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Demo14Arrays

# Demo14Arrays - ECE 3030 Electromagnetic Fields and Waves...

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ECE 3030: Electromagnetic Fields and Waves Fall 2009 DEMO 14 INSTRUCTOR NOTES: Antenna Arrays Reminder: Last Demo! Date: Tuesday 12/1 1. Problem 17.16 Consider an array of N Hertzian dipoles sep- arated by distance d and point- ing towards the +z-direction. The wavelength of the radia- tion is λ . All the dipoles have the same currents (magnitudes and phases). The angle φ 0 is defined from the positive y axis (as shown above). ( Note: The results from this problem will be used in the next problem.) x y d Figure 1: A linear array of Hertzian dipoles. A very general plot of the radiation pattern is shown at the right. The specifics of this plot are not related to this problem. The plot is only for illustrative purposes. a. Show (based on physical reasoning) that there is a maximum in the radiation pattern for φ 0 = 0, irrespective of the wavelength λ and the distance d . This is the 0 th order max- imum. b. Find a condition (without calculating the array factor) in terms of the wavelength λ and the distance d that gives the angles φ 0 1 for the 1 st order maxima (see the figure above). c. Find a condition (without calculating the array factor) in terms of the wavelength and the distance d that gives the angles φ 0 2 for the 2 nd order maxima (see the figure above). y x 0-th 1-st 2-nd Figure 2: A general polar plot of an an- tenna pattern p ( θ = π/ 2 , φ )(not related to problem at hand). Solution: Characteristics of an N-element array.

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