What is meant by impedance

Impedance of a line


A compilation of several news articles from "alt.folklore.computer", translated by Stefan Brix

Most people get a little confused when they hear about the impedance (e.g. 50 ohms) of a line because they initially think a resistance (they think of an ohmic resistance) must be proportional to the length of the line. On the other hand, an alternating current resistance should depend on the frequency. - What was that again?

All lines (coaxial as well as symmetrical) have a certain capacity per unit length (let's call them 'C / l') and specify a certain speed of propagation of the signal along the line (let's call it 'v').

If we now start with a discharged line and apply a voltage 'U' at one end between the inner conductor and the shield, this rising voltage edge will run along the line. Now, in a time 't', the length 'l = v * t' of the line is additionally charged to the voltage 'U'. The capacity of the line length is 'C = C / l * v * t' and therefore requires the charge 'C / l * v * t * U' to be charged. So we put charge of the size 'C / l * v * U' into the line.

But this is precisely the current that is necessary to keep our end of the line at voltage U. This current depends linearly on U and is therefore equal to a real resistance 'C / l * v'! - This is the characteristic impedance of a line that is meant when a "50-ohm cable" is mentioned.

For the sake of completeness, it should be said that if the end of the line is open, the fact that the current stops flowing leads to the reflection of the wave, which then travels back down the line at the same speed. If there is a short circuit at the end of the line, the same thing happens because the voltage cannot increase. Between these two extremes there is a resistor that is exactly the size of the line impedance and ensures that no signal is reflected. Such a resistor is called a terminator.