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**Unformatted text preview: **ECE 3030: Electromagnetic Fields and Waves Fall 2009 DEMO 12 INSTRUCTOR NOTES: Reflectors and 2- and 3-Dimensional Arrays Reminder: Prelim 3 on Thursday night. Date: Tuesday 11/17 1. Prelim 3 Thursday night, November 19...no Workshop 12. 2. Problem 17.8 A short dipole of physical length d , pointing in the z-direction, and carrying a current pha- sor I , is located at ( h,h, 0) in the ( x,y,z ) coordinate system, as shown in the figure to the right. The space for which x < 0 or y < 0 is filled with a perfect con- ductor. a. Find the expression for the far-field electric field vector of the radiation and explain your result. b. Find an exact expression for the gain G ( θ,φ ) of the antenna. What value of h (in terms of the wavelength λ ) will give the maximum value for the gain and in which directions ( θ,φ ) does this maximum value of Gain occur? c. Sketch the radiation pattern p ( θ,φ ) in the x- y plane assuming that the distance h equals λ . y x h • h ∞ = σ Figure 1: A short dipole with a corner reflector. Solution: Pattern from a corner reflector. a. Note that there are three image dipoles in this problem. (Draw the figure.) The far field only exits for x > 0 and y > 0 with ~ E ff ( ~ r ) = { Element Factor } × { Array Factor } The two factors are { Element Factor } = j kId eff 4 πr e- jkr sin θ { Array Factor } = e jk ˆ r · ~ h 1- e jk ˆ r · ~ h 2 + e jk ˆ r · ~ h 3- e jk ˆ r · ~ h 4 where the effective length of the dipole and its images is d eff = d 2 , and the signs account for the current reversals of the images. We need the dot products, but first make sure the class understands the pieces. Thedot products, but first make sure the class understands the pieces....

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