# HW10_solution - ECE 473/TAM 413 Homework Assignment #10...

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Homework Assignment #10 Solutions - 1 ECE 473/TAM 413 Homework Assignment #10 Solutions For your information Hour Exam 2: Thursday, November 20, 2008, 7:00-8:30 pm, 163 EL Hour exams are open book (the text for the course) with one sheet of notes (you can use both sides). Your class notes and lecture notes are not permitted. You can use calculators. 1. An underwater linear array has 30 elements equally spaced at d = 1.5 ! , where ! is the wavelength at its operating frequency. (a) Are there any grating lobes? If yes, determine the angular location of the first grating lobe. (b) Determine the angular width (to the nulls) of the main lobe of the array. (c) If the main beam of the array is steered 25˚ off the array axis, then determine the angle of the grating lobe closest to the axis. a) Yes. Sin ! ( ) = m " d and for m = 1, ! = Sin 2 3 " # \$ % & = 41.8˚ b) Where ! 1 is the angle for the first nodal surface, 2 ! 1 = 2Sin " 1 n # Nd \$ % & ( ) = 2Sin " 1 1 i # 30 i 1.5 # \$ % & ( ) = 2.55˚ c) Sin ! ( ) = Sin ! o ( ) ± m " d where ! o = 25 o ! = Sin " 1 0.4226 ± 0.6667 ( ) , where we choose the minus sign because the closest grating lobe will appear on the negative ! side. Thus, ! = " 14.1 o 2. The main lobe of a linear array (a line array) is scanned between +60˚ and -40˚. The array has 40 equally spaced elements, and operates in sea water (c = 1500 m/s; ! =

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## This note was uploaded on 09/19/2009 for the course ECE 473 taught by Professor Obrian during the Fall '08 term at University of Illinois at Urbana–Champaign.

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HW10_solution - ECE 473/TAM 413 Homework Assignment #10...

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