- 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
If we instead divide these measurements, we find
Therefore:
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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