Chapt4a

Chapt4a - EEE 443 Antennas for Wireless Communications by...

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1 Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 4 Linear Wire Antennas EEE 443 Antennas for Wireless Communications by Constantine A. Balanis Lecture #10 Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 4 Linear Wire Antennas Chapter 4 Linear Wire Antennas Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 4 Linear Wire Antennas 4 Linear Wire Antennas Chapter Effects Ground Conductors Perfect Infinite on or Near Elements Linear Dipole Wavelength Half Dipole Length Finite Separation Region Dipole Small Dipole mal Infinitesi on Introducti 8 . 4 7 . 4 6 . 4 5 . 4 4 . 4 3 . 4 2 . 4 1 . 4 Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 4 Linear Wire Antennas Infinitesimal Dipole (top hat) Fig. 4.1a (/ 5 0 ) λ A Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 4 Linear Wire Antennas Electric Field Orientation Fig. 4.1b Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 4 Linear Wire Antennas , J M , E H , A F Integration Integration Differentiation 1 Path 2 Path Sources Vector Potentials Radiated Fields Fig. 3.1
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2 Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 4 Linear Wire Antennas Spatial And Time-Varying Current (4-1) ˆ (' ) ;) R e [(' ) ] ˆ Re[ ] ˆ ;) c o s ( ) zo j t jt Iz aI zt Ize aIe zt aI t ω = = = = I I Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 4 Linear Wire Antennas Time-Varying Current Distribution Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 4 Linear Wire Antennas /2 Approximatio ) ' 4 ˆ ' 4 n: jkR e jkr R e A d R e r Aa I d z r μ π = = A A A A A Vector Potential Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 4 Linear Wire Antennas Dipole And Geometry Fig. 4.4a Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 4 Linear Wire Antennas ˆ ' 4 ˆ () 4 ˆ 4 jkr o z jkr o z jkr o z Ie A ad z r a r r = = = A A A A (4-4) Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 4 Linear Wire Antennas ˆˆ 4 ; 0 4 jkr o zz z jkr o zx y I e aA r I Ae A A r == = A A = z y x r A A A A A A 0 cos sin sin sin cos cos cos cos sin sin cos sin φ θ ± ± ± ±² ± ± ± ±³ ´ rs T [ ] = s A [ ] rs T [] r A (4-5)
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3 Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 4 Linear Wire Antennas = r A ] [ 1 ] [ rs T = s A ] [ t rs T ] [ = s A ] [ sr A ] [ s A ] [ Provided [ ] is orthonormal T [] [] = = 0 sin - cos cos sin cos sin sin sin cos cos cos sin θ φ t s sr T A = r A ] [ t rs T ] [ = s A ] [ sr A ] [ s A ] [ Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 4 Linear Wire Antennas ˆˆ 4 cos cos 4 sin sin 4 0 jkr o zz z jkr o rz jkr o z I AaA a e r I AA e r I A Ae r A μ π θθ == =− = A A A (4-6a) (4-6b) (4-6c) Copyright©2007 by Constantine A. Balanis All rights reserved Chapter 4 Linear Wire Antennas = × = r A rA r r a A H ) ( 1 ˆ 1 0 1 sin 1 4
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Chapt4a - EEE 443 Antennas for Wireless Communications by...

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