# Transmission Lines as Two-Port Devices

Figure 3.3.1 shows common ways to represent transmission lines in circuit diagrams. In each case, the source is represented using a Thévenin equivalent circuit consisting of a voltage source

in series with an impedance

.^{1} In transmission line analysis, the source may also be referred to as the *generator*. The termination on the receiving end of the transmission line is represented, without loss of generality, as an impedance

. This termination is often referred to as the *load*, although in practice it can be any circuit that exhibits an input impedance of

.

The two-port representation of a transmission line is completely described by its length ll along with some combination of the following parameters:

- Phase propagation constant , having units of rad/m. This parameter also represents the wavelength in the line through the relationship . (See Sections 1.3 and 3.8 for details.)
- Attenuation constant , having units of 1/m. This parameter quantifies the effect of loss in the line. (See 3.8 for details.)
- Characteristic impedance , having units of ΩΩ. This is the ratio of potential (“voltage”) to current when the line is perfectly impedance-matched at both ends. (See Section 3.7 for details.)

These parameters depend on the materials and geometry of the line.

Note that a transmission line is typically not transparent to the source and load. In particular, the load impedance may be

, but the impedance presented to the source may or may not be equal to

. (See Section 3.15 for more on this concept.) Similarly, the source impedance may be

, but the impedance presented to the load may or may not be equal to

. The effect of the transmission line on the source and load impedances will depend on the parameters identified above.

## Footnotes

- 1
For a refresher on this concept, see “Additional Reading” at the end of this section.

## Additional Reading

- “Thevenin’s theorem” on Wikipedia.

Ellingson, Steven W. (2018) Electromagnetics, Vol. 1. Blacksburg, VA: VT Publishing. https://doi.org/10.21061/electromagnetics-vol-1 CC BY-SA 4.0

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