3. Antenna characteristics
Scattering (S)-parameters.
Figure 1. Two port device waves and directions
\[\begin{pmatrix}
b_1 \\
b_2
\end{pmatrix}
= \begin{pmatrix} S_{11} & S_{12} \\ S_{21} & S_{22} \end{pmatrix}\begin{pmatrix} a_1 \\ a_2 \end{pmatrix}\]
At a certain frequency:
-
\(S_{11} = \frac{b_1}{a_1}\) is the input port voltage reflection coefficient (complex)
-
\(S_{12} = \frac{b_1}{a_2}\) is the reverse voltage gain
-
\(S_{21} = \frac{b_2}{a_1}\) is the forward voltage gain
-
\(S_{22} = \frac{b_2}{a_2}\) is the output port voltage reflection coefficient
Relation to VSWR:
-
At port 1, the VSWR is \(= \frac{1+\left|S_{11}\right|}{1-\left|S_{11}\right|}\)