Putting old-wives and baffle-gabbers out of their misery.
 

THE ONLY WAY TO ACCURATELY MODEL A LOADED VERTICAL


and similar coil and capacitance loaded structures, is as follows.


Let's take the most simple structure consisting of 3 sections - top, centre
and bottom.


The top is usually referred to as a whip or a rod.


The centre section is a loading coil.


The bottom section can be referred to as the mast.


All three sections have length and external diameter.


All three sections have uniformly-distributed inductance, capacitance and
resistance per unit length. All calculable from dimensions.


It is inescapable, therefore, the structure consists of -


THREE CASCADED TRANSMISSION LINES SECTIONS.


As with ALL transmissions lines, each section has a characteristic impedance
Zo, attenuation and phase-shift per unit length. All caculable from
dimensions.


The centre section, a solenoidal loading coil, clearly has inductance extra
to that due to the length of the coil former. The extra inductance is
calculable from the number of coil turns per unit length. If necessary
self-capacitance can be included.


ALL sections have a UNIFORMLY DISTRIBUTED radiation resistance which is
extra to conductor loss resistance. The two resistances are combined by
simple addition. Radiation resistance is itself obtained from the length of
a section.


CALCULATING PROCEDURE / PRINCIPLES.


This is done by using classical transmission formulae or by the well known
sufficiently accurate approximations.


Looking upwards from the base of the antenna -


(1) Calculate the input impedance at the bottom of the whip (or rod). The
whip is a transmission line open circuit at the top end.


(2) Calculate the input impedance at the bottom end of the loading coil,
the centre section. The centre section is a transmission line terminated by
the input impedance of the whip above it.


(3) Calculate the impedance looking up from the base of the antenna. The
feedpoint impedance. The bottom antenna section being a transmission line
terminated by the input impedance of the centre antenna section, the loading
coil.


(4) Connect a generator, the transmitter, between the base of the antenna
and ground. The ground will have its own 'input' resistance depending on the
ground electrodes or perhaps the vehicle characteristics.


(5) Using classical transmission line formulae, or their close
approximations, the amps, volts, relative phase-angles, can be calculated,
IF NECESSARY, at any point along the antenna, at any point along the coil,
from its base to the extreme tip of the whip


(6) But a full analysis is unnecessary. Nevertheless there's a big bunch of
calculations to be done to calculate radiating efficiency, a single number,
the ultimate solitary objective. Of what use to anybody is the difference
between input and output currents of the loading coil?


(7) The radiation pattern is eventually available. But even CB-ers are
familiar with the radiation pattern of a simple vertical antenna, loaded or
not, which is less than 5/8ths wavelengths in height.


(8) By an obvious extension of the above principles, a top hat on the top
of the whip, such as a set of radial wires within a ring, can be
automatically accounted for.


Now, you old-wives, what can be more simple than THAT? KISS!


I'm very sorry, due to recommendations by the medical profession, I have to
decline invitations to tea-parties in Boston, Mass.


And stop haggling amongst youselves. You have quite enough problems to sort
out on your side of the Atlantic.


As examples of practical use of the foregoing principles, download in a few
seconds and run immediately short, self-contained programs LOADCOIL and
TOPHAT2 from website below. Free to USA citizens.
----
.................................................. ..........
Regards from Reg, G4FGQ
For Free Radio Design Software go to
http://www.btinternet.com/~g4fgq.regp
.................................................. ..........

"Reg Edwards" wrote in message
...

THE ONLY WAY TO ACCURATELY MODEL A LOADED VERTICAL
snip
All three sections have uniformly-distributed inductance, capacitance and
resistance per unit length. All calculable from dimensions.
snip
THREE CASCADED TRANSMISSION LINES SECTIONS.
snip
Now, you old-wives, what can be more simple than THAT? KISS!
snip

simple or accurate??? you can't have both. in this case you have ignored,
among other things, that the capacitance between each infinitesimal part of
each vertical piece to the rest of the world is different. therefore your
transmission line sections are not uniform from end to end as needed to use
the classical transmission line formulations. Then of course you must also
consider that the actual radiated part of the field makes those
'transmission lines' appear extremely lossy... unfortunately that loss is
not the R and G type loss as the transmission line formulas use, though
those losses do also exist.

David Robbins wrote:

---------------
simple or accurate??? you can't have both. in this case you have ignored,
among other things, that the capacitance between each infinitesimal part of
each vertical piece to the rest of the world is different. therefore your
transmission line sections are not uniform from end to end as needed to use
the classical transmission line formulations.
---------------

But, since the 'classic' antenna calculations are only
approximate, how
much additional error would Reg's method entail, if any? I
think the
"simple -vs- accurate" thingy is one of the things that Reg was
getting at.
Very 'fiddly' (Hey Reg! I picked up an 'English' word, or would
that be
an 'UK-ism', sort of like an 'American-ism'?)...
'Doc

On Fri, 05 Dec 2003 12:06:42 -0600, 'Doc wrote:
But, since the 'classic' antenna calculations are only approximate,
how much additional error would Reg's method entail, if any?
Hi Doc,

Or more to the tenor of the purpose, how much accuracy would they add?
The point was in critical thinking and David's post extended that
horizon. This is all for the purpose of deriving a drive point Z,
which is the Three Card Monty of analysis.

73's
Richard Clark, KB7QHC

When you can write AND DEMONSTRATE QUANTITATIVELY programs which provide
even more accurate models/results than what I have provided then please make
them available to the world.

You have much to learn. From the zero level of bafflegab you have just
produced I'll give you another 40 years. As things are you are well on your
way to joining the 'old wives' brigade.

But please believe me. I have no wish to be unkind or discourage your
admirable young man's enterprise. By all means keep persisting.
---
Yours, Reg.

"Reg Edwards" wrote in message
...

When you can write AND DEMONSTRATE QUANTITATIVELY programs which provide
even more accurate models/results than what I have provided then please
make
them available to the world.

You have much to learn. From the zero level of bafflegab you have just
produced I'll give you another 40 years. As things are you are well on
your
way to joining the 'old wives' brigade.

But please believe me. I have no wish to be unkind or discourage your
admirable young man's enterprise. By all means keep persisting.
---
Yours, Reg.



it would help if you provided your model.

Reg,
I recommend the following pair of wonderful articles.
Part one is in HAM RADIO, April, 1977, pp. 52-58. The second in May,
1977, pp. 29-39.
The full reference is: Boyer, Joseph M. (W6UYH): "The
Antenna-Transmission
Line Analog".

Mr Boyer simplifies the antenna analysis by equating parts of the
antenna to transmission lines along the same lines that you have.
Regards
Nat

David,
I do like your reply to Reg since it evokes more thought
to the transmission line theory talk.
But the main point Reg, is I believe that all the group is in
in agreement with respect to current change and a 'large '
inductance, and those bonded to 50/60 hertz type thinking
have fled.
The only important thing left for some is to not
over react at the knowledge that lumped loads are theoretical
in nature since viewing same can provide advantages in
solutions for networks whether it be household frequency
or broadcast style frequencies.
Knowledge is what is valuable, whether that knoweledge
is inconsequential or not to ones needs.

As far as our problems in the U.S.A. Reg. As I pointed out
in a Letter to the Editor when presented with terrorism by
the Stern gang in London the U.K. handed the problem of
a homeland for Jews to the U.N. The U.N. never anticipated
that the U.S. by virtue of its veto, would support an expansion
of lands in the same way we did against the American Indian,
forgetting that if you can't kill them all then you have a
world wide conflict with respect to those who practice Islam.

Cheers and beers
Art


"David Robbins" wrote in message ...
"Reg Edwards" wrote in message
...

THE ONLY WAY TO ACCURATELY MODEL A LOADED VERTICAL
snip
All three sections have uniformly-distributed inductance, capacitance and
resistance per unit length. All calculable from dimensions.
snip
THREE CASCADED TRANSMISSION LINES SECTIONS.
snip
Now, you old-wives, what can be more simple than THAT? KISS!
snip

simple or accurate??? you can't have both. in this case you have ignored,
among other things, that the capacitance between each infinitesimal part of
each vertical piece to the rest of the world is different. therefore your
transmission line sections are not uniform from end to end as needed to use
the classical transmission line formulations. Then of course you must also
consider that the actual radiated part of the field makes those
'transmission lines' appear extremely lossy... unfortunately that loss is
not the R and G type loss as the transmission line formulas use, though
those losses do also exist.

it would help if you provided your model.

========================

There's a dozen of them to choose from at my website. Some been sitting
there for years. Moneyback guarantee. Present download rate averages around
200 per day.


When can we expect one of yours? Try an easy one first. What about doing a
10 feet length of 14 gauge plastic-insulated stuff? Don't forget end-effect
or you'll receive hate-mail from people suffering from delusions of
accuracy.
---
Reg

"Nat Gurumoorthy" wrote Reg,
I recommend the following pair of wonderful articles.
Part one is in HAM RADIO, April, 1977, pp. 52-58. The second in May,
1977, pp. 29-39.
The full reference is: Boyer, Joseph M. (W6UYH): "The
Antenna-Transmission
Line Analog".

Mr Boyer simplifies the antenna analysis by equating parts of the
antenna to transmission lines along the same lines that you have.
Regards
Nat

================================

Nat, Antennas and transmission lines are not just analogues - Antennas
ARE transmission lines with controlled 'leakage'. In fact, as people
forever complain on these walls, it is impossible to prevent a transmission
line FROM leaking.

Genuine guru's lump the names 'lines' and 'antennas' together in one volume.
They may mention in passing that the mathematics are identical to both in
case a casual reader doesn't realise it. But if Terman disdainfully omits
mention of the obvious there's always the danger that his disciples may
think it doesn't exist.

I produced the brief semi-serious description just for the purpose described
in the subject line ;o)
----
Reg, G4FGQ

"Art Unwin KB9MZ" wrote in message
m...
As far as our problems in the U.S.A. Reg. As I pointed out

politics... plonk!

Reg Edwards wrote:
Antennas and transmission lines are not just analogues - Antennas
ARE transmission lines with controlled 'leakage'. In fact, as people
forever complain on these walls, it is impossible to prevent a transmission
line FROM leaking.

The reason they are considered separately is that their functions are
different. Steps are taken to minimize transmission line 'leakage'.
Steps are taken to maximize antenna 'leakage'.

I was surprised that, for the purpose of a ballpark conceptual analysis,
Kraus considers the reflected current on a dipole to be equal to the
forward current. But then I remembered 50% of the power can be radiated
while the current drops by only 29.3%.

Here's what 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 ... 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."

Exactly the same thing can be said about a lossless unterminated
transmission line. If lumped circuit analysis doesn't work on
transmission lines with reflections, why should it be expected
to work on antennas with reflections?
--
73, Cecil http://www.qsl.net/w5dxp



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Exactly the same thing can be said about a lossless unterminated
transmission line. If lumped circuit analysis doesn't work on
transmission lines with reflections, why should it be expected
to work on antennas with reflections?
--
73, Cecil http://www.qsl.net/w5dxp



While I agree with this statement, it still doesn't prove anything
about the value of the characteristic impedance and electrical
length of a loading coil and the relationship between these
parameters and the inductive reactance of the loading coil.
This is what bothers me about the claims that the "cosine law"
can be used to predict the current taper in the loading coil.
Seems that there is a big leap of faith taking place when going
from the observation (which I believe is correct) that current
taper is caused by standing waves on the resonant antenna,
and a "law" that says what we can predict that taper with a
simple formula without saying anything about the shunt
capacitance per unit length and series inductance per
unit length of the loading coil, quantities which normally
bear directly on the characteristic impedance and velocity
of propagation of the EM structure (at least in an
analogous transmission line case).

73 de Mike, W4EF.............................................



Exactly the same thing can be said about a lossless unterminated
transmission line. If lumped circuit analysis doesn't work on
transmission lines with reflections, why should it be expected
to work on antennas with reflections?
--
73, Cecil http://www.qsl.net/w5dxp



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On Sat, 6 Dec 2003 03:54:24 +0000 (UTC), "Reg Edwards"
wrote:

I produced the brief semi-serious description just for the purpose described
in the subject line

So, are you feeling better? ;o)

You have missed the point again. It is I who should be asking YOU if you are
feeling better ;o)

On Sat, 6 Dec 2003 20:23:12 +0000 (UTC), "Reg Edwards"
wrote:

You have missed the point again. It is I who should be asking YOU if you are
feeling better ;o)

Never been better OM. I'm off to Buenos Aires for a couple of weeks
to escape the rain. Hope you are feeling better soon.

73's
Richard Clark, KB7QHC

Michael Tope wrote:
This is what bothers me about the claims that the "cosine law"
can be used to predict the current taper in the loading coil.

It is certainly NOT a "cosine law". It is at best an approximation.
From _Antennas_For_All_Applications_ by Kraus & Marhefka, third
edition, page 464: "The difference between these (dashed) curves
and the solid curves is not large but is appreciable." The solid
curves are cosine curves. The dashed curves, indicating the actual
current, are not cosine curves but are relatively close approximations.

The only time pure cosine curves will result for net current is in
a lossless situation which is certainly not entirely valid or accurate
for a radiating antenna.

If the magnitudes of the forward current and reflected currents are
not equal, there will be a drift away from a pure cosine shape.
--
73, Cecil http://www.qsl.net/w5dxp



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On Sat, 06 Dec 2003 20:40:31 GMT, Richard Clark
wrote:

|On Sat, 6 Dec 2003 20:23:12 +0000 (UTC), "Reg Edwards"
wrote:
|
|You have missed the point again. It is I who should be asking YOU if you are
|feeling better ;o)
|
|Never been better OM. I'm off to Buenos Aires for a couple of weeks
|to escape the rain. Hope you are feeling better soon.

You don't have to go that far. It was sunny and 82 degrees in Tucson
yesterday :-)

Lovely antenna building weather.

Mike, W4EF wrote:
"---standing waves on the resonant antenna, and a "law" that says what
we can predict that taper with a simple formula---."

It`s as simple as ON4UN`s Fig 9-22 center loading diagram. The resonant
element is 90-degrees long. Any missimg wire length must be provided by
the loading.

Best regards, Richard Harrison, KB5WZI

On Sun, 07 Dec 2003 06:56:16 -0700, Wes Stewart
wrote:

On Sat, 06 Dec 2003 20:40:31 GMT, Richard Clark
wrote:

|On Sat, 6 Dec 2003 20:23:12 +0000 (UTC), "Reg Edwards"
wrote:
|
|You have missed the point again. It is I who should be asking YOU if you are
|feeling better ;o)
|
|Never been better OM. I'm off to Buenos Aires for a couple of weeks
|to escape the rain. Hope you are feeling better soon.

You don't have to go that far. It was sunny and 82 degrees in Tucson
yesterday :-)

Lovely antenna building weather.

Hi Wes,

Well, in truth, I am only going half way (metaphorically speaking) to
meet friends returning from a 3 week Antarctic cruise.

73's
Richard Clark, KB7QHC

Interesting. I don't have this book handy [all I have is my signed
copy of "Antennas, 2ed" :):)]. Is there any indication in the text as
to where the "actual current" data came from? Is it derived from
some sort of EM analysis, or is it measured data I wonder?
I think Kraus spent a lot of time studying helical structures
while he was developing the helical antenna. Since a loading
coil is basically a helical antenna operating in the normal mode
perhaps the answer to this question lies in some of his early
work.

Thanks,

Mike, W4EF.............................................. .........


"Cecil Moore" wrote in message
...
Michael Tope wrote:
This is what bothers me about the claims that the "cosine law"
can be used to predict the current taper in the loading coil.

It is certainly NOT a "cosine law". It is at best an approximation.
From _Antennas_For_All_Applications_ by Kraus & Marhefka, third
edition, page 464: "The difference between these (dashed) curves
and the solid curves is not large but is appreciable." The solid
curves are cosine curves. The dashed curves, indicating the actual
current, are not cosine curves but are relatively close approximations.

The only time pure cosine curves will result for net current is in
a lossless situation which is certainly not entirely valid or accurate
for a radiating antenna.

If the magnitudes of the forward current and reflected currents are
not equal, there will be a drift away from a pure cosine shape.
--
73, Cecil http://www.qsl.net/w5dxp

Mike, W4EF wrote:
"Is there any indication in the text as to where the actual current data
came from?"

Not exactly, on page 464 of the 3rd edition of Kraus` "Antennas", that I
saw. Below the diagrams of current versus distance from the center of
the dipole, the text says:

"It is generally assumed that current distribution on an infinitesimally
thin antenna---is sinusoidal, and that the phase is constant over
1/,2-WL interval, changing abruptly by 180-degrees between intervals."

On page 295, Kraus says:
"If the dimensions (of a helix) are small (nLlambda), the maximum
radiation is in the xy plane for a helix oriented as in Fig 8-69a, with
zero radiation in the z direction."

In other words, radiation is perpendicular (normal) to the axis of small
diameter coils.

On page 295, Kraus says:
In the preceding discussion on the normal mode of radiation, the
assumption is made that the current is uniform in magnitude and in phase
over the entire length of the helix. This condition could be
approximated if the helix is very small (nLlambda) and is end loaded.
However, the bandwidth of such a small helix is very narrow, and the
radiation efficiency is low."

It is obvious that the inductance and delay of a coil depend upon on the
coil`s diameter and pitch, in addition to the length of the coil.

Best regards, Richard Harrison, KB5WZI

Michael Tope wrote:
Interesting. I don't have this book handy [all I have is my signed
copy of "Antennas, 2ed" :):)]. Is there any indication in the text as
to where the "actual current" data came from?

King, Ronold & C.W.Harrison, Jr, "The Distribution of Current along a
Symmetrical Center-Driven Antenna", Proc. IRE, 31, 548-567, October 1943.
--
73, Cecil http://www.qsl.net/w5dxp



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Richard Harrison wrote:
"It is generally assumed that current distribution on an infinitesimally
thin antenna---is sinusoidal, and that the phase is constant over
1/,2-WL interval, changing abruptly by 180-degrees between intervals."

I just realized that the IRE reference I gave in another thread is for
a l/a=75 example, i.e. not for an l/a=infinity example.

But we can deduce the answer from what Kraus says on 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."

And Yes, for a lossless unterminated transmission line, the current
distribution of the standing waves is sinusoidal. But not so for
a transmission line with losses. See "Transmission Lines & Networks",
by Johnson, Fig 4.11 or "Transmission Lines" by Chipman, Fig. 8-10.

We know a radiating dipole has "losses" due to radiation. Therefore,
the current distribution will be more like the two above graphs than
a pure sinusoid. For a real-world current distribution on a real
world dipole, an attenuation factor must be included. That makes
the reflected current less than the forward current which moves
the phase angle away from what it would be on a lossless transmission
line (or on an antenna that didn't radiate).

On a lossless transmission line, the forward current may be 1 at 45 degrees
while the reflected current is 1 at -45 degrees. Thus the net current would
be 1.414 at zero degrees. But on a real-world antenna, the forward current
may be 1 at 45 degrees while the reflected current is 0.85 at -45 degrees.
which would be approximately 1.3 at 4.4 degrees.
--
73, Cecil http://www.qsl.net/w5dxp



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