Distributed L and C model of a transmission line

Consider a uniform two-conductor transmission line.
Assuming that the electromagnetic wave propagates in a TEM mode, the voltage and current satisfies the equations:
where L and C are the inductance and capacitance per unit length along the transmission line. |

We will derive the equations of distributed L and C model.

***

We consider a uniform two-conductor transmission line and assume that the electromagnetic wave propagates in a TEM mode.

The
voltage between conductor-1 and 2 is obtained by integrating **E**_{T}_{ }・d**s** along any path C
from conductor-1 to 2 :

Therefore the gradient of voltage v(z,t) is proportional to the time derivative of current i(z,t), and the proportional coefficient is the inductance between conductor-1 and 2:

***

The
current of conductor-1 is obtained by integrating **B**_{T}_{ }・d**s** along any closed
path C around conductor-1:

Therefore the gradient of current i(z,t) is proportional to the time derivative of voltage v(z,t), and the proportional coefficient is the capacitance between conductor-1 and 2: