Cecil Moore wrote:
Reg Edwards wrote:

It was obvious I introduced G = C * R / L simply to show that a line's Zo
can be purely resistive even when it is NOT lossless. It can have any
loss
you like.


Ramo and Whinnery are the authors of my 50's college textbook on fields
and waves. Of course it could be a misprint, but they say your above
formula is an approximation that is good for low-loss lines.

Certainly good at HF and UHF when the skin depth is likely to be a small
fraction of the conductor radius.

Apparently, something additional happens for high-loss lines.

Not so much high loss, as low frequency. Both L and R are frequency
dependent assuming normal (non superconducting) metallic conductors. G
and C may have a frequency dependency depending on the dielectric
characteristics.

Once the frequency is high enough so that the current can be considered
to flow only on the skin of the conductor, the effective AC resistance
is proportional to the square root of the frequency and the inductance
is constant. At frequencies below the above defined 'critical
frequency', the internal inductance must be considered as well as the
complicated frequency dependence of resistance.

Chipman
seems to agree with Ramo and Whinnery when he introduces some additional
interference terms (discussed some time ago on this newsgroup).

Yep.

At the
time, I didn't realize the additional terms were interference terms but
the impedance of the load apparently somehow interacts with the
characteristic impedance of the high-loss transmission line to upset
the ideal relationships in your equation above.

The relationship is correct for all frequencies and standing wave ratios
as long as the correct frequency dependent values of transmission line
parameters are used. The wave equation still describes the relationship
between current and voltage. The additional 'interference' terms appear
when calculating the energy distribution and loss characteristics.

bart
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