The transmission line theory is common knowledge described e.g. by Küpfmüller (1973) or Meinke and Gundlach (1986).
Motivation
Communication among several nodes requires communication media and unidirectional or bidirectional interfaces which connect each of them. In the electrical use case3 transceivers and bus-drivers work as interfaces while (bus) cables work as media. As long as the distance between the interfaces is very short, (bus) cables between them can almost be interpreted as perfect short circuits. If the distance increases, various equivalent circuits based on discrete components are allowed. Their selection depends on the application. If the distance increases more the interpretation of (bus) cables as transmission lines is recommended.
The transmission line theory is introduced to almost all electrical engineering students during their study programs. Effects like propagation delay, damping, refraction and reflection appear. A clear threshold to decide whether the transmission line theory shall be used is not defined. In case of NRZ coding in the base band it depends on the communication speed and on the edge timing or rather on the expected or required accuracy.
Figure 1.
Serial communication among distributed nodes via bus cables
Usual automotive serial communication based on electrical cables like CAN as well as FlexRay™ use NRZ coding in the base band. They require the interpretation of their (bus) cables as transmission lines. Their communication signals can be seen as superposition of voltage or current steps representing 1\0 and 0/1 edges in the time domain. However, automotive serial communication based on LIN can be seen as exception; its communication speed is slow enough to allow replacing (bus) cables by discrete capacitances, often.
Scope
Transmission lines are built up by two more or less parallel wires (or strands)4. Voltages between the wires and currents through the wires depend on the position of the test plain on the line. The theory describes an approach and solutions covering the measurable behaviors. Idealizations enable the theory deriving straight forward solvable differential equations5. The theory is based on distributed circuits or rather on putting an infinite number of infinitesimal short circuits in a row. Each of these circuits is build by discrete components.
Table 1.
Electrical effects at cables (or rather bus lines)
| Effect when measuring into the … |
| … Input port at an open ended cable |
… Input port at a short circuited cable |
|
|
| Common Usage Definitions |
| Conductance per length |
(1) |
Resistance per length |
(2) |
| Capacitance per length |
(3) |
Inductance per length |
(4) |
Figure 2.
Transmission line with the length ℓ and its infinitesimal representation