#### Re: Mike element

Jerry Gaffke

The "dB SPL" gives the Pascal part of 1V/Pascal, but it does not specify the 1V part.

94 dB SPL means 94 dB above the reference sound pressure level of 20 uPa,
where 20 uPa is around the bottom threshold of human hearing.
https://en.wikipedia.org/wiki/Sound_pressure
When somebody says a rock concert has a sound level of 110 dB, they mean 110 dB SPL.

So  a complete spec for microphone sensitivity might say how many "dB SPL" to give 1V out.
Or they might say how many "dB" to give 1V out, and mean the same thing.
Those acoustic engineers only deal with one kind of dB, and assume any such figure is for dB SPL,
and describes a measured sound pressure level, not a ratio.

In radio work, "dB" refers to a ratio, perhaps the output power of an amp divided by the input power.
To give a power measurement we might say 20 dBm, which is the ratio of the 100 milliwatts we measured
divided by an inferred reference of 1 milliwatt:      10**(20/10) = 100.
So dB is a ratio of two powers, and dBm is a specific power level.

######################
While I'm on a rant, here's a bit more for those still puzzled but vaguely curious.

I've said that dB in radio work means a ratio.
A good receiver might have a dynamic range that can simultaneously deal with incoming
signals of both one microvolt and one volt at the antenna, and still allow us to hear
the small signal.  Since power is the square of voltage divided by resistance,
that's a power ratio of 1,000,000,000,000 between the big and the little signal.
These numbers quickly got out of hand, especially for those folks back in 1930 working
with a slide rule.

It might be easier to say that the big signal has 12 more zeros after it than the little signal.
Though that isn't very precise, if the receiver front end was improved to deal with
a big signal of up to 2 volts it would then have 12.6 more zeros than the little signal.
(Those who remember high school algebra will understand how to deal with a fractional power of ten.)
Rather than deal with fractional numbers like that, they decided to just multiply the zero count by 10,
so we can now say that a receiver capable of dealing with signals between 1uV and 2V has
a dynamic range of 126 dB.

Through the magic of logarithms, when the gains of two amps in series are expressed in dB we can
determine the total gain of the amp by adding a couple 2 digit numbers in our head instead of multiplying
out a couple larger numbers.  You don't see dB used much in hard science such as a physics textbook,
they just deal with the big numbers.  But radio engineers who live and breathe this stuff 12 hours/day
needed an easier way to do the calculations in their head, and dB won out.

The formula to go from a power ratio to dB is  10*log(P1/P2).
Here, "log" is base ten, and log(1000) is 3.
For even powers of 10, the log() function just tells us how many zeros.
In the case above, we have 10*log(2000000*2000000/1) = 126 dB
(where voltages are expressed in microvolts).

I usually use python as my calculator when figuring out this sort of thing.
It's available for almost every computer (unfortunately a Nano is too small)
and fully interactive, highly recommended.  The log function comes from an
external library called "math", so we must first bring in that library to make it available.
Here's a python session to test the above formula, it gives a more precise result
than my approximation of "126 dB".:

import math
10*math.log10(2000000*2000000/1)
>>>  126.02059991327963

We can go from dB back to a power ratio with this:
10**(126.0206/10)
>>>  4000000079872.417

and go back to the voltage ratio by taking the square root of the power ratio:
math.sqrt(4000000079872.417)
>>>  2000000.019968104

Jerry, KE7ER

On Wed, Jul 18, 2018 at 08:14 AM, <k1yw@...> wrote:
Just to throw in another way of specifying microphoen sensitivities . 1V/Pascal is equal to 94 dB SPL.  So you may see either terms when looking at mic specs.

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