Satellite Antenna Pattern

In the section above the link budgets were calculated assuming the max transmit antenna gain. However, per section 6.4.1 of TR 38.811, we know that the normalized antenna gain pattern, corresponding to a typical reflector antenna with a circular aperture, is considered

\[\ \ \ \ \ \ \ \ \ \ \ \ \ 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ for\ \theta = 0\]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ 4\left| \frac{J_{1}(kasin\theta)}{kasin\theta} \right|^{2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ for\ 0 < \ |\theta| \leq 90{^\circ}\]

where J1(x) is the Bessel function of the first kind and first order with argument x, a is the radius of the antenna's circular aperture, \(k\ = \frac{2\pi f}{c}\) is the wave number, f is the frequency of operation, c is the speed of light in a vacuum and \(\theta\) is the angle measured from the bore sight of the antenna's main beam. Note that ka equals the number of wavelengths on the circumference of the aperture and is independent of the operating frequency. The above expression provides the gain in linear scale and it needs to be converted to dB scale. The normalized gain pattern for \(a\ = \ 10\frac{c}{f}\) (aperture radius of 10 wavelengths) is shown below

_images/Figure-113.png

Figure-1: Antenna gain pattern for aperture radius 10 wavelengths, \( a = 10\frac{c}{f} \)