# Lumped-Element Model

It is possible to ascertain the relevant behaviors of a transmission line using elementary circuit theory applied to a differential-length lumped-element model of the transmission line. The concept is illustrated in Figure 3.4.1, which shows a generic transmission line aligned with its length along the

axis. The transmission line is divided into segments having small but finite length

. Each segment is modeled as an identical two-port having the equivalent circuit representation shown in Figure 3.4.2. The equivalent circuit consists of 4 components as follows:

- The resistance represents the series-combined ohmic resistance of the two conductors. This should account for
*both*conductors since the current in the actual transmission line must flow through both conductors. The prime notation reminds us that is resistance*per unit length*; i.e., /m, and it is only after multiplying by length that we get a resistance in . - The conductance represents the leakage of current directly from one conductor to the other. When , the resistance between the conductors is less than infinite, and therefore, current may flow between the conductors. This amounts to a loss of power separate from the loss associated with above. has units of S/m. Further note that is
*not*equal to 1/R′1/R′ as defined above. and are describing entirely different physical mechanisms (and in principle*either*could be defined as either a resistance or a conductance). - The capacitance represents the capacitance of the transmission line structure. Capacitance is the tendency to store energy in electric fields and depends on the cross-sectional geometry and the media separating the conductors. has units of F/m.
- The inductance represents the inductance of the transmission line structure. Inductance is the tendency to store energy in magnetic fields, and (like capacitance) depends on the cross-sectional geometry and the media separating the conductors. has units of H/m.

In order to use the model, one must have values for

,

,

, and

. Methods for computing these parameters are addressed elsewhere in this book.

Ellingson, Steven W. (2018) Electromagnetics, Vol. 1. Blacksburg, VA: VT Publishing. https://doi.org/10.21061/electromagnetics-vol-1 CC BY-SA 4.0

## Explore CircuitBread

Get the latest tools and tutorials, fresh from the toaster.