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.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

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

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