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Workshop14Last

# Workshop14Last - transmitting antenna’s eﬀective area...

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ECE 3030: Electromagnetic Fields and Waves Fall 2009 WORKSHOP 14 INSTRUCTOR NOTES: Sizing Dishes and Q and A Reminder: See TAs and Dr. Swartz for last minute help. Date: Thursday 12/3 1. Problem 17.17: What diameter dish antenna would be required to transmit power to a satellite at 1,000 km so that 70% of the transmitted power would be captured by a 3 m diameter dish on the satellite? Assume the dishes are perfectly aligned and operating at 30 GHz. Solution: Sizing a dish antenna. a. Ask the class if they think the requirement of receiving 70% of the transmitted power is practical. Check the numbers! b. The fractional power received depends on 0 . 7 = P out P in = G ( θ 1 , φ 1 ) A eff ( θ 2 , φ 2 ) 4 πr 2 Since the wavelength for a 30 GHz wave (0.01 m) is much smaller than the diameter of the receiving dish antenna (3 m), assume the effective area is equal to the physical area of 7.07 m 2 . We will also assume that the
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Unformatted text preview: transmitting antenna’s eﬀective area is equal to its physical area. Then the on-axis (max) gain can be written in terms of its radius as: G 1 max = 4 πA 1 eff λ 2 = 4 π 2 R 2 1 λ 2 Now collecting the terms and solving for the radius of the transmitting antenna: R 1 = • . 7 r 2 λ 2 πA 2 eff ‚ 1 / 2 = • . 7 (1000 × 10 3 ) 2 (0 . 01) 2 π 7 . 07 ‚ 1 / 2 = 1 . 78 × 10 3 m 2 So is this a practical antenna size? This is almost 12 times the size of the main reﬂector at the Arecibo Observatory, which is the biggest in the world (305 m in diameter)! So, requiring that 70% of the power transmitted be received is not practical! (Not even close!) A requirement of 1% would still need a dish bigger than Arecibo’s. 2. Items to review? 3. Ask for questions. CORNELL UNIVERSITY c ± WES SWARTZ (09/11/7) 14–1...
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