and when a transmission line is terminated in an open circuit, the input impedance is \[Z_{in}^{(OC)} = -jZ_0 \cot\beta l \nonumber \] Observe what happens when we multiply these results together: \[Z...and when a transmission line is terminated in an open circuit, the input impedance is \[Z_{in}^{(OC)} = -jZ_0 \cot\beta l \nonumber \] Observe what happens when we multiply these results together: \[Z_{in}^{(SC)} \cdot Z_{in}^{(OC)} = Z_0^2 \nonumber \] that is, the product of the measurements \(Z_{in}^{(OC)}\) and \(Z_{in}^{(SC)}\) is simply the square of the characteristic impedance.
