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ecet512hw4

ecet512hw4 - ECE-T 512 Winter 2007 Homework#4 Midterm...

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ECE-T 512 Winter 2007 : Homework #4 Midterm Practice Problems March 11, 2007 1 25.4.3 a)For the Friis’ law to hold, the separation of the two antennas should be at least one Rayleigh distance apart. Rayleigh distance is calculated as: d R = 2 L 2 a λ , where L a is tha largest dimension of the antenna. In our case, L a = 15 m , and λ = 0 . 3 m (1 GHz carrier frequency), so Rayleigh distance is d R = 1500 m > 90 m , so for the specified distance, the Friis’ law cannot be used. b) The effective area of a parabolic antenna is A eff = 0 . 55 A , where A is the physical area. So, in our case, A eff = 0 . 55 πr 2 = 97 . 193 m 2 . The antenna gain is then given as: G = 4 πA eff λ 2 = 13570 . 70 = 41 . 33 dB . If the Friis’ law was used for the link budget, then the received power would be calculated as: P RX = P T X G T X G RX λ 2 (4 πd ) 2 P RX dB = P T X dB + G RX dB + G RX dB + 20 log( lambda 4 πd P RX dB = P T X dB + 82 . 66 - 71 . 53 P RX dB = P T X dB + 11 . 13 dB . In other words, the received power is more (!) than the transmitted one.
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