lecture31 - Lecture 31 Wire Antennas In this lecture you...

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1 ECE 303 – Fall 2006 – Farhan Rana – Cornell University Lecture 31 Wire Antennas In this lecture you will learn: • Generation of radiation by real wire antennas Short dipole antennas Half-wave dipole antennas Three-half-wave dipole antennas Small wire loop antennas – magnetic dipole antennas ECE 303 – Fall 2006 – Farhan Rana – Cornell University Center Fed Wire Antenna Consider the following wire antenna fed via a transmission line: d Z o () ( ) ' ' 4 ˆ ' ' 4 ˆ ' ' ˆ ' 4 ˆ ' ' 4 ' cos ' 2 2 ' ˆ . ˆ ' ˆ ' dz e z I e r z dz e z I r z r A dz e z z r z I z dv e r r r J r A z k j d d r k j o z z r r k j o ff z z r k j o r r k j o θ π µ = = ∫∫∫ = r r r r r r r r r r r r ( ) ( ) ( ) ( ) y x z I z r J δ ˆ = r r x z I If one is interested in radiation far-fields only, then assume: r d r << λ 2 , Far-field approximation - also called the Fraunhoffer approximation ( ) ( ) ( ) ( ) ( ) φ cos ˆ sin sin ˆ cos sin ˆ ˆ z y x r + + = Recall that:
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2 ECE 303 – Fall 2006 – Farhan Rana – Cornell University Center Fed Short Dipole Wire Antenna - I Short dipole wire antenna fed via a transmission line: d Z o () () ()() y x z I z r J δ ˆ = r r x z I π λ 2 << d Short dipole Make an assumption for the current distribution on the antenna – a triangular distribution z I d/2 -d /2 I ( z ) () r k j eff o d d r k j o z k j d d r k j o ff e r Id z dz z I e r z dz e z I e r z r A = = µ θ 4 ˆ ' ' 4 ˆ ' ' 4 ˆ 2 2 cos ' 2 2 r r 2 ' << < d z Since: Where: 2 2 ' ' 2 2 d d d I dz z I d I eff d d eff = = = A Hertzian-dipole-like solution ECE 303 – Fall 2006 – Farhan Rana – Cornell University Center Fed Short Dipole Wire Antenna - II Short dipole wire antenna fed via a transmission line: d Z o ( ) ( ) ()() y x z I z r J ˆ = r r x z I 2 << d Short dipole z I d/2 I ( z ) r k j eff ff e r Id k j r H = φ sin 4 ˆ r r r k j eff o ff e r Id k j r E = η sin 4 ˆ r r The radiation from a short dipole looks like that from a Hertzian dipole except that d is replaced by d eff () () { } 2 2 * sin 4 2 ˆ Re 2 1 , r Id k r r H r E t r S eff o ff ff = × = r r r r r r 2 2 00 2 12 sin ˆ . , eff o rad Id k d d r r t r S P ππ = ∫∫ = r r
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3 ECE 303 – Fall 2006 – Farhan Rana – Cornell University Center Fed Short Dipole Wire Antenna - III Short dipole wire antenna fed via a transmission line: d Z o ( ) ( ) ()() y x z I z r J δ ˆ = r r x z I π λ 2 << d Short dipole z I d/2 -d /2 I ( z ) Antenna Gain: For a short dipole the gain is: () θ φ 2 2 sin 2 3 4 ˆ . , , = = r P r t r S G
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This note was uploaded on 02/02/2008 for the course ECE 3030 taught by Professor Rana during the Fall '06 term at Cornell University (Engineering School).

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lecture31 - Lecture 31 Wire Antennas In this lecture you...

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