## Q. 9.1

Determine
a.  The power levels in dBm for signal levels of 10 mW and 0.5 mW.
b.  The difference between the two power levels in dB.

## Verified Solution

a.  The power levels in dBm are determined by substituting into Equation 3:
dBm = 10 log$(\frac{P}{1\,mW})$          (3)
dBm = 10 log$(\frac{10\,mW}{1\,mW})$ = 10 dBm
dBm = 10 log$(\frac{0.5\,mW}{1\,mW})$ = -3 dBm

b.  The difference between the two power levels in dB is determined by substituting into Equation 2:
dB = 10 log$(\frac{P_{1}}{P_{2}})$          (2)
dB = 10 log$(\frac{10\,mW}{0.5\,mW})$ = 13 dB
or        10 dBm – (-3 dBm) = 13 dB
The 10-mW power level is 13 dB higher than a 0.5-mW power level.