30 Solved Problems on Wave Propagation

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# approimately# 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 3Hz? 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# approimately# 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?