Re: Re: something like dB

• To: mathgroup at smc.vnet.net
• Subject: [mg56644] Re: [mg56629] Re: something like dB
• From: "David Park" <djmp at earthlink.net>
• Date: Sun, 1 May 2005 00:46:46 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Bill,

I know that it is commonly used, but just because something is commonly used
doesn't mean that it is not sloppy, or that it doesn't cause headaches to
many people. The original poster claimed dB was a Unit, and it certainly
isn't. It is a function or mapping.

You can't get the Units package to convert 30 dBm to Watts because dBm isn't
a Unit that has a conversion factor to Watts.

If you had a function f[x_]:= x^2 would it make sense to write 3 f? I
suppose you could state it as a new notation, but this has an existing
meaning in Mathematica. But 3//f would have the intended meaning so maybe
one could do something like the following.

Needs["Miscellaneous`Units`"]
dBm = Milli Watt 10^(#/10) &

30 // dBm
1000 Milli Watt

But we need the // and and expression like 30 dBm will never work usefully
in Mathematica and that's why I say the original notation is sloppy.

David Park

To: mathgroup at smc.vnet.net

On 4/29/05 at 3:20 AM, djmp at earthlink.net (David Park) wrote:

>It is only sloppyness to say that something is x dB. (Maybe I'll
>hear differently from other responders.) In any case, if you use
>0.0 dB then the 0.0 will be retained, but if you write exact 0
>anything Mathematica always returns 0.

No, it isn't just sloppyness to use dB. For example, it is perfectly logical
to talk of an attenuation or gain of say 3 dB which would mean for
attenuation half of the input power is lost. Linear amplifiers increase
power by a fixed ratio for a given setting and attenuators decrease power by
a fixed ratio.

This is made even more useful by measuring power levels in units like dBm.
Here the m tells me the power level is referenced to 1 mW. So, 0 dBm would
be 1 mW of power. And with an input of 0 dBm and an amplifer with a gain of
30 dB, I can easily determine the output power is 30 dBm or equivalently 1
Watt.
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