9: Radiation
- Page ID
- 48175
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
In low-frequency electric circuits and along transmission lines, power is guided from a source to a load along highly conducting wires with the fields predominantly confined to the region around the wires. At very high frequencies these wires become antennas as this power can radiate away into space without the need of any guiding structure
- 9.1: The Retarded Potentials
- Maxwell's equations in complete generality are
- 9.2: Radiation from Point Dipole
- The simplest building block for a transmitting antenna is that of a uniform current flowing along a conductor of incremental length dl as shown in Figure 9-1. We assume that this current varies sinusoidally with time as
- 9.3: Point Dipole Arrays
- The power density for a point electric dipole varies with the broad angular distribution \(\sin ^{2}\theta \). Often it is desired that the power pattern be highly directive with certain angles carrying most of the power with negligible power density at other angles. It is also necessary that the directions for maximum power flow be controllable with no mechanical motion of the antenna. These requirements can be met by using more dipoles in a periodic array.
- 9.4: Long Dipole Antennas
- The radiated power, proportional to \(\left ( dl/\lambda \right )^{2}\), is small for point dipole antennas where the dipole's length \(dl\) is. much less than the wavelength \(\lambda \). More power can be radiated if the length of the antenna is increased. Then however, the fields due to each section of the antenna may not add constructively.
Thumbnail: Animation of a half-wave dipole antenna transmitting radio waves, showing the electric field lines. (Public Domain; Chetvorno via Wikipedia)