# Characteristic impedance

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The characteristic impedance or surge impedance of a uniform transmission line, usually written Z0, is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of reflections. The SI unit of characteristic impedance is the ohm. The characteristic impedance of a lossless transmission line is purely real, that is, there is no imaginary component (Z0 = | Z0 | + j0). Characteristic impedance appears like a resistance in this case, such that power generated by a source on one end of an infinitely long lossless transmission line is transmitted through the line but is not dissipated in the line itself. A transmission line of finite length (lossless or lossy) that is terminated at one end with a resistor equal to the characteristic impedance (ZL = Z0) appears to the source like an infinitely long transmission line.

## Contents

### Transmission line model

Applying the transmission line model based on the telegrapher's equations, the general expression for the characteristic impedance of a transmission line is:

where

The voltage and current phasors on the line are related by the characteristic impedance as:

where the superscripts + and represent forward- and backward-traveling waves, respectively.

### Lossless line

For a lossless line, R and G are both zero, so the equation for characteristic impedance reduces to:

The imaginary term j has also canceled out, making Z0 a real expression, and so is purely resistive with a magnitude of $\sqrt{\frac{L}{C}}$.