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

Jim Kelley wrote:

I have the same recollection as Tom.

If you do, it was from many years ago when I was young
and foolish. :-) For the past 5 years, at least, I have
been telling everyone that both sides of the argument
are wrong as rail-arguments usually are. The facts lie
somewhere in between the two rails.

Or, maybe
3. A less than quarter wave antenna is less than 90 degrees long.

Obviously true for the physical length. Just as obviously
impossible for the electrical length. If you understand
that the feedpoint is purely resistive and
Zfp = (Vfor-Vref)/(Ifor+Iref) then you will understand
that the antenna *must* be electrically an interger
multiple of 90 degrees long.

If you need help with that concept, let me know. If you
are embarrassed to discuss it in public, send me an email.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

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

"Art Unwin" wrote in message
...

At the expense of efficiency per unit length

and what does that refer to?? i don't think i've ever heard of something
with those units... they really don't make any sense.

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

On Apr 21, 5:49*pm, "Dave" wrote:
"Art Unwin" wrote in message

...

At the expense of efficiency per unit length

and what does that refer to?? *i don't think i've ever heard of something
with those units... they really don't make any sense.

Somebody changed the subject. I suppose you can start a new one since
this one has been taken away
Art

Cecil Moore wrote:

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?

Not to intrude, but I thought you were discussing a coil. The above
seems to be about an antenna.

By extension, if an inductor acts the same as an antenna, then a
capacitor also acts like an antenna. QEF.

So I guess that implies that a capacitor isn't much different than an
inductor.

I've misunderstood so much, I think I may just have to end it all.

tom
K0TAR

Perhaps I could share a few thoughts on the "missing degrees" topic;
and again I apologise as the new boy if this has all been covered
before! I found the following argument helpful when trying to get my
head around some of the issues, and it may help others:

Picture the short, base-loaded, 6ft vertical antenna example I gave
earlier which resonates at 3.79MHz with the coil dimensions I quoted.
The 6ft whip represents an electrical length of about 9 degrees. Now
suppose I remove the 12" long loading coil leaving a 12" vertical gap
in the antenna. At this point I find it much more helpful to think in
terms of a "missing" +j2439 ohms reactance, rather than a "missing" 81
degrees, for reasons we shall see later.

Now I run out a couple of horizontal wires from where the top and
bottom of the coil were connected, and short them at the far end
thereby forming a short-circuit stub. That stub will insert some
"loading inductance" in place of the coil. How long do I need to make
the stub to bring the vertical back to resonance?

Using the simplified stub formula Xl=+jZo.tan(Bl), and assuming for
now that the characteristic impedance is 600 ohms, I find that the
electrical length needed to generate +j2439 is 76 degrees - well short
of any "missing" 81 degrees. And if I increase the characteristic
impedance of the stub to 1200 ohms I only need 64 degrees. The Corum &
Corum formulas tell me that the characteristic impedance of my
original loading coil is 2567 ohms at this frequency, so that only
requires an electrical length of 43 degrees.

So, for me, the "missing degrees" question is not really about missing
degrees; rather, it's about a missing inductive reactance which can be
provided by transmission line structures with a wide range of
electrical lengths depending on their characteristic impedance. The
"constant" is the reactance, not the electrical length.

I also find this picture helpful because I can visualize that,
although there must be forward and return waves on the stub, the net
current I would observe is a standing wave whose phase doesn't change
along the length of the stub. Incidentally, taking 43 degrees as the
length of my loading coil I would expect to see a change in current
amplitude along the length of the stub of cos(43); that's 0.73 -
pretty close to the 0.69 observed in the EZNEC model between the ends
of the coil.

Finally, I ask what the transmission line characteristic impedance
would need to be for its length to be exactly the "missing" 81
degrees? Answer: 2349/atan(81)=273 ohms. Isn't that in the right ball
park for the characteristic impedance of a single straight piece of
wire - in fact the piece of wire that's needed to turn the 6ft whip
into a full quarter-wave vertical?

And finally, finally, to Roy: I struggle with the "mental gymnastics"
needed to move from the simple stub model outlined above, to one where
the "transmission line" is a single wire, not two wires, and "in-line"
with the antenna elements. If you read the Curum & Corum paper I'm
sure it will be clearer to you than to me! But until I can understand
it better, I content myself with this thought: if we removed 56ft of
wire from our full-sized quarter-wave vertical to leave just the 6ft
whip, we'd be happy to analyse this 56ft straight piece of wire using
a transmission line approach (including considering forward &
reflected waves, and the resultant standing wave along it), and to
ascribe to it an equivalent inductive reactance. I don't understand
why I (we?) find it intellectually any more difficult to take the same
approach with a piece of wire once it is wound into a helix.

Regards,
Steve G3TXQ

steveeh131047 wrote:

Steve, congratulations on your QST article.

Now I run out a couple of horizontal wires from where the top and
bottom of the coil were connected, and short them at the far end
thereby forming a short-circuit stub. That stub will insert some
"loading inductance" in place of the coil. How long do I need to make
the stub to bring the vertical back to resonance?

I would also ask the questions: How much delay is there through
a series stub? What is the phase shift through the stub measured
by using the current on this standing-wave antenna? See below.

I also find this picture helpful because I can visualize that,
although there must be forward and return waves on the stub, the net
current I would observe is a standing wave whose phase doesn't change
along the length of the stub.

Someone is likely to point out that if one uses a current probe
to observe the current, it looks like a sine wave, i.e. its
phase is obviously changing with time. The point is that the
phase changes very little with length.

What we must be careful to say is that the phase doesn't change,
RELATIVE TO THE SOURCE PHASE, along the length of the stub. Here's
what EZNEC says about the phase in a 1/4WL open-circuit stub.

EZNEC+ ver. 4.0
1/4WL open stub in free space 4/22/2009 7:08:09 AM
--------------- CURRENT DATA ---------------
Wire No. 2:
Segment Conn Magnitude (A.) Phase (Deg.)
1 W1E1 .99665 -0.25
2 .97169 -0.67
3 .92292 -1.01
4 .85155 -1.30
5 .75929 -1.53
6 .64841 -1.72
7 .52163 -1.86
8 .38205 -1.96
9 .23309 -2.03
10 Open .07839 -2.07

Only 2 degrees of current phase shift in 90 degrees of stub.
How can that current be used to calculate delay through the
stub?
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

steveeh131047 wrote:
. . .
And finally, finally, to Roy: I struggle with the "mental gymnastics"
needed to move from the simple stub model outlined above, to one where
the "transmission line" is a single wire, not two wires, and "in-line"
with the antenna elements. If you read the Curum & Corum paper I'm
sure it will be clearer to you than to me! But until I can understand
it better, I content myself with this thought: if we removed 56ft of
wire from our full-sized quarter-wave vertical to leave just the 6ft
whip, we'd be happy to analyse this 56ft straight piece of wire using
a transmission line approach (including considering forward &
reflected waves, and the resultant standing wave along it), and to
ascribe to it an equivalent inductive reactance. I don't understand
why I (we?) find it intellectually any more difficult to take the same
approach with a piece of wire once it is wound into a helix.

Regards,
Steve G3TXQ

The similarities between an antenna and transmission line have been
known for a very long time and described in a number of papers. (See for
example Boyer, "The Antenna-Transmission Line Analog", _Ham Radio_,
April and May 1977, and Schelkunoff, "Theory of Antennas of Arbitrary
Size and Shape", _Proc. of the I.R.E., Sept. 1941.) It's a useful
conceptualization tool but, like comparing electricity to water in a
pipe, has its limitations. If you look at the transmission line
properties of a vertical, you see that the two conductors (the antenna
and ground plane) get farther and farther apart as the distance from the
feedpoint increases. This behaves like a transmission line whose
impedance increases with distance from the feedpoint and, in fact, a TDR
response shows just this characteristic. It's open circuited at the end,
so it behaves pretty much like an open circuited transmission line,
resulting in the same reflections and resulting standing waves you see
on a real antenna. One difficulty is accounting for the radiation, which
adds resistance to the feedpoint. I've never seen an attempt at
simulating it with distributed resistance, which I don't think would
work except over a narrow frequency range. Boyer deals with this by
simply adding a resistance at the model feedpoint, noting that the
resistance doesn't change very rapidly with frequency. So this is one
inherent shortcoming of the transmission line analog. As long as you
incorporate the increasing Z0 with distance from the feedpoint and the
limitations of the resistive part, the model does reasonably well in
predicting the feedpoint characteristics of simple antennas. But one
shortcoming of many antenna transmission line analogies is the attempt
to assign a single "average" or "effective" characteristic impedance to
the antenna, rather than the actual varying value. This is where a lot
of care has to be taken to assure that the model is valid in the regime
where it's being used.

There's no reason you can't also include a loading coil in the
transmission line model, and Boyer devotes much of the second part of
his article to doing just that. A solenoidal coil raises the
characteristic impedance of the length of "line" it occupies, because of
the increase in L/C ratio in that section. The traveling wave delay in
that section of the transmission line also increases due to the
increased LC product. (L and C are per unit length in both cases.) But
don't forget the C which is an essential part of this analysis, and
don't forget that the C is decreasing from the bottom to the top of the
coil, resulting in an increasing characteristic impedance. A very short
coil like a toroid will raise the Z0 only for a very short distance, so
behaves differently from a long solenoidal coil.

Models or analogs can be very useful in gaining insight about how things
work. You have to remain vigilant, though, that you don't extend the
analogy beyond it realm of validity.

Roy Lewallen, W7EL