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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.
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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 betweentwo devices and forget about it. But there is a lot more to know aboutwire than just hooking it up. Characteristic impedance is one importantthing to check, not so much for AC power lines, or even loudspeakerlines, but certainly for video lines and matched impedance lines.

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

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

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

For shielded and unshielded twisted pairs, the characteristicimpedance is

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For unshielded pairs, C is

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For shielded pairs, C is

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