Topic: Ok, trying some crazy acoustic math, could use some sound engineering help

[landshark]

Hi all -

This one's for all you hard-core sound engineers.  I had a problem with my AKG 391's overloading the op amp on my MR-1.  So, what I'm trying to do is to figure out how much attenuation I need to get everything within spec for the MR-1. 

MR-1:

Nominal Level: -6 dBV LINE, -39 dBV MIC
Maximum Level: +6 dBV LINE, -27 dBV MIC

Wow, I didn't realize the mic pre-amp was so sensitive, no wonder I clipped the puppy.

Ok, now the math:

AKG 391 specs here: http://www.akg.com/mediendatenbank2/psfile/datei/32/Blue_Line4055c224ac90f.pdf
AKG 391's have Sensitivity of 10mV/Pa (or -40 dBV) with a max SPL of 132 dB

How do I get from the sensitivity of the mics to the max output of the mics in dBV, and from there, how do I calculate the needed dB of attenuation to make sure I won't clip the op amp even at 132 dB?

I am guessing this is some crazy logarithmic math, so even if you can just link me to a website that explains the process, I'll churn my brain into mush trying to figure it out.  Much appreciated!!!

Mike

edit:

Ok, just found a site, tell me if I'm getting this right. 

http://www.sengpielaudio.com/calculator-volt.htm

1 Pa = 94 db SPL.  So at 94 dB, the 391 should put out 10 mv.  At +20 dB or 104 dB = 100 mv and at +40 db or 124 dB = 1,000 mv or 1 volt.  1 volt ~ 2.2 dBV

Wait a minute, this seems crazy - according to that calculator, RMS voltage of .0446 v (45 mv ) is about -27 dBV, so that represents my maximum (http://www.sengpielaudio.com/calculator-db-volt.htm) or should I be using peak?  So I need to get down to below the equivalent power of 104 db, which for a 132 dB (ears bleeding) signal is about -30 dB of attenuation?  Wow.

As you can tell I have zero training in engineering, hope I'm not making myself look too stoopid...<grin>

[Todd R]

I used to know of a good website for decibels explained, but I couldn't find it.  Here are a couple to check out though:

http://www.jimprice.com/prosound/db.htm

http://www.soundonsound.com/sos/1994_articles/feb94/decibels.html

Basically, the decibel scale is used to represent the logarithmic ratio between 2 values.  For voltages the dB value = 20 * log (V1/Vref).

For a dBu, Vref = 775 millivolts, or 0.775V.  For a dBV, Vref = 1V

So the MR-1 can take a maximum of -27 dBV on the mic input.  Thus you have -27 dBV = 20 * (V1/1volt), and you need to solve for V1.  In this case, V1 = 0.045volts, or 45 millivolts.  (Um, aside:  man that's crappy!!)

Moving to the mics, the 391's have a sensitivity of 10mV/Pa.  A Pascal is a measurement of sound pressure equal to 94dB (these are sound pressure decibels, not voltage-level decibels).  So it will depend what you're recording.  A loud/typical amplified rock show can have SPLs easily around 112dB, maybe say 118dB to be sure.

The voltage your mic will produce will double with each increase of 6dB (by definition, basically).  By the specs, the 391's produce an output of 10mV in a sound environment of 94dB.  At 100dB, they produce 20mV (2* 10mV), at 106dB they produce 40mV (2* 20mV), at 112dB they produce 80mV, and at a SPL of 118dB, they produce 160mV.

Thus, at your basic rock show, you might expect your 391's to put out a signal of 160mV, while your MR-1 can only take a signal of 45mV.

To decide on exactly what level of attenuator you need, you'll need to know (or guess) the highest SPL you expect to record in.  Decide on the SPL, and you can work thru the math to decide how much of an attenuator you need.

Offhand, I'd say that only going with a -10db attenuator would probably work, but is risky.  I'd recommend going with a -15db attenuator (or maybe a -12db if you're building your own).

See this post about building your own:  http://www.uneeda-audio.com/pads/


Edit:  Looks like your edit is answering alot of the things I just tried answering.

[Todd R]

1 Pa = 94 db SPL.  So at 94 dB, the 391 should put out 10 mv.  At +20 dB or 104 dB = 100 mv and at +40 db or 124 dB = 1,000 mv or 1 volt.  1 volt ~ 2.2 dBV

Ok, the part up to the 391 putting out 10mV at 94dB is right, after that it looks wrong.  Not sure where you got these figures.

[landshark]

Was just guesstimating, given the 20 db / log relationship - every 20 dB is like 10x - pure guesstimating, but could be waay wrong. 

[DSatz]

landshark, if your microphones put out 10 mV at 1 Pa (which is about 94 dB SPL) and the upper limit of their dynamic range is 132 dB SPL, then that's 38 dB above 10 mV or a little less than 800 mV.

I hope that you never try to record any actual sound in that range, however, since it would cause permanent damage to your hearing within a very few minutes.

Anyway, the -27 dBV limit of your microphone inputs corresponds to about 45 mV, and the ratio between 800 mV and 45 mV is just under 25 dB. So that'd be the maximum amount of padding which you would need if you were recording something which might approach the 132 dB sound pressure limit of your mikes (with you safely ensconced in a remote, well-padded position I hope).

In reality I think it will be considerably less (like maybe 10 to 15 dB), only because the sound pressure levels are unlikely to reach 120 dB at the listeners' position in any public concert venue.

--best regards

P.S.: Another way to approach this problem would be: The 45 mV limit of your recorder's mike inputs is equal to the voltage which your microphones put out at about 107 dB SPL (since 45 mV / 10 mV is about 13 dB, and 13 dB + 94 dB SPL = 107 dB SPL). If you want 10 dB more headroom than that, use a 10 dB pad, etc.

[landshark]

Dsatz, another great response.

I guess the two calculations I don't know how to do are:

"then that's 38 dB above 10 mV or a little less than 800 mV." - Ok, how do I get from 38 db to 800 mV?  Or is it in reference from the floor at 1 V?   Is it 38 dB = 20 * log ( V / 1 volt ), where solving for V gets you to .8 V / 800 mV?  That doesn't work out right.

Also, you mention, "and the ratio between 800 mV and 45 mV is just under 25 dB"  Ok, so how do I get from the ratio of the mVs to 25 dB?

I know this is basic remedial log math / engineering math, so feel free to shoot me to any good reference source.  As long as it's not too painful <grin>.  With luck, I'll be able to continuously upgrade my gear, so this isn't the last time I expect to run into this issue.  In the future, I'd like to be able to solve for the solution BEFORE I brickwall my op amps!!

Thanks for your responses everyone!!

Mike


ps. And I know that 132 dB is ear bleeding sound levels, I was just using that to work through the math of the problem.

[Todd R]

Mike,

As I said, the basic formula you need to know is:

dB = 20 * log (V1/V2)

That will give you everything you need.  So when DSatz says "and the ratio between 800 mV and 45 mV is just under 25 db" you can get that from:

db = 20 * log (800/45) = 24.9975dB

When DSatz says "the upper limit of their dynamic range is 132 dB SPL, then that's 38 dB above 10 mV or a little less than 800 mV", you can again calculate that from the above formula.  132db is 38db more than the reference point of 94db (at which point the 391 develops a signal strength of 10mv).

So 38db = 20 * log (V1/10mv), solving for V1, you get V1 = 800mv.

Getting back to the rule of thumb I mentioned above, that every increase of 6db leads to a doubling of the output voltage, you can get this as well from the formula:

dB = 20 * log (2*Vref/Vref) = 20 * log (2) = 6.02dB, or about 6db.  I just find this rule of thumb easy to do math in my head, but you can always just use the formula to get there.

For your example, you'll need to decide what is a reasonable upper limit on the SPL in the environment in which you tape.  I'd say at a max, 124dB is a reasonable upper limit.  124dB is 30dB over the reference of 94dB (with the 10mV output level).  Yielding:

30B = 20 * log (V1/10mV), solve for V1 and find V1 = 315mv. 

Your MR-1 can take a max of 45mv, so to find the necessary attenuation you'll have:

dB = 20 * log (315 mV / 45 mV) = 16.9 dB

So a 17dB attenuator would work fine as long as you don't record in environments above 124dB SPL.  Or if you assume a max SPL level of 120dB (again, pretty reasonable assumption), you can get by with 11dB attenuators.  Based on these examples, if you're buying pre-made attenuators, 15dB ones should be fine.

If you want to go completely conservatively, as DSatz calculates, if you record in an environment hitting the max SPL level the 391 can take, you'd need 25db attenuators.

[landshark]

Bingo.  It all becomes clear - thanks Todd!!!

I wasn't starting from 10mV as Vref, now the math works.

Mike