# DIY reciprocity microphone calibration



## Chester (Feb 19, 2007)

So, I have been looking into trying to calibrate my own microphone: I THINK I can do it using what is called the "reciprocity method", I am posting here to get some feedback about my thinking.

As I understand it, the reciprocity method is based on the idea that a microphone can act as a speaker, and a speaker can act as a microphone. The transfer function of a speaker coupled to a microphone is the same as the transfer function of the microphone if it were to act as a speaker and vice versa.

My plan is to utilize three radioshack microphone capsules (a,b,c) and measure the various combinations of the systems transfer functions (a+b, a+c, b+c). Given the responses of those systems, one can solve for the response of each individual capsule. I will then have three calibrated capsules, to which I can calibrate my primary calibration microphone (DBX RTA-M).

The radioshack capsules are 1/4" diameter, and should fit into a standard straw to create a pressure chamber, they supposedly go to 15khz, however I do not see why they would not achieve a higher frequency response being 1/4" diameter... If this does work out, I will probably order some higher quality parts (capsules that can go to 40khz, and design a higher quality pressure chamber. I will have the mic capsules spaced very close together to 1) keep the noise floor down (the larger the volume to pressurize the lower the level that will be measured on the receiving microphone and 2) push any resonances of the straw system above 20 khz... I am probably going to have the capsules 1-2 mm apart, the wavelength of 20khz is ~17mm, so 40 khz is ~8.5mm, then divide by 4 is 2.125 mm: anything less than 2mm and the system should be in 'pressure mode'...

If it doesn't work, I will be out ~$10 

REW allows us to perform all of the functions needed to solve for the response of a given variable!

How to 'solve' for the desired transfer function:
http://www.wolframalpha.com/input/?i=a+b=x,+a+c=y,+b+c=z,+solve+for+a

I will post more details as the project progresses!


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## Barleywater (Dec 11, 2011)

It is simple on the surface, but gets very involved quite rapidly.

Have you read up on how NIS does this?

I would try as first experiments using DBX RTA-M microphone as reference and attempt calibrating the Radio Shack capsules by substitution method. Here as simplification assume the DBX microphone is flat. Set up hard dome tweeter with microphone at <1/4" and measure full range. This is test jig response. With REW you can then do what is usually regularly occurring noobie mistake, and use this measurement as a calibration. If you do this, and don't disturb the microphone on the test jig, you can remeasure the DBX microphone, and REW will show a near perfectly flat response. Now to see what you are up against, move the microphone about 1mm and make another measurement. Result is close, but it demonstrates sensitivity of jig. Now if you have another measurement microphone, substitute it into the test jig, make sure its placed exactly as the DBX microphone, and make measurement. Results will reflect difference in response of two microphones. If microphones are of different body type, diffuser cap design etc., results will reflect this.



Even attempting to drive electret capsule as transmitter, and switching it back to being a receiver requires modifications.


The electret microphone capsule is typically connected directly to jfet as capsule amplifier which is why small DC appears at microphone input jack of microphone input on consumer grade soundcard. For pro gear with 48V phantom power this for capsule preamp, but also used for polarization of some types of non electret condenser capsules. 

It is not simple to define flat response from primary physical standards and mathematics combined with real transducer behavior.

Regards,

Andrew


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## Chester (Feb 19, 2007)

I tried looking into what NIST does, I saw some info on their procedures as far as how they isolate the environment and setup the coupling. As far as finding any applicable equations, especially something I could 'plug and chug' measurements into I did not find.

The substitution method is VERY touchy as you pointed out and requires a calibrated microphone, which I don't have on hand, which is why I am going to give reciprocity a shot. Once I get the response of one of the radio shack capsules, I can then use that to calibrate the DBX RTA-M. Considering I am using just the capsules which when inserted into the contraption (tube) I make up will only have rotational variability: they will only go in to a set point which will be highly repeatable.

The RTA-M is my primary microphone, this is just a project/experiment, to try and calibrate the frequency response myself, I realize what I describe does not find actual SPL, but hopefully will yield a calibration file that will make my DBX mic 'flat'.

You mentioned driving the capsule as a transmitter - I planned to hook it up to a headphone amp, while at the same time maintaining the bias voltage; do you foresee problems in doing this? I gather from your post that you have a good understanding of what is going on here; and while I understand the theory of the acoustics side, the electronics side is not quite as clear to me, especially considering I am doing something less than 'normal' here 

Thank you for your feedback and help!

Take care,
-Matt


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## lcaillo (May 2, 2006)

So when you extract your response, to what will it be referenced other than the set of microphones that you are using? You also seem to be making some assumptions about the behavior of the mic as a speaker. Without knowing the response of something in the system all you are getting is difference information.


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## Chester (Feb 19, 2007)

So when you extract your response, to what will it be referenced other than the set of microphones that you are using? - yes, I am only trying to find relative frequency response of each capsule, so I can make them 'flat'.

The assumptions about a mic acting as a speaker are one thing that definitely concern me, especially with these being condenser (capacitave) mics I have a feeling that 1mV out of the capsule @ a given frequency may not produce the same spl at the transducer surface as 1mV into the capsule @ the same given frequency.

The parts here cost $15 and some odd cents yesterday, so if it doesn't work out no biggie, it a learning experience 

It is my understanding that with the difference information, you can find the response of everything in the system (when there are three variables to solve for) - IF the mic capsules are reciprocal in nature and there aren't *large* non-linearities (lets face it, in the real world everything is non-linear in on way or another) which mess up things being reciprocal I think it will work...

If it doesn't work in this setup, I may try something with earbud headphone transducers (effectively 'dynamic microphones' with a magnet-wire coil-transducer 'film' apparatus) and see what I can do  ...


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## Barleywater (Dec 11, 2011)

The embedded static voltage on electret membrane stays put because the membrane is an insulator. Driving this may prove quite difficult.

For your de novo calibration laboratory a bit of external referencing is good idea. This is why I suggest starting with DBX microphone. If you don't have a calibration file for it, assume it's flat, which if anything similar to ECM8000, it is through a good part of range. Otherwise, send it out for calibration, or mount up Radio Shack capsules and send them out for calibration, or buy a microphone with calibration. With the last option you can do lots with substitution method.

Yes, I've studied this.

Earthworks OM-1 microphone is very flat, even without calibration file.

Here is result of using earbud element and Earthworks OM-1 microphone in tiny sealed coupler:









This gives some information about the microphone's performance, and it gives us some information about the earbud's performance, and it gives us some information about the performances of the various amplifiers in the signal path, as well some information about behavior of small sealed coupler.


So what useful information can we get out of this experiment? 

In the low frequency range the earbud may be considered as completely controlled by amplifier, and resonating cavity of closed coupler. The physics and mathematics dominate.

Here is a great application note from ARTA software folks: ARTA-Measuring Box

Based on the ARTA information, it may be suggested that the low frequency performance of the OM-1 is very good. Correcting for the soundcard improves this a bit more. Using a slightly bigger coupler and an open back driver would yield a smoother result. Reality of non laboratory measurement microphone is that omni capsule is not sealed, it has tiny vent to accommodate changes in ambient air pressure and internal/external temperature changes. Then there are coupling capacitors in OM-1 amplifier, since it is a little more sophisticated than just being a jfet.

Oodles of variables...lots of fun.

Andrew


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