wrote:

Cecil Moore wrote:
is only 40% shortening. I think the lumped inductor
crossover point is probably pretty far below 4 MHz.

There isn't any "crossover point". That point has been made several
times by different people.

One of those people supporting a "crossover point" is Dr.
Corum in his IEEE peer reviewed paper at:

http://www.ttr.com/TELSIKS2001-MASTER-1.pdf (page 6)

Dr. Corum is pretty clear about 15 degrees, i.e. 4% of a
wavelength, being the "crossover point". He considers 15
degrees to 90 degrees to require a distributed network
analysis while below 15 degrees, "one passes to the lumped-
element regime ..."

The "crossover point" would be the same rule as for a
transmission line. How long does a transmission line with
reflections have to be before it is no longer valid to
consider it a lumped piece of wire. 15 degrees is 4% of
a wavelength and sounds reasonable. However, under
the right conditions, one could arrange a current node
at the halfway point of that 15 degrees of feedline thus
causing current to flow into both ends of the feeline
at the same time. 1/2 cycle later, current would be
flowing out of both ends. How would a lumped-circuit
model handle those conditions?

The "crossover point" is obviously arbitrary but if one
locates it very far above 15 degrees, according to Dr.
Corum, one risks invalid analysis results such as have
been reported here.
--
73, Cecil http://www.qsl.net/w5dxp