Transmission Lines

Transmission lines are very important historically since they enabled the communication over long distances. Other than that, they are very interesting from a didactical perspective:

  • one-dimensional systems that can be characterized by very few parameters (in the end, it's only the impedance \(Z\))
  • very good example for slowly varying fields approximation, where \(\nabla\times\mathbf{B}\left(\mathbf{r},t\right)\approx\mu_{0}\mathbf{j}\left(\mathbf{r},t\right)\) and thus the coupling of electric and magnetic field is solely given by Faraday's law \(\nabla\times\mathbf{E}\left(\mathbf{r},t\right)=-\dot{\mathbf{B}}\left(\mathbf{r},t\right)\)
  • fundamental physical effects like wave propagation and reflection can be explained which will be a good bridge to complicated relativistic phenomena

With these facts in mind, we hereby dedicate a whole section to transmission lines.