Decibel reference on Wiki

[PurdueRy]

Can anyone make sense of where these values came from on the following wiki page?

http://en.wikipedia.org/wiki/Decibels

dB(1 mVRMS) ? voltage relative to 1 millivolt, regardless of impedance. Widely used in cable television networks, where the nominal strength of a single TV signal at the receiver terminals is about 0 dBmV. Cable TV uses 75 O coaxial cable, so 0 dBmV corresponds to -78.75 dBW (-48.75 dBm) or ~13 nW.

I don't understand how they arrived at -78.75 dBW. Don't really need to know this for any reason...just interested.

 

[PottedMeat]

P = (1mV)^2/(75Ohms) = 13.33nW

dBm = 10 log ( 13nW / 1mW ) = -48.7506dBm

Difference between dBm and dBW is 30 in log scale and 1000 in linear scale so dBm->dBW = dBm - 30 = -78.7506

 

[PurdueRy]

Thanks pottedmeat. I was on the right track I just didn't realize I needed to compare it to 1mW. Looking back this now seems obvious but you know how it goes when you don't quite put together all the pieces. Thanks again...you've settled my mind on my random puzzle of the day .

 

[Paperdoc]

In a 75 ohm cable TV system, you assume that the actual power-dissipating load at the end of the transmission line (cable) has 75 ohms impedance. A signal of 0 dBmV by definition has an RMS voltage of 1 millivolt, or 0.001 volts. Apply this across a 75 ohm impedance and using P=V²/R we calculate the power dissipated in the load as 1.3333 x 10^-8 W. (That's 13 nanowatts.) Take the base-10 log of that (that's bels) and multiply by 10 to get decibels, and the answer is -78.75. This is the ratio of watts of power referenced to one watt, and the symbol used for that is dBW. As PottedMeat says, the difference between dBW and dBm is just that the latter is referenced to one milliwatt, not one full Watt; the ratio of these is 1:1000 which is a difference of 30 in the number, so -78.75 dBW = -48.75 dBm.