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30 Solved Problems on Wave Propagation 1. How far away is the radio horizon if an antenna 500 ft high? . !t a "ertain time# the $%& for transmissions at an angle of in"iden"e of '5o is 1'$Hz. What is the "riti"al fre()en"y? 3. *f the "riti"al fre()en"y is 10 $Hz in s+y wave propagation# what is the best fre()en"y to )se ass)ming 300 of radiation angle? ,. -he total power delivered to the radiator of an isotropi" antenna is 00#000 W. etermine the power density at a distan"e of 100 meters. 5. What is the free spa"e path loss in d/ between two mi"rowave paraboli" antennas 3.0 +ilometer apart operating at '.0 Hz? 2. What is the angle of in"iden"e of the radio wave signal as it moves from air to glass# if the angle of refra"tion is . o? iele"tri" "onstant for glass is '.. '. al")late the ele"tri" 4eld intensity in millivolts per meter at 30+W from a 5 miles so)r"e. . *n wave propagation# determine the refra"tive inde of an ionospheri" layer with 100 10 2 free ele"trons per ")bi" meter at 5 $Hz fre()en"y. 6. ! line7of7sight radio lin+ over 8at terrain needs to )se antenna towers 50 +m apart. What# approimately# is the minim)m height for the towers ass)ming all the towers are the same? 10.*f a radio re"eiver needs 1 nW9m of power density to f)n"tion# how far away from a 17watt point so)r"e will it "ontin)e to wor+? 11.! "ertain diele"tri" has permittivity of 2.3 10:10 &9m and the same permeability as free spa"e. What is the "hara"teristi" impedan"e of that diele"tri"? 1.&ind the "riti"al angle when a wave passes from glass# with ;r<'. into air. 13.!t a "ertain time# the $%& for transmissions at an angle of in"iden"e of '5 o is 1'$Hz. What is the "riti"al fre()en"y? 1,.*W!-! satellite is lo"ated 32000 +m above earth=s s)rfa"e. !ss)ming free spa"e "ondition# what is the path loss of the signal if the operating fre()en"y is 3Hz? 15.*f the velo"ity of propagation in a "ertain medi)m is 00 102 fps# what is its refra"tive inde? 12. *f ,+W in antenna prod)"es 50>9m in a re"eiving antenna# a 12+W will prod)"e?
1'. If a point source of radio waves transmits 1 watt, what is the power density 10,000 meters from the source?
1. What power must a point-source of radio waves transmit so that the power density at 3000 meters from the source is 1 µW/m2?
19. A microwave-transmitting antenna is 550 ft. high. The receiving antenna is 200 ft. high. The minimum transmission distance is 0.What is the angle of in"iden"e of the radio wave signal as it moves from air to glass# if the angle of refra"tion is o? iele"tri" "onstant for glass is '.. 1.!t a "ertain time# the $%& for transmissions at an angle of in"iden"e of 25 o is 10$Hz. What is the "riti"al fre()en"y? .! line7of7sight radio lin+ over 8at terrain needs to )se antenna towers 150 miles apart. What# approimately# is the minim)m height for the towers ass)ming all the towers are the same?
3.al")late the ele"tri" 4eld intensity in volts per meter at 3+W from a 5+m so)r"e. ,.What is the free spa"e path loss in d/ between two mi"rowave paraboli" antennas .0 +ilometer apart operating at 2.5 Hz? 5.What is the free spa"e path loss in d/ between two antennas 2 miles apart operating at 1'.0 Hz? 26. A microwave-transmitting antenna is 550m. high. The receiving antenna is 200m. high. The minimum transmission distance is '.*f the velo"ity of propagation in a "ertain medi)m is 55 10 2 m9s# what is its refra"tive inde? .-he total power delivered to the radiator of an isotropi" antenna is 1+W. etermine the power density at a distan"e of 50 meters. 6.-he total power delivered to the radiator of an isotropi" antenna is 5.5+W. etermine the power density at a distan"e of 1+m. 30.How far away is the radio horizon if an antenna 5m high?
