aawaveguideaλ=θΩλ==σ22a22aλ=ΩSolid Angle:Receiving Cross Section:λ√4πλ√4πhνhνhνCapture Cross-Section of an Ideal Isotropic Antenna = λ2/4πcaptured power Pin= λ2/4π × Intensityλ = Vacuum WavelengthFor a highly directional antenna, Capture Cross-Section = λ2/ Ωwhere Ω is the acceptance solid-angle.Radiated Power is proportional to{charge×acceleration}2:{}2223o223o223o23oRa6v6v61v61IIcqaNacNqcdtdNqcradiation×=××⎟⎟⎠⎞⎜⎜⎝⎛πεω=⎭⎬⎫⎩⎨⎧×⎟⎟⎠⎞⎜⎜⎝⎛πεω=ω⎟⎟⎠⎞⎜⎜⎝⎛πε⎭⎬⎫⎩⎨⎧⎟⎟⎠⎞⎜⎜⎝⎛πεBy time reversal, the captured power: Intensity × λ2/4π = Pin= I2× RradiationIntensity × λ2/4π = Pin=radiation2RVdepends on geometry,frequency,etc.aThe Concept of Antenna Radiation ResistanceEquation 9-35 of UlabyE(ω)Rradiation≈ 50Ω≈377Ω/2π 377Ω = in MKS unitsin a very good antennaRradiation≈ (a/λ)2×377Ω ≈1Ωin a bad antennaooεµ377Ω = 4π/c in CGS unitsAntenna Radiation ResistanceOhmicResistanceLoadResistorVoltageSourceRlradininRP2V ×=RradiationRΩ1RRRRREfficiencyntennaAradiationradiationradiation<≈+=ΩΩλ/250nmAgAgimpedance match at R1≈ Rrad+RΩRadiation capture-cross-section σ ω
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