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Zo of two wire open line
I have found two common expressions for the Zo of a two wire line in space. One expression is Zo=276log(D/d). The second is Zo=120acosh(D/d). I have been searching for information on whether the acosh expression takes into account proximity effect. Because it does not consider conductivity or permeability of the conductors, one wonders if it does. Laport has a graph that shows the log expression and a proximity corrected line which turns out to be a very close fit to the acosh line over the range that he plots. The curves are compared in http://www.vk1od.net/balun/Ruthroff/R07.png . I have another reference, Marchand (1947), which gives the log expression then, the acosh expresssion and says "The hyperbolic cosine is obtained because the currents are attracted to one another and become more and more confined to the inside surface as the wires are brought closer together." This suggests (states) that the acosh expression (fully) accounts for proximity effect on Zo. Comments? Owen |
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