transmission line parameters

Question

I read that the propagation speed (m/s) of a lossless transmission line, which I know is equal to 1/sqrt(LC), is also equal to 1/sqrt(L'C') where L and C are distributed inductance and capacitance (per length values), and L' and C' are the total line inductance and capacitance (i.e. L'=L*length and C'=C*length) (see slide 21 at http://www.montana.edu/blameres/courses/eele461/lecture_notes/eele461_module_03.pdf

Can someone explain how this is? If L' = L * length and C' = C * length, it seems like 1/sqrt(L'C') would be different than 1/sqrt(LC) by a factor of sqrt(length^2) (i.e. not equal).

The answer to this will help me understand how just two parameters (characteristic impedance and time delay) are sufficient to model a lossless transmission line.

Thank you.

Answer 1

It looks to me like the slides use primed variables for per length quantities, and unprimed for total, but besides that I think you're right. As The-Photon comments, if you check the units you'll find you need the per length quantities to get m/s. For the propagation delay you can say T' = sqrt(L'C') and T = sqrt(LC) and for the impedance you can use either since you divide out any constants. So if you're calculating L and C from T and Z, you get L' and C' if you use T'.