File:Lineare antennen2.svg

Summary[edit]

DescriptionLineare antennen2.svg	Deutsch: Winkelverteilung der Strahlung und Stromverteilung an einem Dipol für verschiedene Wellenlängen Русский: Диаграммы направленности в вертикальной плоскости и диаграммы тока в диполях
Date	15 September 2010
Source	Own work based on: de:Datei:Lineare antennen2.jpg
Author	Averse in Zusammenarbeit mit Ulfbastel. SVG Konvertierung: Wdwd
Other versions	German .svg Russian .svg based on a drawing: Lineare antennen2.jpg
SVG development InfoField	The SVG code is valid.   This diagram was created with Inkscape, or with something else.   The file size of this SVG diagram may be irrationally large because its text has been converted to paths inhibiting translations.

Directivity diagrams[edit]

Calculation of directivity diagrams (E-field) has been done with Gnuplot in polar mode with 500 points per diagram based on the following equations, which are taken from Klaus Kark: Antennen und Strahlungsfelder, ISBN 978-383480216-3, Page 245-250, except the Hertzian ;-) and the expression for "I~sin" (own Mathcad calculation). The third column gives the total radiated power integrated over the full solid angle based on the expressions in the second column.

Dipole	${\displaystyle {\frac {|E|}{r}}=f(\theta )}$	${\displaystyle \int _{0}^{\pi }f(\theta )^{2}\cdot 2\pi \sin(\theta )\mathrm {d} \theta }$
isotropic	1	${\displaystyle 4\pi \approx 12.57}$
Hertzian dipole	${\displaystyle \textstyle \sin \theta }$	${\displaystyle {\frac {8\pi }{3}}\approx 8.38}$
λ/2 dipole	${\displaystyle {\frac {\cos({\frac {\pi }{2}}\cdot \cos(\theta ))}{\sin(\theta )}}}$	${\displaystyle \approx 7.66}$
λ dipole "I~|sin|"	${\displaystyle {\frac {\cos ^{2}({\frac {\pi }{2}}\cdot \cos(\theta ))}{\sin(\theta )}}}$	${\displaystyle \approx 5.21}$
λ dipole "I~sin"	${\displaystyle {\frac {\sin \theta \,|1-e^{2\pi i\cos \theta }|}{2-2\cos 2\theta }}}$	${\displaystyle \approx 2.45}$
3λ/2 dipole	${\displaystyle {\frac {\cos({\frac {3\cdot \pi }{2}}\cdot \cos(\theta ))}{\sin(\theta )}}}$	${\displaystyle \approx 11.05}$
2λ dipole	${\displaystyle {\frac {\sin ^{2}(\pi \cdot \cos(\theta ))}{\sin(\theta )}}}$	${\displaystyle \approx 6.80}$

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