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Problem Set
Electromagnetic Wave propagations
By: Engr. CJRVelasco
1. An isotropic source radiates 100 watts of power in free space. Calculate the electric field intensity at a distance
of 15 km from the source. Ans: 3.65mV/m
2. A signal has a power density of 50mW/m2 in free space. Calculate its electric field strength. Ans: 4.34 V/m
3. Compute for the EIRP for a transmitting power of 30W and an antenna gain of 45 dB. Ans: 948.68 kW
4. A certain antenna has a gain of 7 dB with respect to an isotropic radiator. What is the effective area if it operates
at 200 MHz? Ans: 0.897 m2.
5. A transmitter has an output power of 50 W. It is connected to its antenna by a feed line that is 25 metes long
and properly matched. The loss in the feed line is 5 dB/100m. the antenna has a gain of 8.5 dBi. How much
power reaches the antenna? Ans: 37.5 W
6. How much power would an antenna (gain = 7dB, f = 200 MHz) absorb from a signal with a field strength of
50µV/m? Ans: 5.95pW
7. A radio signal moves from air to glass. The angle of incidence is 200. Calculate the angle of refraction. The
relative permittivity of glass is 7.8. Ans: 7.0340
8. If the critical frequency is 10 MHz, what is the OWF at an angle of 600? Ans: 9.81 MHz
9. At a certain time, the MUF for transmissions at an angle of incidence of 75 0 is 17 MHz. what is the critical
frequency? Ans: 4.4MHz
10. An FM broadcast station has a transmitting antenna located 50m above average terrain. How far away could the
signal be received by a rooftop antenna 12m above the ground? Ans: 43.44 km.
11. A boat is equipped with a VHF marine radio which it uses to communicate with other nearby boats and shore
stations. If the antenna on the boat 2.3m above the water, calculate the maximum distance for communication
with another similar boat, using the shore station with an antenna on a tower 22m above water level as a
repeater. Ans: 51.18km.
12. An FM broadcast signal arrive an antenna via two paths. The first is the direct wave to the antenna, and the
other is the reflected wave from a hill 1.5kms from the opposite direction of the transmitting station. Calculate
the difference in arrived time for the two paths. Ans: 10µs.
13. A transmitter and receiver are separated by water. If the difference in lengths of the direct and reflected paths is
2m, calculate the phase difference at 400MHz. Ans: 2400
14. Determine the maximum usable frequency for a critical frequency of 10 MHz and an angle of incidence of 45 0.
Ans: 14.14 MHz
15. A satellite transmitter operates at 4GHz with an antenna gain of 40dBi. The receiver 40,000km away has an
antenna gain of 50 dBi. If the transmitter has apower of 8W, find the power delivered to the receiver. Ans:
179pW