[Elecraft] Re: I^2*R Losses and Coax Impedance (Was Random Wire)
James R. Duffey
[email protected]
Sat Jan 11 10:36:00 2003
Kevin - Yes, all other things being equal, higher impedance transmission
lines have lower I^2R losses thna do low impedance transmission lines. The
loss for a coaxial transmission line is given by:
loss = loses due to resistance + loses due to dielectric
or
Loss per 100 ft = (0.435/Z*D)(((D/d))(k1+k2))sqrt(f) + 2.78 sqrt(e)(pf)(f)
where Z is the impedance of the line, D the outer diameter, d the inner
diameter, k1 and k2 are factors related to the conductivity of the braid and
inner conductor, f is the frequency of operation, e the dielectric factor
and pf the power factor. At HF the second factor is small unless one is
using a poor dielectric such as flexible vinyl.
So the larger the Z the lower the loss. This is the true and often
unappreciated reason why balanced feeders have lower matched line loss than
coax; the balanced feeder we use is of much higher impedance, 300 or 450
OHms, than the coax we use; 50 or 70 Ohms.
For your superconducting case, K1 and K2 are zero, the resistance losses are
zero (as long as the critical current for the Meissner effect is not
exceeded) and the losses in the cable are all due to the dielectric.
I hope that this helps. - Dr, Megacycle KK6MC/5
--
James R. Duffey KK6MC/5
Cedar Crest, NM DM65