my JAES journals are difficult to get at right now, but I would start with their archives (Journal of the Audio Engineering Society) – Brian Drummond Jan 1 '13 at 11:01
• I assume you are talking about using an impulse, which is more controllable than a frequency sweep? e.g., under control systems in en.wikipedia.org/wiki/Impulse_response. – Archival Jan 1 '13 at 11:17
• Yes - this is impulse testing. Once you have closed the loop of reference mic and reference speaker, you are in a position to use sweeps and simplify future tests. But the question is where you start. – Brian Drummond Jan 1 '13 at 11:39

The method that I have used in the past is to use a reference microphone with a known frequency response, and also a calibrated sound source, e.g. 96dB SPL at 1 kHz.

First you calibrate the reference microphone, analogue electronics, environment, etc, using the calibrated sound source, then you can take absolute dB SPL measurements at any frequency using this one calibration datum and the frequency response curves for the reference microphone.

Note that this method assumes you want to measure absolute sensitivity across frequency, i.e. what voltage you get for a given SPL at a given frequency. If you just want the overall shape of the frequency response, i.e. relative to some arbitrary point (e.g. output level relative to output at 1 kHz) then you don't need the calibrated sound source - you can just use a reference microphone.

• Once one has a reference, it is a piece of cake. The question is, how do we get such a microphone? essentially how was the first reference microphone created. For example, suppose I have some random mic and no reference microphone, how can I accurately get it's frequency response besides getting a reference microphone. (also, a reference microphone will be distorted by all the electronics after it making the problem more complex) – Archival Jan 1 '13 at 11:23