Re: [SI-LIST] : Twisted Pair Impedance

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From: jrbarnes@lexmark.com
Date: Mon Nov 27 2000 - 06:07:18 PST


Barry,
A pair of equations that I ran across a number of years ago concerned the
increase in average relative permittivity EPSILONr' as a function of the twist:
* Using insulation with relative permittivity EPSILONr.
* Center-to-center spacing for the conductors of S meters.
* n twists per meter.

Compute twist angle THETA = arctan(pi * S * n) degrees, then:
* For a hard insulation (enamel) EPSILONr' = 1 + (0.25 +
0.0004*THETA*THETA)*(EPSILONr - 1)
* For a soft insulation (teflon, polyvinyl chloride) EPSILONr' = 1 + (0.25 +
0.001*THETA*THETA)*(EPSILONr - 1)

The soft insulation mashes a little, and fills the space around the conductors
more than a hard insulation does. These equations are in Appendix E:
Properties of Transmission Lines in my book Electronic System Design:
Interference and Noise Control Techniques (Prentice-Hall, 1987). I believe that
I originally found them in Peter Lefferson's article "Twisted Wire Transmission
Line," IEEE Transactions on Parts, Hybrids, and Packaging, PHP-7:4 (December
1971), pages 148-154.

The very slight helix from twisting the wires has no noticeable effect on the
inductance. The reduction in impedance Zo is almost completely due to packing
more insulation around the conductors than for straight wires.

                                                   John Barnes Advisory
Engineer
                                                   Lexmark International

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