Solutions to End of Chapter Problems
1.
Convert power gains of 100, 1000 and 2000 to decibel values.
10 x log10 (100) = 20 dB
2.
10 x log10 (0.001) = −30 dB
10 x log10 (0.0005) = −33 dB
Convert decibel power gains of 13 dB, 33 dB, and 103 dB to power gains.
13 dB ®10 10 = 20
33 dB ®10 10 = 2000
13
4.
10 x log10 (2000) = 33 dB
Convert power gains of 0.01, 0.001, and 0.0005 to decibel values.
10 x log10 (0.01) = −20 dB
3.
10 x log10 (1000) = 30 dB
33
103 dB ®10 10 = 2 ´1010
103
Three amplifiers with gains of 12.5, 4, and 20 are cascaded as shown in the following diagram (from left to
right). The input power is 120 mW. What is the overall gain and the output powers of each stage?
P1 = Pin x AP1 = 120 mW (12.5) = 1500 mW = 1.5 W
P2 = P1 x AP2 = 1.5 W (4) = 6 W
P3 = P2 x AP3 = 6 W (20) = 120 W
AT = AP1 x AP2 x AP3 = 12.5 (4) 20 = 1000
5.
A power amplifier has an output power of 200 W and an input power of 8W. What is the power gain in
decibels?
Ap =Pout / Pin = 200 W / 8 W = 25. Ap,dB =10log(25) = 14 dB
6.
A power amplifier has a gain of 55 dB. The input power is 600 mW. What is the output power in W?
Pout = Pin x AP = 0.6 W x 105.5 = 189.7 kW
7.
An amplifier has an output power of 5W. What is this amount of power in dBm?
æ 5W ö
Pout , dBm = 10 log10 ç
= 37 dBm
è 0.001W ÷ø
8.
A communication system has five stages, with gains and attenuations of 12 dB, -45 dB, 68 dB, -31 dB and 9 dB.
a. What is the overall gain in dB (AT,dB)?
AT,dB = AP1,dB + AP2,dB + AP3,dB + AP4,dB + AP5,dB = 12 dB − 45 dB + 68 dB −31 dB + 9 dB = 13 dB
b. The overall power gain (AT)?
AT = 10
AT , dB
10
= 101.3 = 20
c. If the input power is 1 dBm, what is the output power in dBm?
Pout, dBm = Pin, dBm + AP, dB = 1 dBm + 13 dB = 14 dBm
9.
The signal input power to a receiver is 6 W. The noise power is 25 mW. What is the SNR? What is SNR dB?
P
6W
SNR = s =
= 240
Pn 0.025 W
SNRdB = 10 log10 ( SNR ) = 10 log10 ( 240 ) = 23.8 dB
10.
A receiver’s sensitivity is the minimum received signal power for the receiver to successfully recover the
transmitted signal. If a receiver’s sensitivity is -45 dBm, and the received power is 10 μW, will the receiver be
able to recover the transmitted signal?
Compute received power in dBm, and see if that value is greater than the sensitivity.
 10 106 W 
Prec, dBm  10log10 
  20 dBm
 0.001 W 
Since this value is > receiver sensitivity (-45 dBm), the receiver can recover the signal.