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

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.