homework3f_solution - ECE 5325/6325 Fall 2009: Homework...

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Unformatted text preview: ECE 5325/6325 Fall 2009: Homework 3(d) Solution (3f) What is the approximate E-field magnitude in the two-ray (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.

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