Re: NEC-LIST: Insulator ratings on MF Mast Radiator

Hello Phil,

At 13:22 28.09.2006, Phil_ede wrote:
>I need to calculate the voltage on a set of guy insulators on a shunt-fed
>mast radiator. What is the conventional method adopted for this ?

I had nearly the same assignment almost ten years ago. The particular case
was one of a base-fed 5/8 lambda radiator, which showed evidence of arcing
on modulation peaks. The operator had no precise idea of the location of
the problem, and short of installing an infrared monitoring camera (and
knowing where to point it), the easiest solution was to try to gain some
insight through modelling. This is where I came in.

I was pretty much on my own for this, I couldn't find any "conventional"
method for this, even after a dive in the library stacks. Standard
references such as the NAB Engineering Handbook [4] or the Antenna
Engineering Handbook [3] didn't really say anything very useful about this
subject. The former concentrates on mechanical issues. The latter scarcely
mentions guys in the chapters regarding LF and MF antennas, giving only the
general advice that they should neither be too long nor interfere with the
antenna, or something like that [3, chap. 25, sec. 7]. Oh yes, it did have
a few lines about the isolator themselves [3, chap. 24], which only state
that they are rarely specified at frequencies other than 60Hz.

Indeed, together with the engineering drawing of the tower, I received a
one page data sheet by Litton Industries specifying the dimensions for each
model of the series, as well as capacitance and maximum working voltage at
60Hz. No mention of Q or of derating at higher frequencies.

Here is a view of the antenna system:
http://Radio-BIP.qc.ca/NEC2/isol/3D-projection.jpg

The mast is of galvanized steel with a triangular section.

Since I had had almost no knowledge of the material or earth properties, I
have entirely ignored losses in my model.

>Using NEC2 I have modelled the stays as continuous wires and added
>capacitive loads in the segments containing the insulators.

This was also my approach. I wrote a parametric model in Matlab in which I
could easily change settings and options, and compare the results. The
model generated the input deck, called NEC2, ran an ugly little Pascal
program to extract data from the NEC2 printout, and presented results.

For each of the isolators, including the base isolator, I had a one a
one-segment wire which was loaded by a reactance.
http://Radio-BIP.qc.ca/NEC2/isol/isolator-tags-and-locations.jpg

The isolator parameters are as in the following table:
http://Radio-BIP.qc.ca/NEC2/isol/isolator-table.jpg

I've used the actual length of the isolator for its associated segment.
That length is of the order of 0.001 lambda, the lower recommended segment
length for NEC2. However, NEC2 does not enforce wire surface boundary
conditions for loaded segments, but rather Kirchhoff's Circuit Laws at the
nodes. As far as the MFIE is concerned, the isolators are empty space, and
the difficulties with the NEC2 basis distributions with too short a support
was, IMO, not relevant.

This is the wire model. I used in the end segments of about 0.01 lambda.
The absolute length varied a bit around that value depending on the wire,
in order for the junctions and isolator locations to be at their proper
location.
http://Radio-BIP.qc.ca/NEC2/isol/wire-model.jpg

The parameters of the wires are as follows (the word "grid" in the caption
is of course a mistake).
http://Radio-BIP.qc.ca/NEC2/isol/wire-table.jpg

P0 and P1 are the endpoints. NS the number of Segments in the wire.

The convention I had was to have small tag numbers for segments
representing isolators, and tag numbers greater than 500 to represent
conducting wires. I have then made use of rotational symmetry using a GR
card to triplicate the model with a tag number offset of 1000.

This is a typical resulting NEC2 input deck:
http://Radio-BIP.qc.ca/NEC2/isol/sample-deck.txt

The main tower is represented by three parallel conductors. I wasn't sure
of the way to go about this. I initially wanted to use one fat conductor to
represent the tower.

http://Radio-BIP.qc.ca/NEC2/isol/equivalent-section.jpg

The Antenna Engineering Handbook [3, chap. 25] provides a formula for
calculating the diameter of a wire equivalent to a given tower cross
calculated. The book purports that its formula was drawn from a paper by
Schelkunoff [2], but if I remember well, I couldn't recognize it in the
original reference it when I looked up (I have a copy of it somewhere
around here, but I'm not in the mood for archeology).

I compared three configurations by making a frequency sweep for the
apparent input impedance for an unguyed mast. The configurations were:

1) One fat wire standing in for the tower, with a diameter calculated
according to [3];

2) Three parallel wires converging to a common feedpoint;
http://Radio-BIP.qc.ca/NEC2/isol/base-isolator-pyramid.jpg

3) Three distinct parallel wires, with three separate feeds
http://Radio-BIP.qc.ca/NEC2/isol/base-feed-three-wires.jpg (of course I
used a factor of 3 where necessary to scale the results). This
configuration was tested both with the use of symmetry (GR card) and a full
blown model with thrice as many wires.

The result were very similar. Model 3 gave identical results regardless of
whether a full-blown model or a GR card are used, and gave results which
fell halfway between models 1 and 2 (the feedpoint is more important than
the structure to which it is connected). I remember that I also had
compared the current distibutions, as well as the effect of segment
lengths, with not unsignificant variations. It would be too much work to
dig up that part, as they weren't included in the report in PDF format from
which I extracted the figures. (The figures are in JPEG format, even though
it is not very adapted for text and line drawings, as it was the most
expeditive way).

http://radio-bip.qc.ca/NEC2/isol/frequency-response.jpg

The caption "lambda/36" is in reference to a frequency of 1MHz.

I chose in the end to use model 3 with symmetry. I was a bit unsure about
whether it is a good idea to try to simulate long wire running close in
parallel, I guess I should/could have simulated those wires as a two- or
three-wire transmission line structure, and compare the results with the
predictions of the analytical formula. I did not on the account of lack of
time and/or lazyness. In any case, I thought it was a bit better to try to
keep to the real tower cross-section as much as possible, especially for
the behaviour of the isolators located closest to the tower. A perfect
model would have included cross-arms, but I think this would neither have
been technically feasible in NEC2, nor that it could have improved in any
significant way the results.

I tried two different methods to determine the voltage across isolators:

1) The currents in the structure were extracted from the NEC2 output to
form a multiport admittance matrix. The matrix was inverted numerically to
obtain the equivalent impedance matrix. It appears to me to be the simplest
method, but I needed a check.

2) The alternate verication method was to calculate the near-field at a
number of points within the gap of each isolators (This is the reason why
there are so many NE cards in the example deck above). The Ex and Ez field
vector components were then rotated in order to obtain the field components
tangential and normal to the guy wire. I meant to do a line-integration
across the path, but after a cursory check I saw that the results were
commensurate with the other method, and since it would have required more
work to find the correct scaling factor to bring both results exactly in
line, I relied on the former.

In both methods the effects of the capacitance loads was taken into account
within NEC2.

>Will this give the right answer?

The right answer to which question exactly? That's important.

I would really like to paraphrase the following statement and adapt it to
the context of EM simulation...

"Anyone who considers arithmetical methods of producing random digits is,
of course, in a state of sin". -- John von Neumann (1951) (Cited in [5, p. 1])

You will notice that there are a many variations in the results I present
above depending on the parameters and options. One should perhaps try to
generate random digits using EM simulation methods? :-) :-) :-)

I would be most careful about any statement I would infer from a
simulation, and even also from actual measurements. Even the most perfect
EM simulation method will be undone by a stupid mistake such as a
disconnected wire in the model, or a misguided assumption. In my modelling
I used a step by step approach, and tried to be explicit about my
assumptions. I included plenty of caveats in my report, and recommended
that my conclusions be verified in another fashion before sending men
climbing up a tower in the wee hours of the night.

My conclusion was that basically that isolators 5 and 2 were the most
stressed in the configuration studied, and operated very close to, or above
their, rated voltage. Other isolators were also close to their rating. Even
though I had initially expected the isolators closest to the tower to be
the most sollicited ones, I had initially suspected the topmost ones to be
the possible culprits.

Here is the voltage table calculated according to the inversion of
admittance matrix. I had normalized the results to 1W of input power as
inferred from the apparent input impedance. I should really have obtained
the power by integrating the far-field pattern. I didn't, as it would have
required too much work for the scope of the study, and would have
introduced a scaling factor at best. I was more interested in *relative*
results, and *compare* safety margins between isolators.

http://Radio-BIP.qc.ca/NEC2/isol/voltage-isolators.jpg

Here are the results as obtained by averaging the tangential field:
http://radio-bip.qc.ca/NEC2/isol/gap-integrated-voltage.jpg

The ranking order ("rank") is exactly the same, and the results
approximately scaleable from one table to the other. (Disregard the "Enorm"
column, it is somewhat nonsensical, even though I think that that field
component might also be worth looking into).

The effect of the guy wires is very obvious when the current distribution
on the mast is plotted. The dashed lines indicate the tying points for the
wires.

http://Radio-BIP.qc.ca/NEC2/isol/current-distribution.jpg

The expression "without isolators" means air gaps in place of the
isolators. The guy wires both extract and inject a significant amount of
current into the mast, affecting the base impedance, hinting a rather
complex system of interactions.

I had also tried to show the sensitivity of the input impedance to
variations in isolator capacitance values.
http://Radio-BIP.qc.ca/NEC2/isol/test-table.jpg

Regardless of accuracy issues, I think that one can state with some
confidence that the performance of the antenna is heavily affected by the
nearmost guy wire sections. Reducing the capacitance of the first
isolators, by putting two in series, would increase the input impedance and
improve the safety margin, at the cost of retuning the antenna.

I received little feedback from the customer, but I believe he was
satisfied with my work.

After revisiting my work, I went to my bookshelve and had a look at some of
my newer acquisitions. An old German treatise I recently found had one of
the rare discussions I have seen to this day about the effect of guy wires
[1, vol. 1, pp. 477-483].

The material cited by Vilbig in that section of his book is based on
another person's work, "Gerwig", and is somewhat sketchy. I would have to
look up the original reference, but the bibliography table was published in
a separate booklet which had been lost. I would have to go and look up a
copy at the library, something that I expect would require several visits
(three at least, including obtaining the Gerwig reference, because of the
way the card catalog and book ordering system are structured).

In any case, an equivalent circuit diagram is presented for one stay:
http://radio-bip.qc.ca/NEC2/isol/fig558.png

There is no discussion about how the voltage sources are calculated, nor
how the capacitance values are obtained. I'm a bit wary of that approach
(which predates NEC2 by decades), as I'm not too sure whether one could
replace by a simple static capacitance value a system which is large in
proportion to the wavelength.

It gets more interesting in figure 559, where voltages are presented for
some isolator distributions normalized to 1 Ampère of base current:
http://Radio-BIP.qc.ca/NEC2/isol/fig559.png

The small circles in the lines represent the isolator locations (I find it
rather objectionable to have connected these dots by lines).

Each row represent the upper, middle, and lower guy wires.

Each column represent a different distribution of isolator spacings. In the
first one the isolators are regularly spaced, and in the third one some
isolators (presumably all of the same model, contrary to my case) are
irregularly bunched to the left to reduce the maximum voltage. I'm not too
sure what "equal induced EMF in the stay sections (???)" in the middle one
is supposed to mean, the text does not elaborate on this.

The optimized configuration of column 3 is supposed to improve the power
handling capacity of the antenna by a very large factor.

I found this table quite interesting, as the first column is very
comparable to my own results.

The authors go on to say that a lower radiation resistance, brought about
by a wider conductor size, is also beneficial to decrease isolator working
voltages (and also bandwidth, but not necessarily matching). This was the
object of tests, as documented in this photo:
http://Radio-BIP.qc.ca/NEC2/isol/fig562.jpg

So, that's it. All I can do now is to wish you good luck with your own
tests. I'd be interested to know how you modelled the shunt-feed, and about
your validation attempts.

Regards,

Alexandre

[1] Fritz Vilbig, "Lehrbuch der Hochfrequenztechnik", fourth edition,
Akademische Verlagsgesellschaft, Leipzig, 1944
[2] S.A. Schelkunoff, "Theory of Antennas of Arbitrary Size and Shape",
Proceedings of the IRE, pp. 493-521, Sept. 1942
[3] Richard C. Johnson, Antenna Engineering Handbook, third Edition,
McGraw-Hill, New York, 1993
[4] "Engineering Handbook", eigth Edition, National Association of
Broadcasters, Washington, 1992
[5] Donald E. Knuth, "The Art of Computer Programming - vol. 2 -
Seminumerical Algorithms", second edition, Addison-Wesley, 1981

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