Transient (Time domain) in transmission lines

[radagast_]

Hello.
I am watching this video:
https://www.youtube.com/watch?v=xIQtnQ9XPbE

and he says there:

Note how the reflections "bounce" back and forth along the 100-ohm segment, eventually converging into a steady-state system after the 3rd bounce or so.

I see that the wave turns into a "normal" sinus in the end, but it's not constant.
I think, that even on an unmatched transmission line, the waves should go back and forth, but eventually turn into a constant voltage. Isn't that correct?
If not, and the correct answer is that the steady state IS the final wave there - how do I calculate the voltage? is it the RMS of the wave?

Thank you.

 

[Bob S]

When a TEM wave in a cable goes from one medium (cable) to another, If there is an impedance mismatch (and the signal source is a voltage source), there is a reflection and a standing wave. Furthermore if the propagation velocity changes, the waves "pile up" in the downstream cable. There are two equations that are relevant:

Cable impedance is proportional to

Z = sqrt(1/ε)

and the propagation velocity is proportional to

and v = βc = 1/sqrt(ε)

where ε is the dielectric constant of the dielectric in the cable. A high dielectric constant reduces both the cable impedance and the propagation velocity.

If the signal source impedance does not equal the cable impedance, there is a reflection of the backward-propagating signal, producing a standing wave.

Bob S

 

[radagast_]

Thanks.

 

[Bob S]

For my previous post, the characteristic impedance of a coaxial cable is about

Z = (1/2 pi) sqrt(μ₀/εε₀) Ln(R/r)

where R and r are the outer and inner radii of the coax, and sqrt(μ₀/ε₀) = 377 ohms.

Bob S