Q:

Standing Wave in a transmission line and Resonance

let's consider a transmission line of length L closed on a mismatched load. So, there will be a travelling wave and a reverse travelling wave:
V(z) = V+(z) + V-(z)
My question is: will there always be a standing wave, or does it depend on if it is true that L = n * Lambda/2, with n integer?
Sometimes I read that to have a standing wave it is sufficient to have two waves of same frequency going in opposite direction, while sometimes I read that it is necessary that the length of the medium respects the previous formula.

A:

There will be a standing wave whenever you terminate a transmission line with a mismatched load.
The line is resonant when the standing wave has a minimum or maximum of amplitude at the input (or feed point) of the line. If the termination is short, open, or has purely real impedance, then this occurs when the line length is $L = n\frac{\lambda}{4}$ for some integer $n$. If the termination is capacitive or inductive, resonance will occur for lengths that are offset from $n\frac{\lambda}{4}$, but still spaced by quarter wavelengths.

