There is something I don't understand from a solved exercise of antennas coupling and I hope someone could help me to understand.
This is not an exercise I have to solve.
Given two dipoles each aligned on the z axis and placed at a distance \(0.1\lambda\) on the x axis so
\(\Psi = 0.1(2\pi) \sin(\theta)\cos(\varphi)\)
the array factor given by the example is:
\(F_A(\Psi) = 1 - 0.77\exp(\mathrm i(\Psi + 0.67))\)
and the maximum of radiation given by the exercise is
\(F_A(\Psi) = 1.09\) for \(\theta = \pi/2\) and \(\varphi = 0\).
The exercise explicitly says that the result is given calculating \(F_A(\Psi)\) for the angles just above.
But when I try to solve for \(\varphi\), I fall into a math error:
\(
\begin{align}
& 0.1(2\pi)\sin(\theta)\cos(\varphi) + 0.67 = 0\\
& \cos(\varphi) = -1.066
\end{align}
\)
since \(\arccos(.)\) is not defined for -1.066.
So what's the problem with my math ?
Thank you.
This is not an exercise I have to solve.
Given two dipoles each aligned on the z axis and placed at a distance \(0.1\lambda\) on the x axis so
\(\Psi = 0.1(2\pi) \sin(\theta)\cos(\varphi)\)
the array factor given by the example is:
\(F_A(\Psi) = 1 - 0.77\exp(\mathrm i(\Psi + 0.67))\)
and the maximum of radiation given by the exercise is
\(F_A(\Psi) = 1.09\) for \(\theta = \pi/2\) and \(\varphi = 0\).
The exercise explicitly says that the result is given calculating \(F_A(\Psi)\) for the angles just above.
But when I try to solve for \(\varphi\), I fall into a math error:
\(
\begin{align}
& 0.1(2\pi)\sin(\theta)\cos(\varphi) + 0.67 = 0\\
& \cos(\varphi) = -1.066
\end{align}
\)
since \(\arccos(.)\) is not defined for -1.066.
So what's the problem with my math ?
Thank you.