# Appendix 2D: Nonuniform Transmission Lines

## 2D.1Nonuniform Transmission Lines

A nonuniform transmission line can represent many physical phenomena in an inhomogeneous medium whose medium properties are functions of position. A one-dimensional equivalent ideal transmission line will have the per unit values of series inductance *L*′ and the shunt capacitance *C*′ as functions of one spatial coordinate.

Let

If ε and μ are homogenous in the transverse plane, then

where *u*_{p} is the phase velocity.

The first-order coupled differential equations are

In the phasor form,

From Equations 2D.3a and 2D.3b, we can ...

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