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
Zs = Z0 tanh γl
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
Zoc = Z0 coth γl
By multiplying the above two equations it can be seen that
Z0 = ZocZsc
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.