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A constellation of LEO satellites has an altitude of 400 km. Each satellite has two multiple beam antennas that generate 52 beams for communication with small user terminals on earth. One antenna is used to transmit at 39.0 GHz and the other antenna receives at 43.0 GHz.

A constellation of LEO satellites has an altitude of 400 km. Each satellite has two multiple beam antennas that generate 52 beams for communication with small user terminals on earth. One antenna is used to transmit at 39.0 GHz and the other antenna receives at 43.0 GHz.

Applications and Investigations in Earth Science (9th Edition)
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
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A constellation of LEO satellites has an altitude of 400 km. Each satellite has two multiple beam antennas that generate 52 beams for communication with small user terminals on earth. One antenna is used to transmit at 39.0 GHz and the other antenna receives at 43.0 GHz. a. Using simple geometry, find the coverage angle of the satellite antenna when the lowest elevation angle for an earth station is 40°. (Hint: Draw a diagram of the earth and the satelite and use the law of sines to solve the angles in a triangle. Use an earth radius value of 6378 km.) b. The footprint of the satellite antenna is a circle on the earth's surface, encom- passing the 52 beams. Calculate the diameter of the circle over the surface of the earth, in km. c. Assume that all 52 beams from the satellite antennas have equal beamwidths and beams touch at their -3 dB contours. Nine beams can be fitted across the diameter of the circle you calculated in part (b). What is the beamwidth of an individual beam? How wide is the beam directly below the satelite, in km? Calculate the gain of the beam at the transmitting and at the receiving frequency. d. A phased array with a square outline is used to generate the 52 beams of the transmitting antenna. The element spacing is 0.6 wavelengths. Estimate the number of elements that are required in the phased array.
Transcribed Image Text:A constellation of LEO satellites has an altitude of 400 km. Each satellite has two multiple beam antennas that generate 52 beams for communication with small user terminals on earth. One antenna is used to transmit at 39.0 GHz and the other antenna receives at 43.0 GHz. a. Using simple geometry, find the coverage angle of the satellite antenna when the lowest elevation angle for an earth station is 40°. (Hint: Draw a diagram of the earth and the satelite and use the law of sines to solve the angles in a triangle. Use an earth radius value of 6378 km.) b. The footprint of the satellite antenna is a circle on the earth's surface, encom- passing the 52 beams. Calculate the diameter of the circle over the surface of the earth, in km. c. Assume that all 52 beams from the satellite antennas have equal beamwidths and beams touch at their -3 dB contours. Nine beams can be fitted across the diameter of the circle you calculated in part (b). What is the beamwidth of an individual beam? How wide is the beam directly below the satelite, in km? Calculate the gain of the beam at the transmitting and at the receiving frequency. d. A phased array with a square outline is used to generate the 52 beams of the transmitting antenna. The element spacing is 0.6 wavelengths. Estimate the number of elements that are required in the phased array.
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