Cecil Moore wrote:
Tom Donaly wrote:

I'm going to break my reply up into two pieces. First I
will address the actual number of degrees occupied by
a loading coil.

No, it's not a diversion. You're making up things in your head.
The original controversy involved a claim by you that the coil in
a short, mobile antenna made up for the degrees lost in said
shortened antenna.

Sorry Tom, that is a false statement. Please stop misquoting
me. The coil occupies some number of degrees but not nearly
enough to make up for all of the "lost" degrees which are not
lost at all as I have demonstrated in the past and will do so
again here. Following is a *resonant open-circuit 1/4WL stub*
that is electrically 90 degrees long yet it is only physically
38 degrees long.

Z1
---19 deg 450 ohm feedline---+---19 deg 50 ohm feedline---open
-j145

The 450 ohm feedline occupies 19 degrees of the stub. The 50
ohm feedline occupies 19 degrees of the stub. The stub is
physically 38 degrees long total. It needs another 52 degrees
to make it electrically 1/4WL long and resonant. The "lost"
52 degrees is *not lost at all* and occurs abruptly at the
junction point '+'. Call the impedance at that point Z1. The
52 degrees of phase shift occurs between Z1/450 and Z1/50.
Microsmith says that Z1 = -j145.

Z1/450 = -j145/450 = -j0.3222

Z1/50 = -j145/50 = -j2.9

Take a look at the number of degrees between -j0.3222 and
-j2.9 on a Smith Chart. Surprise! There is the "lost" 52
degrees. Those degrees are not lost at all and are just
a fact of physics concerning phase shifts at an impedance
discontinuity.

Now if we multiply the stub impedances by 10, we have
a reasonable facsimile of a resonant base-loaded monopole.

19 deg coil
///////////////-----19 deg ~500 ohm stinger-----open
Z0= ~4500 ohms
VF= ~0.02

The loading coil occupies 19 degrees and the stinger
occupies 19 degrees. There is a 52 degree phase shift
at the coil to stinger junction. There are no "lost"
degrees. 19+52+19 = 90 degrees.

There were (are) two sides to the argument.

1. The coil furnishes the "lost" degrees.
FALSE!
The coil furnishes some number of degrees but not
nearly enough to make up for the phase shift at
the coil/stinger junction.

2. The coil supplies almost zero degrees.
FALSE!
The phase shift at the coil/stinger junction is not
enough to account for the "lost" degrees. The magnitude
of that phase shift is easily calculated on a Smith Chart.

Please skip the ad hominem attacks and use the laws
of physics and mathematics to prove me wrong.
--
73, Cecil, w5dxp.com

I don't have to prove you wrong, Cecil, you have to prove yourself
right since you came up with this novel way of explaining antenna
behavior. A false analogy won't prove you right, in any case. Anyway,
this has all been chewed over before, and you've already used your hick
style argumentative techniques to little avail. It's too bad some
amateurs take you seriously enough to believe this garbage. They'd do
a lot better, and know a lot more if they'd learn the techniques and
mathematics found in innumerable books on the subject.
73,
Tom Donaly, KA6RUH

Tom Donaly wrote:
I don't have to prove you wrong, Cecil, you have to prove yourself
right since you came up with this novel way of explaining antenna
behavior.

I have offered a proof with which I detect no technical
problems and nobody has offered any valid technical argument
against what I have presented. My argument is not novel
and is based on sound physics as presented by the technical
references I have provided.

What I find difficult to understand is the sandbagging
going on in defense of an old wives' tale.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

Cecil Moore wrote:

What I find difficult to understand is the sandbagging
going on in defense of an old wives' tale.

Your description of the phenomenon is exactly that. Your claims about
standing wave current are unadulterated bull crap. Your understanding
of wave phenomena is significantly flawed in certain respects. You
refuse to recognize where you have erred, and you fend off criticism by
making ludicrous accusations of other people. With all due respect your
behavior is absolutely pathological, which unfortunately, tend to negate
the value in any valid arguments you might otherwise make.

Although some people do occasionally attempt to correct you where you
have made a mistake (others have given up trying), they are not 'out to
get you'. Try to keep it all real and in perspective, OM.

jk ac6xg

Jim Kelley wrote:
Your claims about
standing wave current are unadulterated bull crap.

You are certainly free to produce the physics and
mathematics to prove your assertion. Where is it?

I have provided equations and references. Please
tell me exactly which ones you dispute so I can
quote them.

Although some people do occasionally attempt to correct you where you
have made a mistake ...

The only mistakes of which I have been accused
are poor choices of words to which I plead guilty.
Nobody has accused me of invalid equations.

What you are experiencing is the dumbing down of
technical people where the lumped circuit model
and "mashed potatoes" model of energy in a transmission
line has taken over.

The equation for standing waves has been quoted
from "Optics", by Hecht; "... Optics", by Born and
Wolf, "Fields and Waves ...", by Ramo and Whinnery,
"Antennas ...", by Kraus, and "Antenna Theory", by
Balanis.

I strongly suspect you are capable of understanding
those references.

The following two equations are equivalent and are
the equations for pure standing wave current as
exists as the primary current on standing wave
antennas.

I(x,t) = 2(V+/Z0)cos(kx)*cos(wt)

I(x,t) = (V+/Z0)[e^(jwt-kx) - e^(jwt-kx)]

If you cannot look at those equations and see that
the phase is unchanging relative to all points on
the wire, you need to go back to school and
hone your math skills.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

TEST

As a newcomer to the group I'm hesitant to join a discussion which has
been running for almost 200 postings, and where the protagonists
understand the topic in much greater depth than I do. But here
goes ....

My starting assumption is that EZNEC can model a helical inductor
reasonably accurately, with the exception of the increase in AC
resitance caused by proximity effects.

If I take an EZNEC model of a coil - 40 turns #14 wire, 6" diameter,
12" long - I discover it has a characteristic impedance of about 2550
ohms at a self-resonant frequency of around 6.1 MHz. If I use it as
the base loading coil for a short vertical antenna with a 6ft whip
above it, I notice that EZNEC shows a difference in the current at the
top of the coil compared with the bottom of about 0.69:1, and a
resonant frequency of 3.79MHz.

I then look to see which of the various models might reasonably
predict the values observed in the EZNEC modelling.

Clearly, a simple lumped-element inductor doesn't get close. I've read
various web pages and postings which argue qualitatively that things
like "distributed capacitance" might explain some of the observations,
but as yet I've seen no quantitative analysis which attempts to
predict the numbers.

In contrast, I look at the work of Corum & Corum and of G3YNH who
insist that "coils are best regarded as transmission lines", and I get
quantitative results which closely match the EZNEC results. For my
example coil, I get a self resonant frequency of 6.3MHz (cf 6.1MHz),
a characteristic impedance of 2792 ohms (cf 2550 ohms) and an Iout/Iin
ratio of 0.72 (cf 0.69)

Not only that, the transmission line model predicts an inductive
reactance very close to that needed for antenna resonance at 3.79 MHz

I'm a simple soul, and I don't pretend to understand all the maths
involved; I merely observe that the transmission line approach
delivers "hard numbers" that closely match those predicted by EZNEC.
I've yet to see another model get close. So, until I do, I guess I
have to favour the approach of Corum & Corum, G3YNH et al.

If someone can show me similarly accurate results from an approach
based on a lumped-element model, I'd be interested to see them.

Steve G3TXQ

steveeh131047 wrote:
As a newcomer to the group I'm hesitant to join a discussion which has
been running for almost 200 postings, and where the protagonists
understand the topic in much greater depth than I do. But here
goes ....

My starting assumption is that EZNEC can model a helical inductor
reasonably accurately, with the exception of the increase in AC
resitance caused by proximity effects.

Yes, that's correct. Fortunately, proximity effect is generally
negligible unless the turn spacing is very close.

If I take an EZNEC model of a coil - 40 turns #14 wire, 6" diameter,
12" long - I discover it has a characteristic impedance of about 2550
ohms at a self-resonant frequency of around 6.1 MHz.

A single conductor doesn't have a characteristic impedance -- it's the
impedance between the two conductors of a transmission line. You can
measure a characteristic impedance between, say, a coil and ground, but
its value depends on the spacing between the two. If the coil is tilted
with respect to the ground, the impedance of this two-conductor system
will change with the position along the coil.

If I use it as
the base loading coil for a short vertical antenna with a 6ft whip
above it, I notice that EZNEC shows a difference in the current at the
top of the coil compared with the bottom of about 0.69:1, and a
resonant frequency of 3.79MHz.

I then look to see which of the various models might reasonably
predict the values observed in the EZNEC modelling.

Clearly, a simple lumped-element inductor doesn't get close. I've read
various web pages and postings which argue qualitatively that things
like "distributed capacitance" might explain some of the observations,
but as yet I've seen no quantitative analysis which attempts to
predict the numbers.

It's difficult or impossible to do with lumped elements. A vertical
loading coil has not only series inductance, but also capacitance to
ground or, in the case of a dipole, to the other half of the dipole.
This capacitance varies along the coil, being greatest at the bottom and
increasing toward the top. (This is the cause of the varying Z0 I
mentioned above.) But there's also a delay associated with the
capacitance which complicates the interaction to the point where you
can't easily model it with lumped elements. And the coil radiates, which
alters its current distribution.

That said, a lumped inductor makes a fairly decent model for a
physically very small (in terms of wavelength) toroidal loading coil,
since it has minimal capacitance to ground and a minimal amount of
radiation. I actually built a vertical, loaded it with one, and made
careful measurements which I posted on this newsgroup several years ago.
Cecil is still complaining about it.

The displacement current flowing through those capacitances, not some
"effective degrees of antenna" phenomenon, is what causes the current
along a solenoidal loading coil to vary. If you reduce the capacitances
to a low value as I did in my measurement, the currents at the ends
become nearly the same, which is what the measurement showed.

In contrast, I look at the work of Corum & Corum and of G3YNH who
insist that "coils are best regarded as transmission lines", and I get
quantitative results which closely match the EZNEC results. For my
example coil, I get a self resonant frequency of 6.3MHz (cf 6.1MHz),
a characteristic impedance of 2792 ohms (cf 2550 ohms) and an Iout/Iin
ratio of 0.72 (cf 0.69)

Not only that, the transmission line model predicts an inductive
reactance very close to that needed for antenna resonance at 3.79 MHz

You've kind of lost me here, since I can't see how you've replaced a
two-terminal coil with a four-terminal transmission line. And a
transmission line doesn't radiate, so that sometimes-important property
of a solenoidal coil is ignored.

I'm a simple soul, and I don't pretend to understand all the maths
involved; I merely observe that the transmission line approach
delivers "hard numbers" that closely match those predicted by EZNEC.
I've yet to see another model get close. So, until I do, I guess I
have to favour the approach of Corum & Corum, G3YNH et al.

Be sure to test the approach with other configurations, such as longer
and shorter coils, frequencies well away from resonance, etc. to find
the limits of applicability of the approach. Does it correctly predict
the field strength? Efficiency? Bandwidth?

If someone can show me similarly accurate results from an approach
based on a lumped-element model, I'd be interested to see them.

Me, too. The thing which prompted me to add the automated helix
generation feature to EZNEC was the realization that lumped loads so
often did a poor job of simulating solenoidal loading inductors.

Roy Lewallen, W7EL

Roy Lewallen wrote:
A single conductor doesn't have a characteristic impedance --

On the contrary, that is a false statement. In my
"Electronic Equations Handbook", it gives the
characteristic impedance for a single horizontal
wire about ground. Obviously, ground is the missing
conductor. I believe that equation is also given in
ARRL publications. A horizontal #14 wire 30 feet
above ground has a characteristic impedance very
close to 600 ohms. Since all of our antennas are
located a finite distance from ground, your assertion
seems ridiculous.

I actually built a vertical, loaded it with one, and made
careful measurements which I posted on this newsgroup several years ago.
Cecil is still complaining about it.

Yes, because the current on a standing wave antenna
doesn't change phase through the coil no matter what
the delay through the coil. EZNEC agrees with me.
Here is what EZNEC says about the current through
90 degrees of antenna:

EZNEC+ ver. 4.0
thin-wire 1/4WL vertical 4/21/2009 5:50:11 PM
--------------- CURRENT DATA ---------------
Frequency = 7.29 MHz
Wire No. 1:
Segment Conn Magnitude (A.) Phase (Deg.)
1 Ground 1 0.00
2 .97651 -0.42
3 .93005 -0.83
4 .86159 -1.19
5 .77258 -1.50
6 .66485 -1.78
7 .54059 -2.04
8 .40213 -2.28
9 .25161 -2.50
10 Open .08883 -2.71

How do you explain the fact that the current changes by
less than 3 degrees in 90 degrees of antenna? How can you
possibly measure the delay through a coil, or through a
wire, using a current like that?

The displacement current flowing through those capacitances, not some
"effective degrees of antenna" phenomenon, is what causes the current
along a solenoidal loading coil to vary.

Rhetorical question: Did you know that "displacement current"
is a patch added to the lumped circuit model to try to make
get closer to reality?

You've kind of lost me here, since I can't see how you've replaced a
two-terminal coil with a four-terminal transmission line. And a
transmission line doesn't radiate, so that sometimes-important property
of a solenoidal coil is ignored.

You wouldn't be lost if you knew that a single horizontal
wire above ground is a transmission line.

Me, too. The thing which prompted me to add the automated helix
generation feature to EZNEC was the realization that lumped loads so
often did a poor job of simulating solenoidal loading inductors.

Too bad you don't accept the EZNEC results of that addition
which I have posted on my web page and you have ignored.

P.S. Roy has threatened to refund my purchase price for EZNEC
and declare my copy of EZNEC to be a pirated copy unless I stop
using it to prove him wrong.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

Roy Lewallen wrote:

A single conductor doesn't have a characteristic impedance -- it's the
impedance between the two conductors of a transmission line. You can
measure a characteristic impedance between, say, a coil and ground, but
its value depends on the spacing between the two. If the coil is tilted
with respect to the ground, the impedance of this two-conductor system
will change with the position along the coil.

Roy: I understand what you are saying. But the derivation of
Characteristic Impedance in the Corum Bros. paper depends only on the
coil dimensions and number of turns; it is independent of any
relationship to other conductors or groundplanes. I also note that
ON4AA's inductance calculator predicts the "Characteristic impedance
of n=0 sheath helix waveguide mode at design frequency" based purely
on the coil geometry. The maths is a bit beyond me (trying to solve
Maxwell's equations for a solenoidal helix), but seems to bear analogy
to the derivation of the characteristic impedance of a waveguide.

I'm inclined to try to understand it better, because it's this derived
Characteristic Impedance, along with the axial Velocity Factor, that
generates the reactance values which seem such a good match to
experimental and modelled results.

Regards,
Steve G3TXQ

steveeh131047 wrote:
I've read
various web pages and postings which argue qualitatively that things
like "distributed capacitance" might explain some of the observations,
but as yet I've seen no quantitative analysis which attempts to
predict the numbers.

Hi Steve,

For a more quantitative illustration of how distributed reactance in
transmission lines causes delay see
http://www.rhombus-ind.com/dlcat/app1_pas.pdf

73, ac6xg