# Are voltage and current waves in transmission lines an artifice?

• I
• Txema
In summary: This is the telegrapher's equation. You can also use it to calculate the electric field at any point on the line.
Txema
TL;DR Summary
Are voltage and current waves in transmission lines an artifice or a consequence of electromagnetic waves?
The operation of a transmission line is based on the axial propagation of electromagnetic waves between the two line conductors. However, the study of the transmission lines does not focus on E and B waves but on voltage and current waves.

It is considered that there are resistance, conductance, inductance and capacity distributed throughout the Length of the line conductors. This causes the instantaneous voltage and current values at points of the line to be dependent on both distance and time, that is, they are waves. There are therefore voltage and current waves spreading along the line. The E and B fields are forgotten by the greater ease of the use of voltage and current.

My question is: are the voltage and current waves approach in a line characterized by distributed R, L, G, and C an artifice that ensures electromagnetic equivalence to the existence of E and B waves, or it is a consequence of the E and B Waves E and B that coexist with them?

Kind regards;

Welcome to PF.

Txema said:
My question is: are the voltage and current waves approach in a line characterized by distributed R, L, G, and C an artifice that ensures electromagnetic equivalence to the existence of E and B waves, or it is a consequence of the E and B Waves E and B that coexist with them?
I had to look up the word "artifice" -- today I learned a new word (that I probably will never use).

Txema
You need to always go back to Maxwell's equations for questions like this (not counting QM). Voltage and current are often referred to because of simplistic approximations or measurement results. So, yes, it's E and B fields. Voltage is what your voltmeter reads. They are not necessarily contradictory, but if you think they are, go back to Maxwell.

Also, in practice EEs can be pretty sloppy when discussing this stuff. Not every conversation is in the format of a peer reviewed paper or textbook. I am especially guilty of this. Often there is an assumption that the person your talking to also took physics classes and knows what you are referring too. Often you don't want to do the work required for the rigorous exposition.

Txema and berkeman
berkeman said:
Welcome to PF. I had to look up the word "artifice" -- today I learned a new word (that I probably will never use).

Thank you very much.
English is not my usual language, perhaps the word "artifact" would have been more appropriate...
Web: A lot of pages among which I would highlight: https://www.researchgate.net/publication/260936949_A_qualitative_approach_to_electricity
books:
Introduction to electromagnetic fields and waves - Carles A. Holt (My favorite about electromagnetism)
Theory & Problems On Transmission Lines - Robert A. Chipman

I take note for future occasions.

DaveE said:
You need to always go back to Maxwell's equations for questions like this (not counting QM). Voltage and current are often referred to because of simplistic approximations or measurement results. So, yes, it's E and B fields. Voltage is what your voltmeter reads. They are not necessarily contradictory, but if you think they are, go back to Maxwell.
My doubt came precisely from the fact that in the study of transmission lines, scalar potential and vector potential are not used, a method that guarantees compliance with Maxwell's equations, to reach the E and B fields. Instead they are used geometric similarities between the fields of a TEM wave and the fields of supposed static surface charges and currents whose V and I are dynamized as waves, this is what made me think that perhaps it was simply a model of electromagnetic equivalence. From your answer I deduce that V and I waves are measurable, therefore real.
Thank you very much.

The telegrapher's equation is an effective description of the em. field moving along a land line. It's much simpler to derive than to solve the corresponding boundary-value problem of the Maxwell equations. The idea is that you deal with wave lengths that are long compared to the distance of the two wires (but of course not necessarily long compared to the length of the wires themselves). Then in an infinitesimal region parallel to the wire you can use the integral form of Maxwell's equations in the quasistationary approximation and instead of describing the geometric details of the wire in detail and then solve for the boundary-value problem of the Maxwell equations, you just describe it with the usual effective quantities of a compact circuit, i.e., by resistance, capacitance, and inductivity per unit length. Then you get a wave equation for the "voltage" and "current" along the wire, the telegrapher's equation.

berkeman, Txema and DaveE
Ok, I understand the explanation, thanks a lot.
The fact that telegrapher's equations can be obtained simply by applying Kirchhoff's rules to a circuit of infinitesimal length with lumped R,L in series and G,C in parallel and di, dv difference between input and output was confusing me.

vanhees71 and berkeman

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