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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Reg Edwards wrote:

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

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

Well, I have already posted the equations. During steady-state, there will
be some magnitude of forward current (If) through the coil and some magnitude
of reflected current (Ib) flowing backwards through the coil caused by
reflections from the tip of the standing-wave antenna. The net current at
any position up and down the antenna is Ir+Ib. That's a pretty simple
equation. Since there is a phase shift in Ir and Ib through the large
bugcatcher coil, the sum of Ir and Ib will not be the same at each end.

In an electrical 1/4WL antenna, like a typical 75m mobile antenna with
no top hat, the If+Ib sum at the bottom will always be a larger magnitude
than the If+Ib sum at the top. Modeling the coil as an eight-sided helix
in EZNEC resulted in:

http://www.qsl.net/w5dxp/octcoil.gif

The net current at the bottom of the coil is obviously of a greater
magnitude than the net current at the top of the coil. That's because
If and Ib at the bottom of the coil are nearly in phase. Ir and Ib
are about 58 degrees different in phase at the top of the coil. That
tells me that the coil causes about a 29 degree phase shift when either
Ir or Ib flows through it. It's not that simple but let's stick with
simple for right now.
--
73, Cecil http://www.qsl.net/w5dxp


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Perhaps it's your background as a manager that's in evidence here. I was
one of the people that "concept" people like you "let" provide the
equations. I have an apropos Doonesbury cartoon on my office wall:

Pointy-haired boss, pointing to simple graph labeled "Sales": "Sales are
dropping like a rock."

Pointy-haired boss, pointing to a graph labeled "Future", with single
upward line: "Our plan is to invent some sort of doohickey that everyone
wants to buy."

Pointy-haired boss, to Dilbert: "The visionary leadership work is done.
How long will your part take?"

At review time, the boss judged me on whether the "doohickey" worked
according to specifications that he and some marketing people came up
with in "concept" meetings. All I had to do was to understand the
science, come up with the equations, develop new technology as required,
create the device, and make it work -- all on a schedule and within a
budget which were also dictated by the "visionaries". Just grunt work,
not worthy of the visionary people who were doing more important things.

I don't believe for a minute that the boss really understood how the
device worked. And for the same reason, I don't believe that you really
understand the "concepts" you're promoting. Real science and engineering
are done by understanding the basic concepts, developing mathematical
models of them based on those understandings, then using those models to
test the theory. Without the understanding and models, the theories
can't be tested. Then all you have are smoke, mirrors, and hand waving.
Instead of solid, testable evidence, you just about have to resort to
diversion, evasion, misinterpretation, and the other tools of the
politician and upper level manager. As important and richly rewarded as
those skills are, it isn't science and it isn't engineering, and it
doesn't constitute evidence of any knowledge or understanding.

You seem to have convinced a few readers of the group that you know what
you're talking about. Since you're apparently not able to express your
ideas in concrete form, perhaps one of them will volunteer to do the
mundane work of developing a coherent theory to explain it in scientific
and mathematical terms. My only question to them is:

How long will your part take?

Roy Lewallen, W7EL

Cecil Moore wrote:
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.
. . .

Cecil Moore wrote:

Reg Edwards wrote:

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


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


Well, I have already posted the equations. . .

Well, no you haven't. Why do you keep saying that? I asked a simple
question, and instead of answering it, you've answered some other
question that you prefer, then claim it's the answer to the question I
asked.

I took only one political science course in college, and that was the
technique used by the majority of students. It's also the universal
technique of political candidates. I'm asking techical and engineering
questions, and you're giving political answers. No wonder we don't
communicate.

This isn't a game I like to play and, since leaving the cube farm, it's
one that I no longer have to. So I'll bow out again and leave it to the
folks who do enjoy this form of discourse.

Roy Lewallen, W7EL

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.

Taking a look at just the loading coil, the math is very simple.
Since a loaded mobile antenna is a standing wave antenna, there
exists a forward current through the coil. Balanis labels that
current as 'If'. There also exists a reflected current flowing
backwards through the coil. Balanis labels that current as 'Ib'.
The current at any point in the coil is the superposed sum of
If + Ib. The net current within the coil is approximately a section
of a cosine function.

On my web page is a mobile antenna modeled with EZNEC using a
segmented octal shaped coil.

http://www.qsl.net/w5dxp/octcoil.gif

EZNEC reports that the current at the bottom of the coil is
0.9956 amps and the current at the top of the coil is 0.5326.
Assuming the current is approximately a cosine function through
the coil, the approximate number of degrees occupied by the coil is:

arccos(0.5326/0.9956) = ~58 degrees

The other eight feet of antenna is equal to about 42 degrees
at 13.5 MHz.

58 + 42 = 100 degrees is within 10% of being 90 degrees and
seems reasonable for a ballpark estimate. This seems to be
a clue that a loaded mobile antenna is electrically slightly
longer than 90 degrees.

The forward current and reflected current magnitudes through the
coil are probably within 90% of each other for a mobile antenna.
Kraus considers them to be equal for a dipole discussion
in his book. Considering them to be equal introduces a small error
but is good enough for a reasonable estimate.

The point is that the difference in the net current at each
end of a coil gives us a rough estimate of the number of electrical
degrees that the coil occupies in the antenna. The whip above the
coil can be considered as a load on the source energy at the top
of the coil. It is unlikely that the coil is capable of changing
the characteristics of the load which would be necessary if Tom
were right.

If the coil occupies zero degrees, as implied by Tom, W8JI, then
the other 8 feet of the antenna would have to occupy 90 degrees
to make the feedpoint impedance resistive. I would say that shoving
90 degrees into 8 feet of whip at 13.5 MHz is impossible. That 8
feet of antenna would have to have a velocity factor of 0.46 which
is unlikely. At 4 MHz, that 8 feet of antenna would have to have a
velocity factor of 0.137 to occupy 90 degrees. That's seems obviously
impossible. Tom's requirement that a wire change velocity factor with
frequency is really hard to accept.
--
73, Cecil http://www.qsl.net/w5dxp


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Roy Lewallen wrote:
You seem to have convinced a few readers of the group that you know what
you're talking about. Since you're apparently not able to express your
ideas in concrete form, perhaps one of them will volunteer to do the
mundane work of developing a coherent theory to explain it in scientific
and mathematical terms.

You must have missed some of my postings. I have already expressed my
ideas in concrete form. Maybe you don't like the simplicity of

Itot = I+ + I- (I+ is forward current and I- is reflected current)

Standing wave antennas possess standing waves. Standing waves occur
when forward waves and reflected waves are superposed. The phase
rotation of these two component currents are in opposite directions.
The result is a sinusoidal function for both net voltage and net current.

Any real-world air-core coil has a phase delay that affects the forward
current and the reflected current. Since they are phase rotating in
opposite directions, the overall effect is doubled. It's all explained
on my web page. Have you taken time to read it?
--
73, Cecil http://www.qsl.net/w5dxp


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Roy Lewallen wrote:

Cecil Moore wrote:
Well, I have already posted the equations. . .

Well, no you haven't. Why do you keep saying that?

Because it's true. Here are the equations again.

A loading coil exists in a standing-wave antenna.
The forward current through the loading coil is I+.
The reflected current through the loading coil is I-.
The net current at any point in the coil is I+ + I- (phasor addition)
The magnitude of the net current depends upon the phase of I+ and I-.

Itot = I+ + I-

There's the equation that I have already posted many, many times.
Sorry you missed it.

A rough estimate of the net current at the top of a loading coil
can be had by estimating the number of degrees occupied by the
coil and assuming a net current cosine function through the coil.
--
73, Cecil http://www.qsl.net/w5dxp


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