Decibels and SI Units (was Units (and operators.hpp, too))

From: Bill Seymour (bsey_at_[hidden])
Date: 2001-06-29 13:12:50

Deane wrote:
>
> There are logarithmic units such as decibels and pH.
> I'm not familiar with how these are used in formulas.
> I think these are sufficiently strange so that they
> should be treated specially.
>

I'm a wires-and-pliers guy by training and early vocation,
so I can tell you about decibels in electronics (I'm ignorant
of acoustics).

A Bell (after Alexander Graham Bell) is the common log
of a power ratio.  A more useful unit, it turns out, is
a tenth of a Bell, or a decibel (with just one 'l' for
historical reasons):

    1 dB = 10 log(P1/P0)

Audio engineers like to measure power in decibels over
one milliwatt:

    1 dBm = 10 log(P/1mW)

and RF engineers like decibels over one kilowatt:

    1 dBk = 10 log(P/1kW)

I bring this up in connection with the SI Units presentation
that the Boost group got in Copenhagen, in which units like
"meter" are not dimensions, but multipliers; and it occurs
to me that units like dBm and dBk need to be addends rather
than multipliers.  Does the SI Units system being worked on
have a way to deal with that?

--Bill Seymour