**Subject :**Electromagnetic Field Theory

## Transmission line equations

**Introduction:
**

A two-conductor transmission line supports a TEM wave; that is, the electric and magnetic fields on the line are transverse to the direction of wave propagation

**Mathematically:
**

- An important property of TEM waves is that the fields E and H are uniquely related to voltage V and current /, respectively

- In view of this, we will use circuit quantities V and I in solving the transmission line problem instead of solving field quantities E and H (i.e., solving Maxwell's equations and boundary conditions).
- The circuit model is simpler and more convenient.
- Let us examine an incremental portion of length Δ z of a two-conductor transmission line.
- To find an equivalent circuit for this line and derive the line equations.
- The model in Figure 11.5 is in terms of the line parameters R, L, G, and C, and may represent any of the two-conductor lines.
- The model is called the L-type equivalent circuit; there are other possible types .
- In the model of Figure 11.5, we assume that the wave propagates along the z-direction, from the generator to the load.
- By applying Kirchhoff's voltage law to the outer loop of the circuit in Figure 11.5, we obtain

- Taking the limit of eq. (11.3) as Δ z -> 0 leads to

- Similarly, applying Kirchoff's current law to the main node of the circuit in Figure 11.5 gives

- If