Knarf wrote:
Thanks for the link Yuri. Read the web page, and now understand what is
going on. I have an Excel spreadsheet, complete with graph, prepared from a
NEC2 model of an inductively loaded monopole. The graph clearly shows the
current distribution across the coil. If you are interested I can e-mail it
to you, or can post it on the NG. It is only about 50kB, but not sure if it
is acceptable to post attachments on a NG.

The netnews rules prohibit posting binary files. If you don't have
a web page, you could post it to alt.binary and point to it from
here.

Modeling a helical loading coil in EZNEC and putting loads at the
various segments also clearly illustrates the current taper. All
real-world air-core loading coils are distributed networks. In
a distributed network with reflections, the standing-wave currents
are tapered within a sinusoidal envelope.

Here's an unanswered question: If the loading coil occupies zero
degrees, how can the remaining eight feet of the antenna occupy
the entire 90 electrical degrees? Wouldn't the coil have to
change the frequency for that to happen?
--
73, Cecil http://www.qsl.net/w5dxp


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Cecil,

In a simple monopole with one inductor, let L1 be the distance from the
base of an antenna to the bottom of the loading coil in meters, L2 the
length of the loading coil, L3 the distance from the top of the loading
coil to the top of the antenna. I is the base current, L the inductance
value and F the frequency. You can assume the antenna is very thin.

Since your theory is so elegant and well developed, and you've had such
an excellent education at Texas A&M, it shouldn't be difficult at all
for you to write a couple of simple equations which give the currents at
the two ends of the coil. In the time-honored methods of science, your
equations can then be tested against modeled and measured results to
prove the validity of your theory.

Roy Lewallen, W7EL

Roy Lewallen wrote:

Cecil,

In a simple monopole with one inductor, let L1 be the distance from the
base of an antenna to the bottom of the loading coil in meters, L2 the
length of the loading coil, L3 the distance from the top of the loading
coil to the top of the antenna. I is the base current, L the inductance
value and F the frequency. You can assume the antenna is very thin.

Since your theory is so elegant and well developed, and you've had such
an excellent education at Texas A&M, it shouldn't be difficult at all
for you to write a couple of simple equations which give the currents at
the two ends of the coil. In the time-honored methods of science, your
equations can then be tested against modeled and measured results to
prove the validity of your theory.

Sorry, Roy, my theory is not elegant and/or well developed. Equations may
be possible in the future, but not right now. At the present time, the
theory is qualitative, not quantitative. We are out on the edge of what
has been published so far and are in the process of discovery. It is hard
for me to believe that this material hasn't been covered some time, somewhere,
in a Master's thesis or a PhD dissertation or somewhere in the IEEE proceedings.
I regret that I don't have access to such.

The coil has an 'L' and a 'C' and thus can be regarded as a short piece
of transmission line. For a mental picture, consider two pieces of helix
material, side by side, being used as a balanced transmission line. They
would certainly possess a high velocity factor as does a bugcatcher coil.
Here is the equivalent of 1/2 of a typical loaded dipole using horizontal
#16 wire at a height of 24 feet where Z0=138*sqrt(4h/d).

Feedpoint---Z0=600 ohms---x---coil---y---Z0=600 ohms---

The Z0 of the coil is presently unknown but I am working on getting a
ballpark value for it. In any case since Z0=sqrt(L/C), the Z0 of the
loading coil will be very high. That means, in addition to the
reflections at the tip of the antenna, there will also be reflections
at 'x' and 'y', both ways. That situation is pretty complicated but
the result is apparently to put the forward voltage out of phase with
the forward current at the feedpoint. It also apparently puts the reflected
voltage out of phase with the reflected current at the feedpoint. The only
requirement is that Vf+Vr be in phase with If+Ir at the feedpoint. I hope
you can appreciate the complexity of that situation, stop asking for a
"simple equation", and assist us in the apparently complicated solution.

When someone doesn't understand the topic, one asks for a "simple
equation" and when none is forthcoming, one rationalizes that the
new information is not worth knowing. How about working with me
instead of against me on this complicated problem for which neither
one of us has the complete answer (yet)?

P.S. If you had demanded a "simple equation" from Maxwell, you would
have been disappointed also. :-)
--
73, Cecil http://www.qsl.net/w5dxp


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Cecil Moore wrote:
For a mental picture, consider two pieces of helix
material, side by side, being used as a balanced transmission line. They
would certainly possess a high velocity factor as does a bugcatcher coil.
^^^^
Sorry, this should have been a *LOW* velocity factor.
--
73, Cecil http://www.qsl.net/w5dxp


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Cecil Moore wrote:

Sorry, Roy, my theory is not elegant and/or well developed. Equations may
be possible in the future, but not right now. At the present time, the
theory is qualitative, not quantitative. . .

Somehow I expected this.

Roy Lewallen, W7EL

Roy Lewallen wrote:

Cecil Moore wrote:
Sorry, Roy, my theory is not elegant and/or well developed. Equations may
be possible in the future, but not right now. At the present time, the
theory is qualitative, not quantitative. . .

Somehow I expected this.

The technical information published on this particular subject is
non-existent. Therefore, there is nothing published that contradicts
what I am saying. Why do you think that gives you an advantage?
--
73, Cecil http://www.qsl.net/w5dxp


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Roy Lewallen wrote:
Cecil Moore wrote:
Sorry, Roy, my theory is not elegant and/or well developed. Equations may
be possible in the future, but not right now. At the present time, the
theory is qualitative, not quantitative. . .


Somehow I expected this.

I didn't mean to imply that I don't know the equations - I do. I just
don't know the value of all the constants in the equations.

Given that a horizontal dipole 24 ft. above ground and constructed from
#16 wire will have a natural Z0 of 600 ohms:

The forward current will be an If-max value multiplied by an exponential
relating to frequency multiplied by an exponential relating to the loss
of energy due to conductor resistance and radiation.

The reflected current will be an Ir-max value multiplied by the same
exponential relating to frequency multiplied by the same exponential
relating to the loss of energy due to conductor resistance and radiation.

We know that (Vf+Vr)/(If+Ir) equals 50 ohms for a dipole whose feedpoint
impedance is 50 ohms. With a 1/2WL dipole the current equation is clear.

Here is the equation you asked for, unfortunately in ASCII:

Itot = If-max*e^-yz*e^-2az + Ir-max*e^+yz*e^-2az

same as it is for a transmission line. The I^2*R losses plus the
radiation "losses" are combined into the attenuation factor 'a'.

So I can indeed write you an equation for a wire dipole. The coil
in the mobile antenna causes another level of complication, and
that is the equation with which I am struggling at the moment.
In addition, the vertical nature of a mobile antenna means that
the Z0 is changing with length. That is a minor problem compared
to including the reflections from both ends of a loading coil in
both directions. But I have no doubt that I can solve that problem.
--
73, Cecil http://www.qsl.net/w5dxp


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Cecil Moore wrote:
. . .
Here is the equation you asked for, unfortunately in ASCII:

Itot = If-max*e^-yz*e^-2az + Ir-max*e^+yz*e^-2az

same as it is for a transmission line. The I^2*R losses plus the
radiation "losses" are combined into the attenuation factor 'a'.
. . .

No, that isn't the equation I asked for. Nowhere in your equation are
L1, L2, L3, L, I, or F. Whatever your equation is supposedly solving
for, it isn't what I asked.

I feel strongly that if you really understand what you're talking about,
you should be able to express it mathematically as an equation or
equations. I haven't seen any evidence of this.

Roy Lewallen, W7EL

If you really understand what you're talking about,
you should be able to express it mathematically as an equation or
equations.

Roy Lewallen, W7EL

-----------------------------------------------------

By far, the most sensible statement yet made in these interminable 'coil'
threads.

No need to quote Kelvin.

Maths comes first - THEN the arguments if there are any.
----
Reg.

Roy Lewallen wrote:
I feel strongly that if you really understand what you're talking about,
you should be able to express it mathematically as an equation or
equations. I haven't seen any evidence of this.

Well, You're right. I should be able to express it as an equation. Truth
is, personality wise, I tend to deal in concepts, not equations. That's
why the field of digital electronics was so appealing to me. "If it's
not a zero or a one, it's broke!" I seem to have been born with a Boolean
Algebra processor built in. (It's similar to the fact that I can read
Spanish but I can't speak it.)

I have been satisfied all my life to let someone else provide the equations
and so far, I have been able to stand on the shoulders of giants. But in this
case, if anyone has ever provided the equations, I am not aware of it. If
one is so inclined, one might get to be famous by generating those equations.

The S-parameter equations should work just fine at each individual impedance
discontinuity. The trick is in knowing how much to reduce the incident and
reflected voltages because of radiation. It's one approach to think about.

One possible solution would be to model the antenna as a transmission line,
as Balanis and Kraus suggest. If we made a 1/4WL open-circuit stub out of
resistance wire with Z0=600 ohms such that it's feedpoint impedance is 50
ohms, it should be a good approximation to an antenna wire.

In any case, the loading coil has a steady-state forward current (If) and
reflected current (Ib) each of which undergo a phase shift through the coil.
Any phase shift in phasors traveling in opposite directions is cause for
their sums to be different at each end of the coil. I'm surprised that such
a concept is controversial. Exactly the same concept applies to 'X' degrees
of a transmission line with reflections.
--
73, Cecil http://www.qsl.net/w5dxp


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