# Non-uniform transmission line

Is there a way to model a transmission line (TL) with different values of R and C along the line? Usually when one wants to model TL, he refers to an infinitely short piece of line, defines a R, L, G, C per unit length and solve all the equations. In my case, the values of R and C per unit can vary along the line. I was wondering if there is a way to model such TL.

• Do you mean continuously varying R(x), L(x), etc. (for x position along the line), or step changes (individual TL segments, of constant parameters, joined together), or given loads at positions (lumped elements)? (These are subsets of each other of course, but the latter cases are easier to work with.) Commented Jul 13, 2023 at 13:13
• If an answer suggests a work-around that runs in a simulator, it could be a useful tool for modelling an antenna such as a monopole. Commented Jul 13, 2023 at 14:33
• @TimWilliams I have individually different TL segments, each of them with constant R and C, but joined together in an unique TL. Commented Jul 14, 2023 at 14:49

Is there a way to model a transmission line (TL) with different values of R and C along the line?

I was wondering if there is a way to model such TL.

Yes, that is a very basic thing that you do in transmission line design, and the design of distributed component filters etc.

You will need to get a bit deeper into transmission line theory, and then, it'll become pretty natural to you: You start by modelling your transmission line as segments of constant¹ impedance, then calculate the effects on the wave on each transition, and combine that into one full view of the complex transmission line system.

Usually when one wants to model TL, he refers to an infinitely short piece of line, defines a R,L,G,C per unit length and solve all the equations.

You typically leave the "R-C transmission line" model behind at that point – it's a bit unwieldy, has problems dealing with losses, etc. Your different transmission line segments have what we call characteristic impedance, and that single number together with the length of the segment suffices.

ABCD matrices and the Smith chart are two tools you'll find paramount when learning about that. This is all really well-covered and non-trivial to explain without drawing a lot of figures, so I'll leave you up to find a textbook on transmission line theory (for me, that was the scriptum to a third or fourth semester lecture, Basics of High Frequency Technology).

¹ or sometimes, as segments of continuously changing impedance, but I'll put bowties and PCB antennas under "advanced concepts" here