1. Faraday’s law of induction

\[V = - N \dfrac{\mathrm{d}}{\mathrm{d}t}\Phi_B\]

2. Transmission lines

3. Antenna characteristics

Scattering (S)-parameters.

TwoPortNetworkScatteringAmplitudes
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 \(= \frac{1+\left|S_{11}\right|}{1-\left|S_{11}\right|}\)