In this example, we calculate the far field radiation pattern of a center-fed, linear antenna in free space. The antenna is created in FDTD with a large number of electric dipole sources with appropriate amplitude and phase values.
Simulation setup
The above screenshot shows a thin, center fed, linear antenna of length d, oriented in the z direction. When driven with a sinusoidal input, the current density is approximately
$$ J(\vec{x})=I \sin \left(\frac{k d}{2}-k|z|\right) \delta(x) \delta(y) \vec{\varepsilon} $$
for |z|
In FDTD, we can create such a current density with a series of dipoles. The amplitude of each dipole is set based on the above formula.
A box of power monitors records the radiation pattern from the antenna, and calculates the far field radar cross sections.
The group called "linear antanna" is a construction group that creates the linear antenna from a number of electric dipoles.
Far field radiation pattern
After running the simulation, use antenna_do_far_field.lsf to plot the far field radiation pattern as calculated by the analysis group called "scat_ff". The cross sections are measured in the x-z plane, and phi=0 corresponds to the x-axis. The far field radiation pattern is plotted both is both on linear and polar scales.
There is a simple analytic formula for the radiation cross section when the antenna length is equal to 1/2 lambda, or lambda. The script will plot the FDTD result together with the theoretical result. As the figures show, the agreement is very good.
Half-wavelength antenna results
Full-wavelength antenna results
Related publications
- J. D. Jackson, "Classical Electrodynamics, Second Edition", John Wiley & Sons, 1975, p. 401