Exactly the same thing can be said about a lossless unterminated
transmission line. If lumped circuit analysis doesn't work on
transmission lines with reflections, why should it be expected
to work on antennas with reflections?
--
73, Cecil http://www.qsl.net/w5dxp



While I agree with this statement, it still doesn't prove anything
about the value of the characteristic impedance and electrical
length of a loading coil and the relationship between these
parameters and the inductive reactance of the loading coil.
This is what bothers me about the claims that the "cosine law"
can be used to predict the current taper in the loading coil.
Seems that there is a big leap of faith taking place when going
from the observation (which I believe is correct) that current
taper is caused by standing waves on the resonant antenna,
and a "law" that says what we can predict that taper with a
simple formula without saying anything about the shunt
capacitance per unit length and series inductance per
unit length of the loading coil, quantities which normally
bear directly on the characteristic impedance and velocity
of propagation of the EM structure (at least in an
analogous transmission line case).

73 de Mike, W4EF.............................................



Exactly the same thing can be said about a lossless unterminated
transmission line. If lumped circuit analysis doesn't work on
transmission lines with reflections, why should it be expected
to work on antennas with reflections?
--
73, Cecil http://www.qsl.net/w5dxp



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Michael Tope wrote:
This is what bothers me about the claims that the "cosine law"
can be used to predict the current taper in the loading coil.

It is certainly NOT a "cosine law". It is at best an approximation.
From _Antennas_For_All_Applications_ by Kraus & Marhefka, third
edition, page 464: "The difference between these (dashed) curves
and the solid curves is not large but is appreciable." The solid
curves are cosine curves. The dashed curves, indicating the actual
current, are not cosine curves but are relatively close approximations.

The only time pure cosine curves will result for net current is in
a lossless situation which is certainly not entirely valid or accurate
for a radiating antenna.

If the magnitudes of the forward current and reflected currents are
not equal, there will be a drift away from a pure cosine shape.
--
73, Cecil http://www.qsl.net/w5dxp



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Interesting. I don't have this book handy [all I have is my signed
copy of "Antennas, 2ed" ]. Is there any indication in the text as
to where the "actual current" data came from? Is it derived from
some sort of EM analysis, or is it measured data I wonder?
I think Kraus spent a lot of time studying helical structures
while he was developing the helical antenna. Since a loading
coil is basically a helical antenna operating in the normal mode
perhaps the answer to this question lies in some of his early
work.

Thanks,

Mike, W4EF.............................................. .........


"Cecil Moore" wrote in message
...
Michael Tope wrote:
This is what bothers me about the claims that the "cosine law"
can be used to predict the current taper in the loading coil.

It is certainly NOT a "cosine law". It is at best an approximation.
From _Antennas_For_All_Applications_ by Kraus & Marhefka, third
edition, page 464: "The difference between these (dashed) curves
and the solid curves is not large but is appreciable." The solid
curves are cosine curves. The dashed curves, indicating the actual
current, are not cosine curves but are relatively close approximations.

The only time pure cosine curves will result for net current is in
a lossless situation which is certainly not entirely valid or accurate
for a radiating antenna.

If the magnitudes of the forward current and reflected currents are
not equal, there will be a drift away from a pure cosine shape.
--
73, Cecil http://www.qsl.net/w5dxp

Mike, W4EF wrote:
"Is there any indication in the text as to where the actual current data
came from?"

Not exactly, on page 464 of the 3rd edition of Kraus` "Antennas", that I
saw. Below the diagrams of current versus distance from the center of
the dipole, the text says:

"It is generally assumed that current distribution on an infinitesimally
thin antenna---is sinusoidal, and that the phase is constant over
1/,2-WL interval, changing abruptly by 180-degrees between intervals."

On page 295, Kraus says:
"If the dimensions (of a helix) are small (nLlambda), the maximum
radiation is in the xy plane for a helix oriented as in Fig 8-69a, with
zero radiation in the z direction."

In other words, radiation is perpendicular (normal) to the axis of small
diameter coils.

On page 295, Kraus says:
In the preceding discussion on the normal mode of radiation, the
assumption is made that the current is uniform in magnitude and in phase
over the entire length of the helix. This condition could be
approximated if the helix is very small (nLlambda) and is end loaded.
However, the bandwidth of such a small helix is very narrow, and the
radiation efficiency is low."

It is obvious that the inductance and delay of a coil depend upon on the
coil`s diameter and pitch, in addition to the length of the coil.

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:
"It is generally assumed that current distribution on an infinitesimally
thin antenna---is sinusoidal, and that the phase is constant over
1/,2-WL interval, changing abruptly by 180-degrees between intervals."

I just realized that the IRE reference I gave in another thread is for
a l/a=75 example, i.e. not for an l/a=infinity example.

But we can deduce the answer from what Kraus says on page 187. "A
sinusoidal current distribution may be regarded as the standing wave
produced by two uniform (unattenuated) traveling waves of equal
amplitude moving in opposite directions along the antenna."

And Yes, for a lossless unterminated transmission line, the current
distribution of the standing waves is sinusoidal. But not so for
a transmission line with losses. See "Transmission Lines & Networks",
by Johnson, Fig 4.11 or "Transmission Lines" by Chipman, Fig. 8-10.

We know a radiating dipole has "losses" due to radiation. Therefore,
the current distribution will be more like the two above graphs than
a pure sinusoid. For a real-world current distribution on a real
world dipole, an attenuation factor must be included. That makes
the reflected current less than the forward current which moves
the phase angle away from what it would be on a lossless transmission
line (or on an antenna that didn't radiate).

On a lossless transmission line, the forward current may be 1 at 45 degrees
while the reflected current is 1 at -45 degrees. Thus the net current would
be 1.414 at zero degrees. But on a real-world antenna, the forward current
may be 1 at 45 degrees while the reflected current is 0.85 at -45 degrees.
which would be approximately 1.3 at 4.4 degrees.
--
73, Cecil http://www.qsl.net/w5dxp



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Michael Tope wrote:
Interesting. I don't have this book handy [all I have is my signed
copy of "Antennas, 2ed" ]. Is there any indication in the text as
to where the "actual current" data came from?

King, Ronold & C.W.Harrison, Jr, "The Distribution of Current along a
Symmetrical Center-Driven Antenna", Proc. IRE, 31, 548-567, October 1943.
--
73, Cecil http://www.qsl.net/w5dxp



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Mike, W4EF wrote:
"---standing waves on the resonant antenna, and a "law" that says what
we can predict that taper with a simple formula---."

It`s as simple as ON4UN`s Fig 9-22 center loading diagram. The resonant
element is 90-degrees long. Any missimg wire length must be provided by
the loading.

Best regards, Richard Harrison, KB5WZI