Transmission Lines for Serial Communication: Theory and Practice

Transmission Lines for Serial Communication: Theory and Practice

Jürgen Minuth
Copyright: © 2013 |Pages: 33
DOI: 10.4018/978-1-4666-2976-9.ch006
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Abstract

Automotive bus systems like e.g. LIN, CAN, and FlexRay™ distribute their serial data streams NRZ1 coded in the base band among the communication nodes. The nodes are interconnected by passive nets. Depending on the type of application some of these nets may consist of up to one hundred meters of different bus cables arranged in various topologies. The individual pieces of information inside the data streams are represented by voltage steps and current steps. They have to be passed among all connected nodes via the bus cables. The succeeding sections introduce the commonly known transmission line theory focused of the physical effects being relevant for automotive serial bus communication in the time domain.
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Transmission Lines

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

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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 length978-1-4666-2976-9.ch006.m05 (1)Resistance per length978-1-4666-2976-9.ch006.m06 (2)
Capacitance per length978-1-4666-2976-9.ch006.m07 (3)Inductance per length978-1-4666-2976-9.ch006.m08 (4)
Figure 2.

Transmission line with the length ℓ and its infinitesimal representation

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