A Million Times

[Robert Wall]

Gene Lawson put a blurb on his website's newspage about the operation of a large condenser capsule. It was fun to imagine, and helpful to visualize, but flawed, I think, in its arithmetic.

He said,
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" Condenser microphones are the most accurate microphones in terms of frequency and transient response because they use extremely light-weight diaphragm materials which are moved easily by sound pressures. Diaphragm motion in the presence of normal sound pressures is microscopic. To give an idea of the scale of diaphragm motion in a condenser microphone, let's increase the dimensions of the capsule by 1 million times and assume a sound pressure level of 74 dB (conversational level). The diaphragm would then be almost ten feet thick. The diaphragm to backplate spacing would be 142 feet, and the capsule would be 22 miles in diameter. The diaphragm motion would only amount to 1 millimeter (4/100 of a inch)! You can see that the diaphragm motion is truly microscopic and that the condenser microphone is very efficient at converting these small diaphragm motions into electrical outputs. "
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OK.

Since Gene's diaphragms are 3 microns thick, and since that is 3/1000 of a millimeter, and since there are about 25 millimeters in an inch, multiplying the 3 microns by one million and converting to inches and feet, it comes out to about 10 feet. So far, so good.

Gene's LDC mikes use a 1" capsule. A million inches= 83333.33 feet and that's 15.78 miles rather than Gene's 22. Oops! But it's still a pretty big capsule !

This is where finishing the image gets real foggy. Unless we know the overall thickness of the capsule, the actual backplate spacing and the actual measured amount of diaphragm deflection in response to the stated sound pressure, we can't really know if his (x 1 million) diaphragm motion claim of 1mm is accurate.

And frankly, if it were MY microphone I was blowing up to 1 million times its real size, should I give you truly accurate numbers ? Wouldn't I be giving away the farm in re: distance from diaphragm to backplate and diaphragm tension, etc. ? Isn't that the secret stuff ?

I'd like to see this illustration complete and be able to verify the numbers myself. See -- if you go back to Gene's numbers and divide his 1mm diaphragm motion number by a million, it comes out to .001 micron. That's a millionth of a millimeter !

Is that as far as the sucker really MOVES ???

The only guy I know who could answer this is Stephen Paul, but if he told me he'd have to shoot me. (Just kidding.)

Anybody?

 

[Recording Engineer]

Sounds Like...

Sounds like... A job for Stephen Paul. You already called it! But I bet he'd actually tell you. Because if you understand it...

 

[Gidge]

https://homerecording.com/bbs/showthread.php?s=&threadid=50515&highlight=Paul

yep, we all know how eager SP is to share info.....

 

[Harvey Gerst]

Gene's "gotcha" line is this one:

"assume a sound pressure level of 74 dB (conversational level)."

All his listed figures are linear, except this one, which is logarithmic. Logarithmic numbers are very funny; they don't hafta be very much bigger to represent way more.

Going up to 77 dB will double the motion of the diaphragm, and going to 80 dB will move the diaphragm 4 times the original distance. Every 3 dB doubles the previous pressure.

Clever, but slightly misleading.

 

[darrin_h2000]

Funny but all of the logrithmic graghs I plotted at Devry doubled pressure every 6dB.

 

[Harvey Gerst]

Yup, you're right; it's 6 dB, not 3.

 

[crazydoc]

To answer the original question, my guess is that the diaphragm moves several meters in the model, or several microns in reality.

I didn't have anything better to do this evening, so I got out the old physics text and went thru some calculations. (A better use of time would have been to actually do some recording.) If you want to have the absolute shit bored out of you, read it. If you find any flaws (and I'm sure there are many) let me know.

Harking back to elementary electricity, we remember that capacitance=Area of the plates divided by distance between the plates times a constant, or C=8.85X10exp-12 A/d. Assuming that the distance between the plates is about 40 microns (if 3 microns =10 feet, then 140 feet = (3)140/10 =42 microns), and the area of the plates is about 3 square cm = 3X10exp-4 square meters, then the capacitance is (8.85X10exp-12)(3X10exp-4/(4X10exp-5) = 6.64X10exp-11 farads =66pF.

Remembering that capacitance also equals charge divided by potential difference (volts), or C=Q/V or Q=CV, and that the phantom voltage is 48V, the charge on the mic capsule is (6.6X10exp-11)(48) = 3X10exp-9 Coulombs.

If we change the distance between the plates (by sound pressure) by 1mm in the model, this is (10exp-3)(10exp-6) = 10exp-9 meters in reality. This will change the charge on the capsule by about 10exp-13 coulombs. Since current in amperes is coulombs per second, this gives a current of 10exp-13 amps in one second, times approximately 400 Hz, or 4X10exp-11 amps ac. This is .00004 microamps or .00000004 ma. Multiply this by 2500 to get it to the microamp range.

The question is, how much current does a condenser mic capsule actually put out? My absolutely uninformed guess would be in the microamp range, and if this is so, then the flexion of the diaphragm in the capsule in the million-times model would be in the order of 2500 times more than the millimeter, or 2 1/2 meters, or 2.5 microns in reality.

I guess the real question is how much current does the capsule put out? If we know this, and assume the separation of the diaphragm and the backplate is 40 microns, then by the above formulas we can calculate the flexion of the diaphragm. Of course, this is still a ballpark value as the whole diaphragm doesn't uniformly change its distance from the backplate - the center flexes and the edges remain fixed.

Does anyone know how much current a condenser capsule puts out?

 

[littledog]

yep, we all know how eager SP is to share info.....

Actually, that is the type of question Stephen LOVES to answer - if you post it in his room at recording.org you'll probably get about a 2000 word answer! You may have to wait a bit though until he has a few moments of free time (and his pain medication is working).

 

[Harvey Gerst]

And it's important to understand that before Stephen Paul came along (if we keep the million time analogy going), the wall thickness of these 16 mile across diaphragms was on the order of 20 to 40 feet thick. Stephen was the first to reduce the wall thickness reliably to 10 feet, and some of his newer diaphragms are equivalent to a wall 16 miles high by only one foot thick!!

Using the million times example, every large condenser mic diaphragm being made today is still in the 10 to 20 foot thickness, although I believe AT has one model which would be around 6 and 1/2 feet thick, but I think that's on a smaller diameter mic. That's as thin as anyone has been able to achieve, except for Stephen's mods, which are in the 1 to 3 foot thick range.

 

[crazydoc]

What is the advantage to decreased diaphragm thickness, besides increased sensitivity? It seems there would be a point at which it would be so thin and flexible that standing waves would form causing resonance and increase distortion. I suppose you could stretch it tighter if the ever thinner material could bear the increasing tension.

Why are so many capsules about an inch in diameter? Is this a magic size for some reason? Why not make it larger and increase the sensitivity this way, essentially doing the same thing by increasing the diameter to thickness ratio?

 

[Harvey Gerst]

You'd have some really bad off-axis response, and there would be more difficulty in keeping the tensioning even.

This is really one for Stephen Paul to answer, since there would be some other problems as well.

Largest capsule I know of is the Russian LOMO at around 1-1/3" (33mm).

 

[Robert Wall]

I don't wanna pester Stephen with something that will prompt him to give time and effort to answering something that I can't make any use of -- he is just too pressed for both time and energy to handle my odd curiosity.

But it looks like I'm not the only one who is curious!!

Maybe this gives us a lil' peek at the kind of burning curiosity that lights a fire in a mind like Stephen's. He just had to know the answer -- and he dug and he dug 'til he found it.

Then he fixed it.