Editing Transmission line (section)

===Special case of a lossless line===
When the elements <math>R</math> and <math>G</math> are negligibly small the transmission line is considered as a lossless structure. In this hypothetical case, the model depends only on the <math>L</math> and <math>C</math> elements which greatly simplifies the analysis. For a lossless transmission line, the second order steady-state Telegrapher's equations are:

:<math>\frac{\partial^2 V(x)}{\partial x^2}+ \omega^2 L\,C\,V(x) = 0</math>

:<math>\frac{\partial^2 I(x)}{\partial x^2} + \omega^2 L\,C\,I(x) = 0 ~\,.</math>

These are [[wave equation]]s which have [[plane wave]]s with equal propagation speed in the forward and reverse directions as solutions. The physical significance of this is that electromagnetic waves propagate down transmission lines and in general, there is a reflected component that interferes with the original signal. These equations are fundamental to transmission line theory.