Chapter: Transmission Lines and Waveguides : Transmission Line Theory

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.

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 = 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

Z_oc = Z₀ coth γl

By multiplying the above two equations it can be seen that

Z₀ = Z_ocZ_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 |