On Apr 29, 4:09*am, Cecil Moore wrote:
Jim Kelley wrote:
Cecil Moore wrote:
Itot = Imax*cos(kx)*cos(wt)

Noting the linear variables and constants in there, and the absence of
anything that would change abruptly at certain particular values of x,
what would the expression for a standing wave on a shortened coil loaded
90 degree monopole have to look like?

Ideally, it would be of the form:

For x = 0 to top of coil,
Itot = k1*cos(k2*x)cos(wt)

For x = bottom of stinger to top of stinger,
Itot = k3*cos(k4*x)*cos(wt)

where k1-k4 are constants

Note: The above is a conceptual simplification as it
ignores the current "bulge" in a real-world loading
coil.

Note that at the coil/stinger junction:

Itot = k1*cos(k2*x)*cos(wt) = k3*cos(k4*x)*cos(wt)

- as required by the laws of physics. Remember, it is
always implied that we are considering only the real
part of the phasor. Thus a current phasor can undergo
an abrupt amplitude and phase shift without changing
the real value.

10*cos(0) = 14.14*cos(45) = 10

The above phasor has abruptly rotated its phase by
45 degrees and increased its amplitude by 41% with
no violation of the laws of physics.
--
73, Cecil, IEEE, OOTC, *http://www.w5dxp.com

Cecil -

Mathematics is NOT a toy.

:-)

ac6xg

On Apr 29, 5:09*am, Cecil Moore wrote:
Jim Kelley wrote:
Cecil Moore wrote:
Itot = Imax*cos(kx)*cos(wt)

Noting the linear variables and constants in there, and the absence of
anything that would change abruptly at certain particular values of x,
what would the expression for a standing wave on a shortened coil loaded
90 degree monopole have to look like?

Ideally, it would be of the form:

For x = 0 to top of coil,
Itot = k1*cos(k2*x)cos(wt)

For x = bottom of stinger to top of stinger,
Itot = k3*cos(k4*x)*cos(wt)

where k1-k4 are constants

Note: The above is a conceptual simplification as it
ignores the current "bulge" in a real-world loading
coil.

It ingores almost everything about the antenna.

Note that at the coil/stinger junction:

Itot = k1*cos(k2*x)*cos(wt) = k3*cos(k4*x)*cos(wt)

Uh, what units did you say your constants k1-k4 had again?

- as required by the laws of physics.

Is that supposed to automatically add credibility to any remark which
preceeds it? Thusly, the nano-particles emitted by the framistat at
an impedance discontinuity carry only re-reflected energy - as
required by the laws of physics. It does sound impressive.

10*cos(0) = 14.14*cos(45) = 10

The above phasor has abruptly rotated its phase by
45 degrees and increased its amplitude by 41% with
no violation of the laws of physics.

Cecil -

Mathematics is NOT a toy.

:-)

ac6xg

"Jim Kelley" wrote in message
...
Is that supposed to automatically add credibility to any remark which
preceeds it? Thusly, the nano-particles emitted by the framistat at
an impedance discontinuity carry only re-reflected energy - as
required by the laws of physics. It does sound impressive.

It sounds like something art would say!

Jim Kelley wrote:
Mathematics is NOT a toy.

Sorry that it is beyond your comprehension level.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

Cecil Moore wrote:
Jim Kelley wrote:
Mathematics is NOT a toy.

Sorry that it is beyond your comprehension level.

So I take it you weren't able to answer the question, address the
issues, or resist posting insults.

ac6xg

Jim Kelley wrote:
So I take it you weren't able to answer the question, address the
issues, or resist posting insults.

I posted the math. You posted opinions devoid of
any technical content. Your assertions about
"nano-particles emitted by the framistat" do not
deserve a serious response.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

Jim Kelley wrote:
Cecil Moore wrote:
Note: The above is a conceptual simplification as it
ignores the current "bulge" in a real-world loading
coil.

It ingores almost everything about the antenna.

According to Kraus, the standing waves are the *primary*
effect associated with a standing-wave antenna. Everything
else is indeed a secondary effect. The standing wave current
is about 90% of the total steady-state current. Like a low-
loss transmission line, a loaded mobile antenna can be
analyzed by assuming that it is lossless.

"Antennas", by Kraus, 3rd edition, Standing Wave Antennas

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."

Page 464: "It is generally assumed that the current
distribution of a thin-wire antenna is sinusoidal, and
that the phase is constant over a 1/2WL interval, ..."

Both of Kraus' statements assume a lossless antenna.

Note that at the coil/stinger junction:
Itot = k1*cos(k2*x)*cos(wt) = k3*cos(k4*x)*cos(wt)

Uh, what units did you say your constants k1-k4 had again?

k1 and k3 have the units of current and are the magnitude
of the two standing-wave current phasors on each side of
the coil/stinger junction.

k2 and k4 have the units of degrees/unit-length so when
they are multiplied by x, the result is degrees. Of course,
it could be radians/unit-length.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

Cecil Moore wrote:
Jim Kelley wrote:
It ignores almost everything about the antenna.

"Antennas", by Kraus, 3rd edition, Standing Wave Antennas

Kraus on the other hand ignores almost nothing about antennas. (for ref.
I'm looking at his 2nd edition.)

Uh, what units did you say your constants k1-k4 had again?

k1 and k3 have the units of current and are the magnitude
of the two standing-wave current phasors on each side of
the coil/stinger junction.

k2 and k4 have the units of degrees/unit-length so when
they are multiplied by x, the result is degrees. Of course,
it could be radians/unit-length.

So the constants in your equations for current on the segments of a coil
loaded monpole a maximum current, wave number, and frequency; and the
linear variables are time, and distance.

Of those things, only maximum current would have any dependence at all
on the nature of the antenna. How does one know what value Imax to
plug-in for each segment?

ac6xg

Jim Kelley wrote:
Kraus on the other hand ignores almost nothing about antennas. (for ref.
I'm looking at his 2nd edition.)

On the contrary, for the purposes of current analysis on
a standing-wave antenna, Kraus ignores everything except
the current in the standing wave. I don't have the 2nd
edition but the graphic I am referencing was in the 1st
and 3rd editions.

Chapter 14 in the 3rd edition is "The Cylindrical Antenna
and the Moment Method".

In the 3rd edition, it is Figure 14-2, Relative current
amplitude and phase along a center-fed 1/2WL antenna. He
gives the curves for length/diameters of infinity and 75.
Please take a look at that graph in your 2nd edition and
in particular, note the current phase plot. This is the
same current that Roy used for his coil delay "measurements".

Kraus shows that phase angle varying by about 3 degrees over
180 degrees of antenna. How can that phase possibly be used
to measure the delay in a wire? Since it cannot be used to
measure the delay in a wire, why would anyone attempt to
measure the delay in a loading coil using the same current?

Of those things, only maximum current would have any dependence at all
on the nature of the antenna. How does one know what value Imax to
plug-in for each segment?

Kraus normalizes the feedpoint current to 1.0 and that's
good enough for me. The actual value of Imax obviously depends
upon the power incident upon the antenna. If one assumes a
current of 1.0 at the feedpoint of the coil, then one can calculate
the Imax at the base of the stinger given the Z0 of the loading
coil and the Z0 of the stinger. I can lead you through a
qualitative analysis if you so desire.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

Cecil Moore wrote:
Jim Kelley wrote:
Kraus on the other hand ignores almost nothing about antennas. (for
ref. I'm looking at his 2nd edition.)

On the contrary, for the purposes of current analysis on
a standing-wave antenna, Kraus ignores everything except
the current in the standing wave.

Kraus, in his book entitled "Antennas" ignores almost nothing about
antennas. I don't believe that is a controversial point of view.

Of those things, only maximum current would have any dependence at all
on the nature of the antenna. How does one know what value Imax to
plug-in for each segment?

Kraus normalizes the feedpoint current to 1.0 and that's
good enough for me.

Yes, unless of course you're talking about a real antenna with actual
current on it. That is what I thought we were talking about. My
recollection is that it was resonant on 75 meters, and the coil and
stinger have very specific dimensions.

The actual value of Imax obviously depends
upon the power incident upon the antenna. If one assumes a
current of 1.0 at the feedpoint of the coil, then one can calculate
the Imax at the base of the stinger given the Z0 of the loading
coil and the Z0 of the stinger.

It might even be better to measure it - with some type of current probe
device. Then you could solve for phase at any x or t you want.

ac6xg