Discussion
The reflection coefficient \(k_{r}\), characteristic impedance \(Z_{0}\), and load impedance \(Z_{L}\) of a transmission line are connected together by the relation :
Answer: C
The relation is \(k_{r} = \frac{Z_{L} - Z_{0}}{Z_{0} + Z_{L}}\).
At the load, the voltage and current must satisfy \(V/I = Z_{L}\), while each travelling wave on the line has \(V/I = \pm Z_{0}\). With incident wave \(V^{+}\) and reflected wave \(V^{-}\):
\[ \begin{aligned} Z_{L} &= Z_{0}\frac{V^{+} + V^{-}}{V^{+} - V^{-}} \\ k_{r} &= \frac{V^{-}}{V^{+}} = \frac{Z_{L} - Z_{0}}{Z_{L} + Z_{0}} \end{aligned} \]
Checks: a matched load (\(Z_{L} = Z_{0}\)) gives no reflection, a short circuit gives -1 and an open circuit +1. The first option becomes infinite for a matched load, and the others do not even have the dimensionless form a reflection coefficient needs.
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