Question about computing an average

Let’s say you measured the output power of two transmitter radios using a power meter. One transmitter had an output power of 20 dBm (where 0 dBm is defined as 0.001 watts), while the other transmitter had an output power of 30 dBm.

What would be the average output power for the two radios? Would it be 25 dBm or 27.4 dBm? I’m thinking the latter would be the most correct answer, but just wanted a second opinion.

I would consider 27.4 dBm to be more correct (and also more meaningful). The average power is 550 mW, which is 27.4 dBmW.

It’s unfortunate, but the answer is “it depends”. An average is simply a number that gives you a measure of the “typical” value of a quantity. There’s not going to be a “most correct” answer.

When giving values for transmitted power, it’s pretty common to use RMS average (but also to note in any documentation that you are using an RMS average instead of a different average). But that’s generally for a single source. If you mean to use both these transmitters to push the same signal at the same time, that’s a reasonable average.

If you are simply measuring some kind of ‘average’ performance of identical transmitters, the straight mean can be a reasonable value to give.

So, it’ll depend on what you are trying to measure and it would still be a good idea to document the sort of average you use in any case.

Yeah, it depends on what average you really want. dBm is a logarithmic scale, so 25 dBm would be a logarithmic mean in terms of absolute power, which might be what’s needed in the circumstance. 27.4 dBm sounds right for the arithmetic mean, converted back to dBm, according to my scratch calculations:

  • Take 20 dBm as a temporary zero point, thus equalling 1 unit of absolute power.
  • 30 dBm would thus be 10 units of absolute power.
  • Average of 1 and 10 is 5.5
  • The base-ten-log of 5.5 is 0.74, thus 7.4 dB above our zero point. 27.4 dBm

I hope that this helps.