TOTAL CHANNEL POWER WHEN 1% IS -33.9 dBm

Question

If a power meter measures 1% of the total channel power to be -33.9dBm, what is the total channel power?

Answer 1

The key concept here is that dBs enable the use of addition vs. multiplication:

Pt[in Watts] = 100 * Pm[in Watts]  ==>
Pt[in dBm's] = 10 log10(100) + Pm[in dBm's] =
               20            + -33.9 =
-13.9dBm

Check:
Pm = (10^(-33.9dBm/10))*0.001 = 0.000000407380278 Watts
Pt = (10^(-13.9dBm/10))*0.001 = 0.00004073802778 Watts

Pt[in milliWatts] = 100 * Pm[in milliWatts] =
0.00004073802778 =? 100 * 0.000000407380278 =
0.0000407380278