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Mar 1, 2002 12:00 PM, GLEN BALLOU

Wire Math

Wire is one of those things we take for granted. Hook it up between two devices and forget about it. But there is a lot more to know about wire than just hooking it up. Characteristic impedance is one important thing to check, not so much for AC power lines, or even loudspeaker lines, but certainly for video lines and matched impedance lines.

The characteristic impedance of any transmission line is the impedance that must be connected to the far end of the line in order to make the input impedance of the line equal to the terminating impedance. If the line is very long, the input impedance will equal the characteristic impedance of the line, irrespective of the terminating impedance.

The characteristic impedance depends on the parameters of the line and the applied frequency. The resistive component is generally high at the low frequencies as compared to the reactive component, with the reactive components taking over with an increase of frequency. The general equation for all lines is:

If the line is of infinite length, the current in the line is hardly affected by the value of the terminating impedance at the far end of the line. If there is 20 dB of attenuation in a line, and the far end is short-circuited, the characteristic impedance as measured at the sending end will not be affected by more than 2%.

For shielded and unshielded twisted pairs, the characteristic impedance is