# Power and Noise calculations using decibel conversions

Convert the following numbers to dB with the correct dB units

a. A transmitter power of 250 watts

b. A received power of 2 x 10^6 watts

c. A noise temperature of 100 K

d. A bandwidth of 4.0 MHz

e. A radio receiver has a noise power N = kTB watts, with T = 100 K and B = 1.0 MHz. The value of k is 1.38 x 10^-23 J/K. What is the noise power in dBW?

f. If the radio in part (e) above receives a signal with power -100.0 dBm, what is the CNR (carrier to noise ratio) in the receiver?

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#### Solution Preview

a. The main unit for power is the dBW which can be derived from

dBW = 10*Log(Po/1 W)

where Po is the power one wants to derive the unit in dBW and the Log is to the base 10

Thus power 250 W = 10*Log(250/1) = 10 x 2.4 = 24 dBW

b. Again we use the definition of dBW = 10*Log(Po/1 W)

thus for a received power of 2 x 10^6 W we get an equivalanet power expressed as dBW as

2 x 10^6 W = 10*Log(2 x 10*6/1) =10 x 6.3 = 63 dBW

c. A noise temperature of 100 K can be expressed in dB-K ie a dB value referenced to 1 K ...

#### Solution Summary

Conversion of linear power figures to dB and writing units in variuos dB forms