dBm and watt

"ten times log to the base ten of twenty over zero point zero zero one".

So 10 log(20/0.001) is correct if you assume that it's log to the base

1. "10log" will usually be taken to be ten times log to the base 10.

You could do it that way, or you could do it in your head if you can remember that a watt is +30 dBm (*). Ten times that (10 watts) is +10 dB, or 40 dBm. Double that to twenty watts is another 3 dB, or 43 dBm.

(*) Or from the definition, a milliwatt is 0 dBm, ten milliwatts is +10, a hundred is +20, a thousand is +30...

Jim

Although the answers you've gotten are fine, this seems like kind of an odd question to be asking in the first place. The sort of systems (line-level audio) that are specified in dBm don't usually involve power levels anywhere near 20W. Indeed, dBm is kind of an obsolete measurement, even for audio; more commonly these days, we see dBu, which is essentially a voltage measurement rather than a power measurement. (0dBu = 0.7748V, which happens to be the voltage that would produce 1mW into a 600 ohm load.)

Are you sure you're asking the right question? What is the context?

I think this could be a transcription error - it is ten times the log to the base ten of power one over power two. I surmise that 10log looked like log10. :-)

Cheers! Rich

Yup.

Graham

Shouldn't that be 10*10log(20/0.001)?

Ted

It's quite common in RF technology also, and 20W is not exactly super power...

Paul

More like 10*log10(20/0.001) if you like but since ln is normally used for natural logs then log without a suffix may be reasonably taken to mean base10.

Graham

Sorry, my bad - I'm not an RF guy, didn't realize it was common there. Now I know better!

Though I still do wonder what the context of the OP's question was.

Let's not start this again. dBm is very commonly used for 50 Ohm systems and equipment, including signal generators, amplifiers, spectrum analyzers, etc.

--Mac

In "low power" RF engineering, dBm is *much* more commonly used to indicate power than any other unit - including the pW, nW, uW, mW or any other multiplier in front of the W.

However, once you get to 1~10 W or so, normally Watts would start being used. So 20 W would be close to the upper limit where dBm would be used

- the use of W would be more common then.

I've also known dBW to be used (dB relative to 1 W) for higher power things, but usually people use W, kW or MW then.

What he said....we care always using dbm and dbW in satellite comm's.

Ken

I read in sci.electronics.design that Pooh Bear wrote (in ) about 'dBm and watt', on Tue, 13 Sep

Those nice people on IEC TC25, who gave us 'kibis' and 'mebis', also gave us 'ld' for logs to base 10 and 'lb' for logs to base 2, to go with 'ln' for logs to base n, well, no, to base e actually (why not 'le', then?)..

The log abbreviations are useful. Does ANYONE use the binary multiplier prefixes?