Chapt6c

Chapt6c - EEE 443 Antennas for Wireless Communications by...

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1 Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 6 Arrays: Linear, Planar, & Circular EEE 443 Antennas for Wireless Communications by Constantine A. Balanis Lecture #22 Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 6 Arrays: Linear, Planar, & Circular x x y y d d d d d 1 2 3 N-1 N z θ Uniform Linear Array Fig. 6.5(a) Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 6 Arrays: Linear, Planar, & Circular Copyright©2005 by Constantine A. Balanis All rights reserved Chapter 6 Arrays: Linear, Planar, & Circular Linear Array Phase Excitation Broadside = 0, Array Type 2 , 0,1,. . Ordinary End-Fire Phase Excit ation ( ) nn kd β βπ ±= = m 0 0 Hansen-Woodyard End-Fire ( for 0 , 180 ) 0 , 1 80 ) o o f N or for kd π θθ ⎛⎞ =+ −= + = + = ⎝⎠ m o Scanning ( = ) cos o kd = Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 6 Arrays: Linear, Planar, & Circular Planar Array Fig. 6.28b Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 6 Arrays: Linear, Planar, & Circular Half-Power Beamwidths for a Conical Main Beam Oriented Toward θ=θ o , φ=φ o Fig. 6.36 sin co sin cos 0 sin sin s sn 0 in si xx o o xxoo x yyo o y yy o o kd kd kd kd ψ θφβ θφ φ = += = =−
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2 Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 6 Arrays: Linear, Planar, & Circular Half-Power Beamwidth () 00 22 2 0 1 cos si n c 6-95 os h xy φφ θ Θ= ⎡⎤ ⎛⎞ ⎢⎥ + ⎜⎟ ΘΘ ⎝⎠ ⎣⎦ 0 x HPBW of corresponding broadside linear array of M elements 0 y HPBW of corresponding broadside linear array of N elements Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 6 Arrays: Linear, Planar, & Circular Effective Length as a Function of Scan Angle 0 0 L 0 0 cos sec L L = z 0 0 If hx y h x y y x MN θθ = Θ Θ=Θ = (6-95a) Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 6 Arrays: Linear, Planar, & Circular 0 0 6-96 1 sin cos I 6-96a f h y Ψ= + Ψ = Θ =Θ =Θ Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 6 Arrays: Linear, Planar, & Circular Directivity , corresponding directivities of linear broadside arrays, respectively, with lengths & elements ( , ),( , ) DD L MLN = cos oo x y D π = 2 32,400 ( ) (degrees ) o AA D rads ≅= ΩΩ (6-101) (6-100) Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 6 Arrays: Linear, Planar, & Circular A Beam Solid Angle Ω 0 sec( ) sin cos ( ) sin cos ( ) (6 97) hh yx A A φ =Θ Ψ = ++ Ω Ω 6-98 Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 6 Arrays: Linear, Planar, & Circular Circular Array
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3 Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 6 Arrays: Linear, Planar, & Circular Uniform Circular Array Fig. 16.50 Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 6 Arrays: Linear, Planar, & Circular Planar Uniform Circular Array Fig. 16.51 Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 6 Arrays: Linear, Planar, & Circular Spherical Array Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 6 Arrays: Linear, Planar, & Circular Geometry of an N-element Circular Array Fig. 6.37 Copyright©2007 by Constantine A. Balanis
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This note was uploaded on 11/01/2009 for the course EEE 443 taught by Professor Balanis during the Spring '08 term at ASU.

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Chapt6c - EEE 443 Antennas for Wireless Communications by...

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