Current through coils
 

Objection, your Honor! Answer is unresponsive to the question.

Sustained.

8-)

Gee Cecil, how does one learn of such a "hidden mathematical concept",
when it does not seem to be embodied in the formalism?

Let's try again.

Suppose the standing wave is examined to perfection. Everything that can
be determined is measured without error. Now we take the superposition
in reverse; specifically we divide the standing wave into forward and
reverse traveling components. It would seem that we have a complete and
accurate definition for the two traveling wave components. The
interrelations, as you call them, between the variables and parameters
are fully defined by the basic math and the carefully measured standing
wave.

What else is needed to describe the traveling waves? Additional
variables? Additional coefficients or parameters? Additional hidden
mathematical concepts?

There seems to be a lack of understanding and appreciation for what the
concepts of "linear" and "superposition" really mean. These are not just
mathematical concepts. When they apply it means that the system under
study is fully and completely described by ** either ** the individual
functional subcomponents ** or ** the full superimposed functional
component. It is not necessary to use both formats, and there is no
added information by doing so.

Take a look at any of your favorite antenna references with an eye
toward the treatment of standing wave antennas. I believe you will find
only passing discussion of traveling waves. There will be some mention
of the equivalence between the two types of waves, but little else. It
is unlikely that you will find anything that says you will get more
information if you take the time and trouble to analyze traveling waves.

73,
Gene
W4SZ


Cecil Moore wrote:
Gene Fuller wrote:

As you have stated, including references from Hecht, it is customary
to mathematically show traveling waves in the form: cos (kz +/- wt)
Through straightforward addition and simple trigonometry is is seen
that the standing wave corresponding to the sum of equal magnitude
forward and reverse traveling waves has the form: cos (kz) * cos (wt)


I see I made a typo and typed a '+' sign in my previous equation.
Of course, it should have been a '*' sign for multiply.

Are there some hidden variables that have not been considered?


Not a hidden variable, but there seems to be a hidden
mathematical concept, at least hidden from some individuals.

In case some might not know, 'z' is the position up and down
the wire, omega (w) is our old friend 2*pi*f, and 't' is, of
course, time.

In the traveling wave equation, cos(kz +/- wt), the position on
the wire and omega*time are added or subtracted *before* the cosine
function is taken. That means that the position on the wire and the
phase velocity are inter-related. One cannot have one without the
other. And that is indeed a characteristic of a traveling
wave. Physical position, frequency, and time all go into
making a traveling wave. It is modeled as a rotating phasor.

However, in the equation, cos(kz) * cos(wt), the physical position,
'z' is disconnected from the phase velocity, 'wt'. The standing wave
is no longer moving in the 'z' dimension. If you pick a 'z' and hold
it constant, i.e. choose a single point on the wire, the standing
wave becomes simply some constant times cos(wt). Thus at any fixed
point on the line, the standing wave is not moving - it is just
oscillating at the 'wt' rate and a current probe will certainly pick
up the H-field signal. The phase of the standing wave current is
everywhere, up and down the 1/2WL thin-wire, equal to zero. The sum
of the forward phasor and reflected phasor doesn't rotate. Its phase
doesn't change with position. Only its magnitude changes with position
and if the forward wave magnitude equals the reflected wave magnitude,
it is not flowing in the real sense that current flows. It is a
standing wave and it is just standing there.

The main thing to realize is that the standing wave equation
divorces the position of the standing wave from its phase
velocity such that the phase velocity is not active in the
'z' dimension, i.e. up and down the wire. The standing wave
current "pseudo phasor" is not rotating. The standing wave
is not going anywhere. It is not flowing along a wire or
through a coil. Measuring its phase is meaningless because
the phase is already known to be constant and unchanging from
tip to tip in a 1/2WL dipole or across a loading coil in a
mobile antenna.

Thinking that standing wave current flows from the middle of a
dipole to the ends is just a misconception. The equation for
a standing wave indicates that it doesn't flow. What is flowing
are the forward and reflected waves.

Current through coils
 

Richard Harrison wrote:

Tom, K7ITM wrote:
"FWIW, the "aingle loop terminated in a diode" that provides both
magnetic and electric coupling at the same time" is not the only way to
make a directional coupler."

Agreed, but the Bird Electronic Corporation has been successful making
the plug-ins for their "Thruline Wattmeter" that way for about 50 years.

My old Heathkit HM-15 SWR meter has a short slotted through-line
with two parallel pick up wires located about halfway between the
center conductor and the shield. A 50 ohm resistor to ground at
one end kills the voltage in that direction. A diode at the
other end rectifies the voltage in the opposite direction.
With two resistors and two diodes on opposite ends of the two
pickup wires, they separate the forward wave from the reflected
wave.

The operation of the slotted line + pickup wires seems to be
a lot like the Thruline element in a Bird but with no slug
to rotate.
--
73, Cecil http://www.qsl.net/w5dxp

Current through coils
 

Cecil,

WOW! Thanks! I took all of those endless physics and math classes before
the Internet arrived, so I had no idea how a standing wave was formed.

8-) 8-) 8-)

OK, the same question. It is a pretty picture, but what extra
information would be gained if somehow the traveling wave components
could be measured?

73,
Gene
W4SZ


Cecil Moore wrote:
Gene Fuller wrote:

Again, what extra information would be gained if somehow the traveling
wave components could be measured?


Here's a pretty good animation of forward, reflected,
and standing waves.

http://users.pandora.be/educypedia/e...stwaverefl.htm

Current through coils
 

On Wed, 15 Mar 2006 15:02:23 GMT, Cecil Moore wrote:
Your 11.4 meter value assumes a VF of zero.

:-)

The crippling symptoms of Xerographic research strike again.

A quarter wave tall, two inch diameter coil is not resonant - at least
not at a fundamental in the 80M band.

Current through coils
 

Gene Fuller wrote:
... how does one learn of such a "hidden mathematical concept",
when it does not seem to be embodied in the formalism?

The standing wave function equation, cos(kz)*cos*wt), is different
in kind and function from the traveling wave function equation,
cos (kz ± wt).

When two traveling waves are moving along the same path in opposite
directions, their two phasors are rotating in opposite directions. It
is the sum of their phase angles that is a constant number of degrees.
It is that constant phase angle that has been measured and reported
here. Kraus shows a plot of the standing wave angle for a 1/2WL thin-
wire dipole. It is zero from tip to tip. Kraus has already told us that
its value is zero degrees. For a non-thin-wire, it deviates from zero
degrees, but not by much. There's no good reason to keep measuring it
over and over. A quantity whose phase is fixed at zero degrees cannot
tell us anything about the phase shift (delay) through a coil or even
through a wire.

Given: The phase shift in the standing wave current through 1/8WL of
wire in a 1/2WL thin-wire dipole is zero degrees.

What valid technical conclusions can be drawn from that statement?
That there is no phase shift in 45 degrees of wire in a 1/2WL dipole?

Suppose the standing wave is examined to perfection. Everything that can
be determined is measured without error. Now we take the superposition
in reverse; specifically we divide the standing wave into forward and
reverse traveling components. It would seem that we have a complete and
accurate definition for the two traveling wave components. The
interrelations, as you call them, between the variables and parameters
are fully defined by the basic math and the carefully measured standing
wave.

No argument. What some individuals seem to have missed are key
concepts involved in that process. In fact, that very process is
what I am presenting here.

What else is needed to describe the traveling waves? Additional
variables? Additional coefficients or parameters? Additional hidden
mathematical concepts?

What else is needed is already there but unrecognized by a number of
individuals. The equations for the forward and reflected waves are
different in kind and function from the equations for the standing
wave. Assuming equal magnitudes and phases for the forward and
reflected waves, the superposition of those two phasors yields a
result that is really not a bona fide phasor because it doesn't
rotate.

One cannot use a quantity whose phasor doesn't rotate to measure
phase shifts (delays) through coils or through wires. Pardon me
for having to state the obvious.

Picture one end of the 1/2WL thin-wire dipole and set the reference
phase of the forward current at 90 degrees. This is for reference
only to make the math easy. When the forward current hits the end
of the dipole, it undergoes a 180 degree phase shift and starts
traveling in the opposite direction as the reflected current. For
ease of math, let's assume the magnitude of the forward current and
reflected current at the end of the dipole is one amp.

Here's what the standing wave current will be at points along the
dipole wire looking back toward the center. The first column is
the number of degrees back toward the center from the end of
the dipole, i.e. the end of the dipole is the zero degree reference
for 'z'. The center of the dipole is obviously 90 degrees away
from the end.

Back forward current reflected current standing wave current
0 deg 1 at 90 deg 1 at -90 deg zero
15 deg 1 at 75 deg 1 at -75 deg 0.52 at 0 deg
30 deg 1 at 60 deg 1 at -60 deg 1.00 at 0 deg
45 deg 1 at 45 deg 1 at -45 deg 1.41 at 0 deg
60 deg 1 at 30 deg 1 at -30 deg 1.73 at 0 deg
75 deg 1 at 15 deg 1 at -15 deg 1.93 at 0 deg
90 deg 1 at 0 deg 1 at 0 deg 2.00 at 0 deg

Seven points on the standing wave current curve have been produced
by superposing the forward current and reflected current. One can
observe the phase rotation of the forward and reflected waves.
Please note the phase of the standing wave current is fixed
at zero degrees. Measuring it in the real world will produce
a measurement close to zero degrees. Its phase is already known.
Measuring it multiple times over multiple years continues to
yield the same close-to-zero value. Except for proving something
already known, those measurements were a waste of time.

The above magnitudes and phases of the standing wave current are
reproduced in a graph by Kraus, "Antennas for All Applications",
3rd edition, Figure 14-2, page 464.

There seems to be a lack of understanding and appreciation for what the
concepts of "linear" and "superposition" really mean. These are not just
mathematical concepts. When they apply it means that the system under
study is fully and completely described by ** either ** the individual
functional subcomponents ** or ** the full superimposed functional
component. It is not necessary to use both formats, and there is no
added information by doing so.

No argument there. But the individual doing the superposition needs to
understand exactly what he is doing or else he may make some conceptual
mental blunders. Trying to measure the phase shift of a quantity that
doesn't shift phases is one of those mental blunders.

Take a look at any of your favorite antenna references with an eye
toward the treatment of standing wave antennas. I believe you will find
only passing discussion of traveling waves. There will be some mention
of the equivalence between the two types of waves, but little else. It
is unlikely that you will find anything that says you will get more
information if you take the time and trouble to analyze traveling waves.

My only bona fide antenna references are Kraus and Balanis. Quoting:

Kraus: "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."

Balanis: "The sinusoidal current distribution of long open-ended linear
antennas is a standing wave constructed by two waves of equal amplitude
and 180 degree phase difference at the open-end traveling in opposite
directions along its length."

Balanis: "The current and voltage distributions on open-ended wire
antennas are similar to the standing wave patterns on open-ended
transmission lines."

Balanis: "Standing wave antennas, such as the dipole, can be analyzed
as traveling wave antennas with waves propagating in opposite directions
(forward and backward) and represented by traveling wave currents ..."
--
73, Cecil http://www.qsl.net/w5dxp

Current through coils
 

Gene Fuller wrote:
OK, the same question. It is a pretty picture, but what extra
information would be gained if somehow the traveling wave components
could be measured?

Hopefully, some individuals would gain enough information
that they would cease trying to use a quantity that doesn't
change phase for the measurement of phase shifts. Maybe
iteration would help.

The phase shift of standing wave current through 30 degrees
of coil or wire is close to zero degrees.

The phase shift of standing wave current through 45 degrees
of coil or wire is close to zero degrees.

The phase shift of standing wave current through 75 degrees
of coil or wire is close to zero degrees.

Measuring the phase shift of standing wave current through
a wire or a coil is pointless. One cannot use a quantity
that doesn't change phase for the measurement of phase
shifts.
--
73, Cecil http://www.qsl.net/w5dxp

Current through coils
 

Cecil Moore wrote:
Tom Donaly wrote:

If
he applies his reference formulae to one of Tom's coils and it
doesn't show the correct phase shift, though, his theory is in trouble.


His reference formulae are for traveling waves, not standing waves.
We already know that the phase of the standing wave current on a
1/2WL thin-wire dipole varies not one degree over that entire
180 degrees. Yet we know the forward wave undergoes a 90 degree
phase shift from feedpoint to tip and the reflected wave undergoes
a 90 degree phase on the trip back to the feedpoint. Standing wave
phase is virtually unchanging and is therefore useless for trying
to determine the electrical length of a wire or a coil.

Tell me a couple of things, Cecil: 1. the diameter of your bugcatcher
coil, and 2. the turn to turn wire spacing. I'd like to use the
information, using the formulae in your reference, to see just how
long your bugcatcher coil is electrically.
Thanks,
Tom Donaly, KA6RUH

Current through coils
 

Richard Clark wrote:

Cecil Moore wrote:
Your 11.4 meter value assumes a VF of zero.

A quarter wave tall, two inch diameter coil is not resonant - at least
not at a fundamental in the 80M band.

Nobody said it was resonant. The electrical length at 4 MHz
can be *estimated* from the self-resonant frequency of 16 MHz.

90 degrees at 16 MHz estimates to be approximately
90(4/16) = ~23 degrees at 4 MHz. Dr. Corum's strongly suggested
minimum electrical length for valid application of the lumped-
circuit analysis is 15 degrees.

Let's do a simple calculation to see how much error would be
had by using the lumped-circuit model in the following:

X---15 degrees of 450 ohm ladder-line---50 ohm load

The lumped-circuit model says the impedance at X is 50 ohms.

The impedance at X is really 53.5+j119

According to Dr. Corum, that's the maximum acceptable error
when using the lumped-circuit model. His standards apppear
to be lower than mine.
--
73, Cecil http://www.qsl.net/w5dxp

Current through coils
 

On Wed, 15 Mar 2006 17:30:10 GMT, Cecil Moore wrote:

Richard Clark wrote:

Cecil Moore wrote:
Your 11.4 meter value assumes a VF of zero.

A quarter wave tall, two inch diameter coil is not resonant - at least
not at a fundamental in the 80M band.

Nobody said it was resonant.

You seem to be shy of many details from your reference. VF of zero
indeed.... You can't even plug-n-chug your own referred equations.
Such are the hazards of a Xerox research method.

Hi Tom,

As you, I didn't expect to see any concrete numbers from that last
flurry of equations. I don't see how with his free mix of quarterwave
substituted as resonant to backfill an argument of a short coil
justified as a long one.

Tom's simple example, a 2 inch diameter coil of 10 inches with 100
turns seems to have buffaloed his finding the Velocity Factor or
Characteristic Impedance. And how would it compare in contrast to
Reggie's formulas? That would seem to invite discussion of results
instead, which would have collapsed this opus to a thread of three
postings.

As such, it serves only to entertain on a rainy morning (your weather
may vary - but in Seattle, never).

73's
Richard Clark, KB7QHC

Current through coils
 

Tom Donaly wrote:
Tell me a couple of things, Cecil: 1. the diameter of your bugcatcher
coil, and 2. the turn to turn wire spacing. I'd like to use the
information, using the formulae in your reference, to see just how
long your bugcatcher coil is electrically.

Please note that when my 75m bugcatcher coil is mounted
just above my GMC pickup ground plane, it is electrically
almost four times longer than it is laying on a stack of
books in my hamshack. The coil capacitance to ground is
obviously a lot higher when mounted over a ground plane.
The ground plane reduces the VF to approximately 1/4
the value obtained in isolation.

1. The measured self-resonant frequency of the coil
mounted on my pickup is ~6.6 MHz.

2. The measured self-resonant frequency of the coil
on a mag mount on my all-metal desk is ~6.6 MHz.

3. The measured self-resonant frequency of the coil
isolated from any ground is ~24.5 MHz.

The self-resonant frequency needs to be measured in
the environment in which it is installed. That means
one needs to model the coil 3 inches above a perfect
ground plane before calculating the self-resonant
frequency, Z0, or VF. I doubt that Dr. Corum's equations
take that into account since it would seem self defeating
to operate a Tesla coil over a physically close ground
plane. But I could be wrong on that point.

The coil data is: ~6" dia, ~6.7" long, 26.5 T, seems
very close to 4 TPI. Looks to be #14 solid wire.
--
73, Cecil http://www.qsl.net/w5dxp