• Electromagnetics I
  • Ch 3: Transmission Lines
  • Loc 3.18
  • Electromagnetics I
  • Ch 3
  • Loc 3.18

Measurement of Transmission Line Characteristics

This section presents a simple technique for measuring the characteristic impedance

, electrical length

, and phase velocity

of a lossless transmission line. This technique requires two measurements: the input impedance

when the transmission line is short-circuited and

when the transmission line is open-circuited.

In Section 3.16, it is shown that the input impedance

of a short-circuited transmission line is

and when a transmission line is terminated in an open circuit, the input impedance is

Observe what happens when we multiply these results together:

that is, the product of the measurements

and

is simply the square of the characteristic impedance. Therefore

(3.18.1)

If we instead divide these measurements, we find

Therefore:

(3.18.2)

If

is known in advance to be less than

, then the electrical length

can be determined by taking the inverse tangent. If

is of unknown length and longer than

, one must take care to account for the periodicity of tangent function; in this case, it may not be possible to unambiguously determine

. Although we shall not present the method here, it is possible to resolve this ambiguity by making multiple measurements over a range of frequencies.

Once

is determined, it is simple to determine

given

,

given

, and then

. For example, the phase velocity may be determined by first finding

for a known length using the above procedure, calculating

, and then

.

 

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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