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Unformatted text preview: 8 Radiation fields of dipole antennas • Radiation fields of a ˆ z-directed Hertzian dipole are repeated in the margin. x y z θ φ r ˜ J = ˆ z ˜ J z ˜ E = ˆ θ ˜ E θ ˜ H = ˆ φ ˜ H φ ˜ E × ˜ H * Radiation fields: ˜ E = jη o Ik Δ z sin θ e- jkr 4 πr ˆ θ and ˜ H = jIk Δ z sin θ e- jkr 4 πr ˆ φ. • In this lecture we will first obtain the radiation fields of short dipole antennas by superposing the Hertzian dipole fields. x z Δ z L 2- L 2 (a) Short dipole--- undriven x z Δ z L 2- L 2 (b) Driven short dipole modeled as a stack of Hertzian dipoles ˜ I ( z ) Gap, input port ˜ I (0) = I o • A “short dipole” is a practical antenna — as opposed to a hypothetical Hertzian dipole — consisting of a pair of thin straight conducting wires of equal lengths L 2 placed along a common axis leaving a short gap between them (see margin). – A short dipole is typically used by connecting a “source” across the gap that constitutes the “input port” of the dipole antenna. – Let’s assume that the source is an independent current source I ( t ) = I o cos ωt A ⇔ ˜ I = I o ∠ 0 = I o A and that the gap is an infinitesimal Δ z so that the dipole and its input port occupy the region- L 2 < z < L 2 in total. – We can then envision the entire dipole, including its input port, to be a stack of Hertzian dipoles of lengths Δ z , with each Hertzian dipole centered about position z (in the interval- L 2 < z < L 2 ) carrying a current ˜ I ( z ) , subject to boundary conditions ˜ I (0) = I o ∠ A and ˜ I ( ± L 2 ) = 0 . 1 In conformity with these boundary conditions we will assume that ˜ I ( z ) is a triangular current distribution x z Δ z L 2- L 2 ˜ I ( z ) = I o ( z L ) ˜ I (0) = I o Triangular current distribution ˜ I ( z ) = I o ( z L ) A . • What are the radiation fields of the short dipole antenna described above?...
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