Confusion in understanding characteristic impedance and input impedance of an open circuited transmission line

Question

The characteristic impedance Zo can be derived by considering LC sections throughout the line with open circuit at the end of the line, and this value is independent of length of the transmission line but when we calculate the input impedance for the line of finite length(l) with open circuit at the end of the line, we get Zo * coth(gamma x l).

Since characteristic impedance is independent of length, we get same value everywhere but when we calculate the input impedance for open circuit, we get different value.

I am unable to understand why is that happening? Since I believe both are impedances and can be calculated in a similar fashion, so the value in both the case should be same.

Answer 1

If the transmission line is either infinitely long or terminated with the characteristic impedance, there are no reflections back to input port so input impedance equals characteristic impedance.

If you have reflections, like in the case of leaving transmission line end open, signal reflects back from the end to input. So the signal being fed to input port not only drives the transmission line but it has to drive against the reflected wave too. Phase of reflected wave depends on time travelled on the line and thus the length of the line, so this is why the input port appears to have different impedance based on transmission line length.