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Unformatted text preview: ECE 5325/6325 Fall 2009: Homework 3(d) Solution
(3f) What is the approximate Eﬁeld magnitude in the tworay (ground reﬂection) model from Section 4.6 for vertical polarization (i.e., when the reﬂection coeﬃcient is 1, rather than 1)? What is the approximate received power as a function of path length, for large path lengths? Solution: Starting from (4.47) and the note that follows it, we will replace the “” with a “+” in (4.47) for vertical polarization. ET OT (d) = E0 d0 d 2 + 2 cos θ∆
θ∆ 2, The trig identity we need is cos 2u = 2 cos2 u − 1, which, letting u = ET OT (d) = E0 d0 d 2 + 4 cos2 means E0 d0 θ∆ θ∆ −2=2 cos 2 d 2 For small angles θ∆ /2, the cosine term is approximately 1. So ET OT (d) ≈ 2 E0 d0 . Thus the d power (which is proportional to the electric ﬁeld squared) is proportional to 1/d2 : PT OT (d) = E 2 d2 ET OT 2 0 =4 0 2. η0 η0 d ...
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This note was uploaded on 02/25/2011 for the course ECE 5325 taught by Professor Dr.nealpatwari during the Spring '10 term at University of Utah.
 Spring '10
 Dr.NealPatwari

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