Roy, W7EL wrote:
"When asked for the justification of the "cosine rule", he never offered
any, so its origin remains obscure."

It comes from the similarity of a standing wave antenna to a
transmission line. It isn`t a prominent feature of antenna texts because
energy isn`t confined to an antenna as it is to a transmission line.
Antenna behavior is more complicated. Terman refers the reader to his
transmission line section to explain standing wave antenna action
innstead of making a detailled explanation in his antenna section. Maybe
he was limited in number of pages. The explanation is available from a
collection of sources.

From "Transmission Lines, Antennas, and Wave Guides" by King, Mimno,
and Wing, page 93:
"---the distribution of current in antennas with h=WL/4 and with a wide
range of radii can be represented quite accurately by:

Iz = Io cos beta(z)

beta(z) is the distance from the antenna input in degrees.

It is obvious that the current must reverse directions at the open
circuit end of the antenna. This results in a total of forward and
reflected current of nearly zero while 1/4-wave back from the open
circuit, a current maximum results.

Kraus says that at the center of a 1/2-wavelength dipole, the effect of
wave cancellation is least and radiation is maximum perpendicular to the
wire at the center of the dipole, or words to that effect. The same is
true of the 1/4-wave vertical which along with its reflection in a
ground plane constitutes a 1/2-wavelength dipole.

Kraus also says that the tip cancellation accounts for the dipole
radiation pattern shaped as a doughnut impaled at the center of a
dipole. Again, these are my interpretations of Kraus` words as I
remember them.

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:

Roy, W7EL wrote:
"When asked for the justification of the "cosine rule", he never offered
any, so its origin remains obscure."

It comes from the similarity of a standing wave antenna to a
transmission line. It isn`t a prominent feature of antenna texts because
energy isn`t confined to an antenna as it is to a transmission line.
Antenna behavior is more complicated. Terman refers the reader to his
transmission line section to explain standing wave antenna action
innstead of making a detailled explanation in his antenna section. Maybe
he was limited in number of pages. The explanation is available from a
collection of sources.

From "Transmission Lines, Antennas, and Wave Guides" by King, Mimno,
and Wing, page 93:
"---the distribution of current in antennas with h=WL/4 and with a wide
range of radii can be represented quite accurately by:

Iz = Io cos beta(z)

beta(z) is the distance from the antenna input in degrees.

It is obvious that the current must reverse directions at the open
circuit end of the antenna. This results in a total of forward and
reflected current of nearly zero while 1/4-wave back from the open
circuit, a current maximum results.

Excellent. Roy is telling us that beta(z) at one end of the coil is
essentially equal to beta(z) at the other end of the coil. And Reg
might have us believe it's the length of the bobbin that matters in this
regard.

73, Jim AC6XG

Cecil Moore wrote:

Jim Kelley wrote:


Richard Harrison wrote:
Iz = Io cos beta(z)

Excellent. Roy is telling us that beta(z) at one end of the coil is
essentially equal to beta(z) at the other end of the coil.

Which requires a lossless, non-radiating coil with zero capacitance.

Just out of curiosity, to which of those characteristics do you
attribute the phase delay?

73, Jim AC6XG

Richard Harrison wrote:
Roy, W7EL wrote:
"When asked for the justification of the "cosine rule", he never offered
any, so its origin remains obscure."

Roy, I posted a reference for the cosine rule weeks ago. Perhaps you
missed it. If you had read it, you wouldn't have wasted your time
measuring the phase angle of the net current through a loading coil.
My "odd theory" is based on Kraus' treatment of the cosine rule.
See below:

It comes from the similarity of a standing wave antenna to a
transmission line. It isn`t a prominent feature of antenna texts because
energy isn`t confined to an antenna as it is to a transmission line.

Kraus says that at the center of a 1/2-wavelength dipole, the effect of
wave cancellation is least and radiation is maximum perpendicular to the
wire at the center of the dipole, or words to that effect.

The reference for the cosine rule is from _Antennas_For_All_Applications_,
by Kraus & Marhefka, 3rd edition, pages 463-465, section 14-3, Current
Distributions, Figure 14-2, Relative current amplitude and phase along a
center-fed 1/2WL cylindrical antenna.

This is where my "odd theory" comes from. Kraus says: "It is generally
assumed that the current distribution of an infinitesimally thin antenna
is sinusoidal, and that the phase is constant over a 1/2WL interval, changing
abruptly by 180 degrees between intervals."

Kraus is making the assumption that the forward current is equal to the
reflected current such that their superposition sum has constant phase.
Setting the center of the dipole as the origin and normalizing the
feedpoint current to 1.0, the current at any point on the dipole can
be calculated as the cosine of 'x' where 'x' is degrees away from the
center. Thus, if one knows the normalized current at any point on the
dipole, one can calculate the number of degrees one is away from center
using ArcCos(I). This is how I calculate the number of degrees associated
with a loading coil. Assuming the input current is 1.0 and the output
current is 0.95, ArcCos(0.95) = 18 degrees.

All this "odd theory" is based on Kraus. I suggest anyone who thinks
this is "odd theory" take time out and read Kraus.
--
73, Cecil http://www.qsl.net/w5dxp



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Jim Kelley wrote:


Richard Harrison wrote:
Iz = Io cos beta(z)

Excellent. Roy is telling us that beta(z) at one end of the coil is
essentially equal to beta(z) at the other end of the coil.

Which requires a lossless, non-radiating coil with zero capacitance.
Where can I get one of those?
--
73, Cecil http://www.qsl.net/w5dxp



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Jim Kelley wrote:

Cecil Moore wrote:
Which requires a lossless, non-radiating coil with zero capacitance.

Just out of curiosity, to which of those characteristics do you
attribute the phase delay?

Speed of light? :-) Seems the primary cause of the phase delay would
be the capacitance.

In many ways, this discussion has become ridiculous. On 440 MHz, one
inch of wire is ~13 degrees. Some gurus would have us believe that
a physically small one inch coil is zero degrees??????
--
73, Cecil http://www.qsl.net/w5dxp



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Cecil Moore wrote:

Jim Kelley wrote:

Cecil Moore wrote:
Which requires a lossless, non-radiating coil with zero capacitance.

Just out of curiosity, to which of those characteristics do you
attribute the phase delay?

Speed of light? :-)

The finite speed of light though a finite length of wire, yes.

Seems the primary cause of the phase delay would
be the capacitance.

With regard to coils, I think inductance is probably the more relevant
parameter. It's proportional to the number of turns and the length of
each turn of wire, and inversely proportional to the length of the
bobbin.

73, Jim AC6XG

Jim Kelley wrote:
With regard to coils, I think inductance is probably the more relevant
parameter. It's proportional to the number of turns and the length of
each turn of wire, and inversely proportional to the length of the
bobbin.

Is that "bobbin" a part of a coil winding machine? Coil form?
--
73, Cecil http://www.qsl.net/w5dxp



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Cecil Moore wrote:

Jim Kelley wrote:
With regard to coils, I think inductance is probably the more relevant
parameter. It's proportional to the number of turns and the length of
each turn of wire, and inversely proportional to the length of the
bobbin.

Is that "bobbin" a part of a coil winding machine? Coil form?

It's a spool-like object used to constrain the length and diameter of a
coil of wire to prescribed values.

73, Jim AC6XG

Esteemed Antenna Gentlemen.

I am sorry I could not participate in the heated discussions and do experiments
and measurements in the past few weeks. I was QRL, weather was lousy and I
caught the nasty flu that I hope to shake off in the South next few days.

It looks to me like some made statements (contrary to facts) and now are
defending them or going all out to prove they are right. Rather than
concentrating on the original question, is the current in the antenna loading
coil in typical mobile quarter wave whip same or different on its ends, we are
drifting to side shows like how precisely you measured it, what is your guess,
theory, toroids etc.

To recap, W9UCW measured, I witnessed and new that bottom of the coils get
hotter than top ergo, more current at the bottom. W8JI attacked that it can't
be, he stated it HAS to be equal, Kirchoff, bla, bla. (Now it is maybe not so
equal, length of coil, stray capacitance, phase of moon, but it is the same,
even when it isn't. Go figure.)

W8JI also proved that he lied when stated that he measured thousands of (what?)
coils and they all had equal current. Now he posted some measurements and
proved that he was wrong, he measured differences. He doesn't describe his
setup, and as Cecil explained, one can rig the coils to have the same current,
but in a center loaded resonant quarter wave vertical - no way.

Now we drifted to ferrites, we guessed Roy's difference and he measured it,
THERE WAS A DIFFERENCE 5% at the base. Is difference not a difference?

The first experiment I will do is the "thermal test" - I will take Hustler 80m
coil, I have two fishing tank LCD strip thermometers ($2.50 in any pet store) I
will stick them on the coil at the bottom, at the top, or in between. I will
fire TX to it and video tape the change in temperature with timer running.
Really smart gurus should be able to calculate the power and currents from
that. If gurus object that thermometers are disturbing the coil. Then the
thermal test No2 will be done. I will put higher power to it and see the coil
unshrink the tubing from the bottom up. I have done it before and it made me
true believer in the phenomena.

Next test will be with thermocouple ammeters and next with current probe
similar (but better) as W8JI used on his tests and showed on the web page.

Then we will try to correlate it with our "obscure theories", then we will
write the nice, detailed article that hopefully will help to understand the
thing for the other side of the fence gurus.

The proof is in reality, W9UCW done it, but that CAN'T BE?

Thanks Cecil and others for Herculean task and effort in digging out references
and trying to 'splain it. Looks like Krause and others are wrong, but old
Belrose error perpetuated in ARRL Antenna Book is right, oh and EZNEC modeling
0 size coil and loading stub differently is right too. W8JI used it as a proof
that current can be increasing from the base up to the coil. How come that
straight piece of wire (as antenna) can exhibit different current along its
length (where is Kirchoff) but when you insert the coil and retune it, that
coil "refuses" for current to taper?
Take the coaxial wound chokes, coil wound of coax at the antenna terminals can
reduce the current flowing in the shield. We know that, or are we going to deny
that? How is that COIL different that it has different RF current at its ends?
That you can check even with MFJ current meter.

I hope that weather gets better, flu goes away and life gives me more time. In
the mean time, if you are contemplating to get TenTec Orion, read my first part
of review on my web www.K3BU.us

73 Yuri