I'm just a bit confused. Consider an example where an antenna receives two signals - one with a power of -25dBm and one with a power of -47dBm and we are asked to find the total power received by the antenna
Now, if I just add -25 with -47 dBm, I get -72dBm which is a lower total power. How come? Am I not allowed to just add these two? Intuitively, we should get a higher total power surely? Maybe something closer to 1 or 2dBm maybe but not -72dBm?
As the difference in levels between the two signals is 'large' (more than 20dB, more than 100x in power), you can pretty much ignore the smaller signal.
The total power of two signals of -25dBm and -47dBm will be 'about' -25dBm.
If you want to convert both to power, add, and convert back to dB to get the exact figure, as Transistor has done, then you get -24.975dBm. The difference of 0.025dB is insignificant.
You'd have to make very careful measurements in a wired system to believe measurements to that precision. In an antenna system, you can be many dBs adrift without even trying due to direction of arrival, impedance mismatch, path loss, proximity effects etc.
I haven't done this for a long time so check my answer.
Remember that the decibel, dB, is a logarithmic scale. Adding logs is the same as multiplication of the "un-logged" version of the numbers so that isn't going to work.
Instead we need to get the anti-log of each, sum them and get the log of the result.
$$ \begin{align} P & = 10 log_{10}( 10^{\frac {-25}{10} } + 10^{\frac {-47}{10} } ) \\ & = 10 log_{10}( 0.003162 + 0.00001995 ) \\ & = 10 log_{10}(0.003182) \\ & = -24.975 \ \text {dBm} \end{align} $$
I'm expecting it to make a little bit more of a difference than that. Can anyone see an error?
The benefits of using dB are explained well in the Wikipedia decibel article:
Level values in decibels can be added instead of multiplying the underlying power values, which means that the overall gain of a multi-component system, such as a series of amplifier stages, can be calculated by summing the gains in decibels of the individual components, rather than multiply the amplification factors; that is, log(A × B × C) = log(A) + log(B) + log(C). Practically, this means that, armed only with the knowledge that 1 dB is approximately 26% power gain, 3 dB is approximately 2× power gain, and 10 dB is 10× power gain, it is possible to determine the power ratio of a system from the gain in dB with only simple addition and multiplication.
