# Calibration with Two Mics?



## RandomLamer (Oct 15, 2012)

Hi everybody! I'm just now getting into the exciting world of room correction and acoustics. I ordered a Behringer ECM 8000 mic but I didn't realize it had to be individually calibrated for best results. That got me thinking how I could calibrate it myself. Do you think this technique could work? (There could be glaring errors in my thinking)

So we have two mics, both uncalibrated and possessing identical directional response (like both totally omni, or just two specimens of the same model), one soundcard with mic input, and one set of amplifier + speakers. And a room to do measurements in, which has to be quiet enough.

We want to measure the frequency response of the two mics. Assuming everything is sufficiently linear, if we play and record noise, we get (for some frequency and mic position):

E + R + M = L, where

E = soundcard output stage + amplifier + soundcard input stage response (in dB),
R = speaker + room (+ mic directional) response,
M = mic response,
L = response of this loop as measured from the recording.

How do we get microphone responses out of this? Well, we take the two mics M1 and M2 and place them in different positions in the room, and record noise. These positions have responses R1, R2... Rn (speaker is included in R to take radiation patterns into account). Let's say we use 4 positions and get:

E + R1 + M1 = L11, E + R1 + M2 = L12, E + R2 + M1 = L21, E + R2 + M2 = L22... and so on up to R4.

We end up with a system of linear equations. We have 8 equations (2 mics times 4 positions) and 7 unknowns (E, M1, M2, R1, R2, R3, R4). Now we just need to solve this system for each frequency, and to reduce noise we probably would have to introduce some constraints (like the frequency response of a mic should be smooth). And/or use more positions to overconstrain the system.

Is this possible in any way, or did I miss something crucial?! :gulp:


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## RandomLamer (Oct 15, 2012)

Heh, I must be missing some crucial bit of information about linear equations. I mean, this can't work, can it? It would be like magic, having two mics with no reference, and poof, they calibrate themselves. :blink:

I think I need to pick up a math book... or two... 

EDIT: Okay, reading the Wiki page on linear systems, I see that the individual equations would not be independent, and thus all that would be measured at the end would be random noise from imperfect microphone placements . LOL.


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## AudiocRaver (Jun 6, 2012)

Always fun to forge new trails, isn't it, and it never hurts to try... The best you would get is a relative curve, or noise, as you concluded. Nice try, though.

How about: order a dozen identical cheap mics, one with a publoshed "typical" curve, test to find the most average among them, and it's pretty safe that one matches the curve. Then return the rest for refund. A lot of work and not very ethical, but cheap. OTOH, my Beyerdynamic MM1 was only $200 (4years ago). Or pay someone $30 to run an unofficial curve on a Behringer mic for you. Of course you know that already; enjoyed your fun math exercise.

"Keep thinking, Butch, that's what you do best" (Sundance Kid to Butch Cassidy).


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## hjones4841 (Jan 21, 2009)

I got a headache reading thru all that math. Way too early in the morning for all that.


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## lcaillo (May 2, 2006)

RandomLamer said:


> Hi everybody! I'm just now getting into the exciting world of room correction and acoustics. I ordered a Behringer ECM 8000 mic but I didn't realize it had to be individually calibrated for best results. That got me thinking how I could calibrate it myself. Do you think this technique could work? (There could be glaring errors in my thinking)
> 
> So we have two mics, both uncalibrated and possessing identical directional response (like both totally omni, or just two specimens of the same model), one soundcard with mic input, and one set of amplifier + speakers. And a room to do measurements in, which has to be quiet enough.
> 
> ...


The problem is that the responses are dependent on each other and not independent. The relationships between the room response, mike, and system has infinite possible solutions that are not accounted for.


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