ELEG413lec8 - Fundamental Antenna Parameters 1. Radiation...

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Unformatted text preview: Fundamental Antenna Parameters 1. Radiation Pattern An antenna radiation pattern is defined as “a graphical representation of the radiation properties of the antenna as a function of space coordinates. In most cases, the radiation pattern is determined in the far-field region. Radiation properties include radiation intensity, field strength, phase or polarization. Coordinate System Idealized Point Radiator Vertical Dipole Radar Dish Isotropic Omnidirectional Directional Types of Radiation Patterns Full Null Beamwidth Between 1st NULLS Radiation Pattern Lobes Main lobe Side lobes Back lobes Radiation Pattern Lobes Field Regions D R 1 R 2 Reactive near-field region λ 3 1 62 . D R = Radiating near-field (Fresnel) region λ 2 2 2 D R = Far-field (Fraunhofer) region Radiation Intensity Aside on Solid Angles ρ ρ = length arc rad . 1 = θ r sr . 1 = Ω 2 r area surface = radians ce circumfran total π 2 = 2 2 4 r r S area surface total o Ω = = = π sr r S o 2 = Ω φ θ θ d d r ds ) sin( 2 = infinitesimal area of surface of sphere φ θ θ d d r ds d ) sin( 2 = = Ω Radiation Intensity ∫ ∫ Ω = ⇒ Ω = π 4 d U P sr W d dP U tot rad tot rad ∫ ∫ = ⇒ = ds P P m W ds dP P rad tot rad tot rad rad 2 rad P r U 2 = ) , , ( r P rad φ θ decays as 1/r 2 in the far field since ) , ( φ θ U will be independent of r Radiation Intensity max 2 2 2 2 2 2 * ) , ( ) , ( 2 ) , ( 2 1 ~ 2 1 ~ ~ 2 1 ) , , ( U U U E E r U E E E H E r P rad ϕ θ ϕ θ η ϕ θ η η ϕ θ ϕ θ ϕ θ = + = + = = × = Radiation Intensity Examples . 1 ) , ( ) , ( 4 ) , , ( ) , ( 4 ) , , ( max 2 2 = = = = = = U U U const P r P r U r P r P tot rad rad tot rad rad ϕ θ ϕ θ π ϕ θ ϕ θ π ϕ θ 1. Isotropic radiator 2. Hertzian Dipole ) ( sin ) , ( ) , ( ) ( sin 4 2 ) sin( 4 2 1 2 1 ) , ( ) , , ( ) sin( 4 ) , , ( 2 max 2 2 2 2 2 2 2 θ ϕ θ ϕ θ θ π β η θ π β η η η ϕ θ ϕ θ θ π β η ϕ θ β φ θ φ β θ = = ∆ = ∆ ⋅ = + = = ∆ =-- U U U I l r e I l r E E r U r E r e I l j r E r j r j Directive Gain ) ( 1 4 ) , ( 4 4 ) , ( ) , ( ) , ( max max y directivit P U D D P U P U U U D tot rad o tot rad tot rad ave ≥ = = = = = π ϕ θ π π ϕ θ ϕ θ ϕ θ Directivity Examples . 1 . 1 ) , ( 4 ) , ( 4 ) , ( = = = = = o tot rad tot rad o D P U D P U U ϕ θ π ϕ θ π ϕ θ 1. Isotropic radiator 2. Hertzian Dipole 2 3 ) ( sin 2 3 ) , ( 4 ) , ( 3 8 4 2 ) sin( ) ( sin 4 2 ) , ( ) ( sin 4 2 2 1 ) , ( ) , , ( ), sin( 4 ) , , ( 2 2 2 0 0 2 2 4 2 2 2 2 2 = = = ∆ = ⋅ ∆ = Ω = ∆ = + = = ∆ = ∫∫ ∫ ∫- o tot rad tot rad r j D P U D I l d d lI d U P I l E E r U r E r e l j r E θ ϕ θ π ϕ θ π π β η θ φ θ θ π β η ϕ θ θ π β η η ϕ θ ϕ θ θ π β η ϕ θ π π π φ θ φ β θ Antenna Gain input P U G ) , ( 4 ) , ( ϕ θ π ϕ θ = POWER DENSITY IN A CERTAIN DIRECTION DIVIDED BY THE TOTAL POWER RADIATED...
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This note was uploaded on 12/13/2011 for the course ELEG 413 taught by Professor Mirotznik during the Spring '11 term at University of Delaware.

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ELEG413lec8 - Fundamental Antenna Parameters 1. Radiation...

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