Glenn Booth wrote:

Hi,

In message , gecwhite
writes

The twenty comes in because the "voltage dB" is essentially derived from
the "power dB," but power is a non-linear function (square law) of
voltage.

Yes, I got that; I just needed to know which came first :-)

By _Bell System Blue Book definition_:

X(dB) = 10*log(P/P_ref)

*That's* what I was looking for; many thanks.


I would like to add that I don't believe the "origin" notes at

http://www.madengineer.com/blunders/decibels.htm.

There are no sources cited and the author fails to decently answer his own
questions: "Why is the log multiplied by twenty? If it's deci, why not multiply
(or divide!) by 10? That is, why the deci?"

It is "deci" because of the '10' multiplying the log. The -bel was "already"
log-based-10; so that would not explain it. The only thing that made it deci-
was the 10 multiplier for the log-base-10. For electrical work, how the '20'
comes in has been demonstrated. I'll leave the '20,' as a sound pressure, as an
exercise for the student, hah hah.



On the other hand, the site

http://www.sizes.com/units/decibel.htm

does cite sources and very old ones at that. I have many engineering texts, and
*every one* defines the original dB as a power ratio. One of my physics texts
(R. Serway) gives the original definition in the chapter on sound waves as

/ I \
x(dB) = 10*log(-----)
\ Io/


where the intensity 'I' of a sound wave is

P_sound_wave
I := --------------.
Area

So the definition is definitely a power (or energy) relationship, and the work
is relevent to that carried in an acoustical wave. 'Io' is defined as the
intensity of a sound wave at the threshold of hearing. Note that the area of
any individual's ear is constant, regardless of wave intensity. Therefore, the
above acoustically related definition has the area simply "drop out," since it
is identical in the numerator and denominator. We are then left with

/ P_sound_wave \
x(dB) = 10*log(------------------).
\P_sound_wave_ref/


This is a _power ratio_ and once it is reduced to that, it makes no difference
"where" the power is. It could be in an acoustical wave, a resistor, a light
wave..... the definition does not then require the statement of any particular
medium, or energy carrying means; although it probably was _sourced_ in the
acoustical world. The basic power definition of the dB is therefore a highly
generalized one. It is doubtful that the original work was concerned with
anything other than sound intensity. So bet 20*log(pressure_ratio), as an
original definition, to be wrong. A good rule is to demand citations.


Is the Bell System Blue
book available?

You might see them on ebay from time to time. They seem to get high prices
($50).

I should note my language is sloppy. The term "Blue Book" is not well defined
and I know Bell labs published more than one. How many were "blue," I don't
know.

My particular "blue book" is

_Transmission Systems for Communications_
3rd Ed, (c) 1964
Bell Telephone Laboratories, Inc.


Still an excellent text, ime.


[Much good stuff snipped to the clipboard for later]

I hope this clears up some of your questions.

All of them. Thanks very much.


You're welcome!