As limited cases it is convenient to consider lines terminated in open circuit or short circuit, that is with ZR = ∞or ZR =0.

**OPEN AND SHORT CIRCUITED
LINES**

As limited cases it is
convenient to consider lines terminated in open circuit or short circuit, that
is with *ZR* = ∞or *ZR* =0. The input impedance of a line of length l is

And for the short circuit case *ZR* =0., so that

*Z _{s} *=

Before the open circuit case
is considered, the input impedance should be written. The input impedance of
the open circuited line of length l, with *ZR*
= ∞, is

*Z _{oc} *=

By multiplying the above two equations it can
be seen that

*Z*_{0} =* Z _{oc}Z_{sc}*

This is the same result as was obtained for a
lumped network. The above equation supplies a very valuable means of
experimentally determining the value of z0 of a line.

Also from the same two equations

Use of this equation in experimental work
requires the determination of the hyperbolic tangent of a complex angle. If

tanh *γl*
= *tah*(*α* + *jβ* )*l* = *U*
+ *jV*

Then it can be shown that

The value of *β* is uncertain as to quadrant. Its proper value may be selected if
the approximate velocity of propagation is known.

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Transmission Lines and Waveguides : Transmission Line Theory : Open and Short Circuited Lines |

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