Fishrod anìtennas - transformer and twin-lead
 

Use of fishrod antennas is getting more and more common to cover all bands 7 ...
28 MHz, including WARC. The typical length of the radiating wire is about 25
feet, that is about one quarter wavelength at 10 MHz.

On lower frequencies (e.g. 7 MHz) that antenna shows a low radiation resistance
and a strong capacitive reactance. On higher frequencies resistance goes up and
down with frequency, showing very high peaks, and reactance does the same,
though obviously with a different pattern.

Typical configuration used is:
- 1:4 transformer (balun or unun) at the antenna
- 300-ohm or 450-ohm flat twin-lead
- tuner at the transmitter

SWR is generally high, except on certain specific frequencies (which may not
fall in the amateur bands).

I would like to hear some opinions on the usefulness of using the transformer
and the twin-lead. My arguments a

- above 10 MHz, where impedance is generally fairly high, the transformer could
(??) be helpful to reduce SWR, but below 10 MHz it should be harmful, as its
transformation goes on the wrong side.

- use of the twin-lead is usually justified by its low attenuation, that limits
the extra attenuation caused by the high SWR existing on the line. In my opinion
the 300-ohm twin-lead attenuation is reported to be low mainly because it is
measured in presence of a 300-ohm load, that draws low RF current. But in the
subject application, where the antenna impedance is uncontrolled, what should
count is the ohmic resistance of the twin-lead conductors which is not
particularly low due to their fairly small diameter. Wouldn't an RG-213 do
better than the twin-lead?

Thanks for your comments & 73

Tony I0JX
Rome, Italy

Fishrod anìtennas - transformer and twin-lead
 

On Sat, 3 Oct 2009 21:08:57 +0200, "Antonio Vernucci"
wrote:

I would like to hear some opinions on the usefulness of using the transformer
and the twin-lead. My arguments a

- above 10 MHz, where impedance is generally fairly high, the transformer could
(??) be helpful to reduce SWR, but below 10 MHz it should be harmful, as its
transformation goes on the wrong side.

Hi Tony,

Good of you to notice that the 1:4 can also be viewed as 4:1 (or did
you notice?) with it reversed. This is not strictly so, as the
classic BalUn consists of wound transmission lines with characteristic
Z at the geometric mean of the load and source Z. However, lacking
this doesn't always stop the experimenter.

- use of the twin-lead is usually justified by its low attenuation, that limits
the extra attenuation caused by the high SWR existing on the line. In my opinion
the 300-ohm twin-lead attenuation is reported to be low mainly because it is
measured in presence of a 300-ohm load, that draws low RF current. But in the
subject application, where the antenna impedance is uncontrolled, what should
count is the ohmic resistance of the twin-lead conductors which is not
particularly low due to their fairly small diameter. Wouldn't an RG-213 do
better than the twin-lead?

If your BalUn has already done the bigger job of turning a High Z to a
modest one, the common logic for the need for twin line has also been
diminished.

Working with, designing, and building BalUn applications demands a
good tool for validation. Do you have something that will measure Z
with accuracy?

73's
Richard Clark, KB7QHC

Fishrod anìtennas - transformer and twin-lead
 

Good of you to notice that the 1:4 can also be viewed as 4:1 (or did
you notice?) with it reversed.

That is obvious, but in common designs there is no provision (e.g. a relay) for
reversing the transformer when operating on frequencies where the antenna
resistance is lower. So the transformer remains there as it is, doing the
opposite job of what it should do.

Working with, designing, and building BalUn applications demands a
good tool for validation. Do you have something that will measure Z
with accuracy?

No, I am not building that antenna or doing any experiment. I am only trying to
understand the rationale behind what people proposes and I am seeking advice
from people having specific experience on the issue.

73

Tony I0JX.

Fishrod anìtennas - transformer and twin-lead
 

"Antonio Vernucci" wrote in
:

Use of fishrod antennas is getting more and more common to cover all
bands 7 ... 28 MHz, including WARC. The typical length of the
radiating wire is about 25 feet, that is about one quarter wavelength
at 10 MHz.

By fishrod antenna, I assume that you mean a telescopic fibreglass pole
of about 10m height, used to support a straight or approximately straight
(including a very coarse pitch helical) vertical wire of the same length.

This has a lot in common with the popular 43' vertical, just the lengths
are different, and the frequency coverage will be different.

The use of a 4:1 balun on all of these things seems inspired by one
antenna manufacturer's recommendation and supply of 4:1 voltage baluns
for the application. Their site shows testimonials, and claims thousands
sold. Eham reviews abound with glowing testimonials.

However... the application of a 4:1 voltage balun seems to me not only to
lack design rationale, but to be quite undesirable in driving common mode
current on the coax feedline, and potentially very lossy in
configurations where the feedline is buried.

I discuss the use of an untuned vertical as a multiband antenna, and
raise the insanity of the voltage balun application at
http://www.vk1od.net/antenna/multiba...ical/index.htm .

Owen

Fishrod anìtennas - transformer and twin-lead
 

It's interesting to model this sort of arrangement, note the wide
range of feedpoint impedances that will be seen on the different
bands, and observe the feedline losses that might be incurred when it
is directly fed with 50 ohm coax. If you then introduce an ideal
transformer at the feedpoint and repeat the exercise you will
generally find that feedline losses increase on some bands and
decrease on others.

With the vertical length I tried, the effect of a 1:9 transformer was
to limit the more extreme losses at the cost of making some very low
losses higher. I guess over the several bands I tried you could say
there was a net improvement with the transformer.

But one question would be how to build this ideal 1:9 transformer
which maintains its transformation ratio and exhibits zero loss across
the wide range of impedances and frequencies involved.

Steve G3TXQ

Fishrod anìtennas - transformer and twin-lead
 

In message
,
steveeh131047 writes
It's interesting to model this sort of arrangement, note the wide
range of feedpoint impedances that will be seen on the different
bands, and observe the feedline losses that might be incurred when it
is directly fed with 50 ohm coax. If you then introduce an ideal
transformer at the feedpoint and repeat the exercise you will
generally find that feedline losses increase on some bands and
decrease on others.

With the vertical length I tried, the effect of a 1:9 transformer was
to limit the more extreme losses at the cost of making some very low
losses higher. I guess over the several bands I tried you could say
there was a net improvement with the transformer.

But one question would be how to build this ideal 1:9 transformer
which maintains its transformation ratio and exhibits zero loss across
the wide range of impedances and frequencies involved.

You might like to refer to the thread "UNUN Cores?How To Wind?",
started on 1 August. In particular, the last posting (by 'UK Monitor')
suggests a link to this website:
http://g8jnj.webs.com/currentprojects.htm

--
Ian

Fishrod anìtennas - transformer and twin-lead
 

steveeh131047 wrote:
It's interesting to model this sort of arrangement, note the wide
range of feedpoint impedances that will be seen on the different
bands, and observe the feedline losses that might be incurred when it
is directly fed with 50 ohm coax. If you then introduce an ideal
transformer at the feedpoint and repeat the exercise you will
generally find that feedline losses increase on some bands and
decrease on others.

With the vertical length I tried, the effect of a 1:9 transformer was
to limit the more extreme losses at the cost of making some very low
losses higher. I guess over the several bands I tried you could say
there was a net improvement with the transformer.

But one question would be how to build this ideal 1:9 transformer
which maintains its transformation ratio and exhibits zero loss across
the wide range of impedances and frequencies involved.

Steve G3TXQ

Some time ago I made a series of careful measurements of a transformer
which was at the feedpoint of a multiple band antenna. At frequencies
where the feedpoint impedance was very much different from the (purely
resistive) design impedance, the transformation wasn't equal to the
design transformation, and the transformer introduced both series and
shunt impedance. At some frequencies, these effects were extreme, and
the transformer acted nothing at all like an ideal transformer.

Modeling a system like this with an ideal transformer might be an
interesting intellectual exercise. But that's all it is -- the real
system won't behave anything like the model. You can extend a
transformer's range of impedances and frequencies by using great care in
the initial design and construction, then adding compensating circuitry.
The job gets more difficult as the transformation ratio increases. I
seriously doubt you'll ever come close to making a transformer anything
like the one described in the last paragraph.

The amateur way is to build a system with a transformer, then figure out
how to live with whatever you get. An engineering approach usually
involves designing a system with predictable and repeatable performance,
and that precludes depending on a transformer over a wide impedance range.

Roy Lewallen, W7EL

Fishrod anìtennas - transformer and twin-lead
 

On Oct 4, 7:59*pm, Roy Lewallen wrote:

Modeling a system like this with an ideal transformer might be an
interesting intellectual exercise. But that's all it is -- the real
system won't behave anything like the model.

Roy,

I didn't express myself well - the final paragraph was meant to be a
rhetorical question which cast doubt on the validity of the
conclusions!

73,
Steve G3TXQ

Fishrod anìtennas - transformer and twin-lead
 

steveeh131047 wrote in news:5e53bd91-a69c-452f-9dab-
:

It's interesting to model this sort of arrangement, note the wide
range of feedpoint impedances that will be seen on the different
bands, and observe the feedline losses that might be incurred when it
is directly fed with 50 ohm coax. If you then introduce an ideal
transformer at the feedpoint and repeat the exercise you will
generally find that feedline losses increase on some bands and
decrease on others.

With the vertical length I tried, the effect of a 1:9 transformer was
to limit the more extreme losses at the cost of making some very low
losses higher. I guess over the several bands I tried you could say
there was a net improvement with the transformer.

But one question would be how to build this ideal 1:9 transformer
which maintains its transformation ratio and exhibits zero loss across
the wide range of impedances and frequencies involved.

Steve,

My article on the unloaded vertical includes a discussion of the unun /
balun thing. I did run models incorporating an ideal 4:1 current balun,
and found that coax loss is better on some frequencies and poorer on
others.

The model is not directly applicable to a generic end user installation
because the coax loss depends on line type, length etc, and the ideal
balun assumption is not a good estimator for practical baluns with
extreme loads.

I haven't published an article on the unun model, I should one day
perhaps.

Practical baluns are likely to have higher losses under extreme operating
conditions, and that will result in lower VSWR than otherwise, so the
added complexity of a real world balun is that at those extremes, it will
tend to be lossier, its transformation departs from ideal, and line
losses will tend to be lower.

I have created a model of a practical ferrite cored 4:1 unun, and explore
it with different core materials, dimensions, and windings. The models
reconcile well with G8JNJ's experimental ununs and my own prototypes...
but reconciliation on extreme loads taxes both Martin's and my own
measurement capabilities.

I cannot guess what inspired the application of 4:1 voltage baluns to
these antennas, much less why a reputable manufacturer would recommend
the configuration which to my mind defies sound principles. Nevertheless,
it does appear that thousands are successfully in use, and many hams have
the QSLs to prove that an antenna that lacks sound explanation "works
real good" anyway.

I do think there is good reason to apply a common mode current choke to
such antennas, not to recommend them as a matter of routine (though they
won't hurt much), but in some implementations one could expect a
significant common mode current problem, and a commom mode current choke
may be part of an effective mitigation.

As to whether a 4:1 transformation is universally better than 1:1, ideal
or otherwise, I doubt it. If the coax loss is a problem, and it will be
for all but lowest loss configurations), an ATU at the feedpoint seems
the better solution.

In making the observation that loss helps to reduce line VSWR, which in
turn reduces line VSWR, perhaps the only sensible design rationale behing
the 4:1 voltage balun applied on the subject antenna is that it drives
common mode current on the feedline, and in the case of a buried feedline
(as they often are), the power lost in heating the soil tames the
feedpoint impedance, reducing line loss. But, does that maximise system
efficiency? (Though it may work in that way, I doubt the 'designers' had
that in mind.)

Owen

Fishrod anìtennas - transformer and twin-lead
 

steveeh131047 wrote:
On Oct 4, 7:59 pm, Roy Lewallen wrote:

Modeling a system like this with an ideal transformer might be an
interesting intellectual exercise. But that's all it is -- the real
system won't behave anything like the model.

Roy,

I didn't express myself well - the final paragraph was meant to be a
rhetorical question which cast doubt on the validity of the
conclusions!

73,
Steve G3TXQ

Sorry, Steve. It's really hard to express subtlety or sarcasm in this
sort of written venue -- as I've found out so many times myself.

Roy Lewallen, W7EL

Fishrod anìtennas - transformer and twin-lead
 

steveeh131047 wrote:
But one question would be how to build this ideal 1:9 transformer
which maintains its transformation ratio and exhibits zero loss across
the wide range of impedances and frequencies involved.

Has there been any information published on loss and
transformation measurements for real world TLTs used
far outside of their design impedances?
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

Fishrod anìtennas - transformer and twin-lead
 

Owen,

If I've managed to read my lab notes correctly, these were the
differences in loss (ground+feedline+tuner) - with and without an
ideal 9:1 transformer at the feedpoint - for a 33ft vertical over
average ground fed with 50ft of RG213. I assumed ground losses of 20
ohms. Positive figures indicate that the losses were lower with the
transformer:

160m -1.6dB
80m +6.02dB
40m -2.3dB
30m +2.1dB
20m +4.4dB
17m +3.86dB
15m -0.55dB
12m +1.6dB
10m +2.9dB

Of course this data was for one specific scenario, but I guess you'd
look at it and say that for this case, on balance, the inclusion of
the transformer was of benefit. But now factor in some realistic
transformer losses and it might not look so clear cut.

73,
Steve G3TXQ

Fishrod anìtennas - transformer and twin-lead
 

On Oct 5, 2:10*am, Cecil Moore wrote:

Has there been any information published on loss and
transformation measurements for real world TLTs used
far outside of their design impedances?
--
73, Cecil, IEEE, OOTC, *http://www.w5dxp.com

Cecil,

Martin has some data under the heading "33ft Verticals and 4:1 Ununs "
he
http://g8jnj.webs.com/currentprojects.htm

73,
Steve G3TXQ

Fishrod anìtennas - transformer and twin-lead
 

steveeh131047 wrote in news:46a67bfc-c375-4533-8df0-
:

On Oct 5, 2:10*am, Cecil Moore wrote:

Has there been any information published on loss and
transformation measurements for real world TLTs used
far outside of their design impedances?
--
73, Cecil, IEEE, OOTC, *http://www.w5dxp.com

Cecil,

Martin has some data under the heading "33ft Verticals and 4:1 Ununs "
he
http://g8jnj.webs.com/currentprojects.htm

Steve,

Here are the input impedance and VSWR(50),Loss graphs for my model of a
FT240 #61 with 12 bifilar turns with a 1000+j0 load.

http://www.vk1od.net/lost/Clip045.png

http://www.vk1od.net/lost/Clip046.png

Non-ideal transformation ratio is not a big issue for an unun used with
an ATU, voltage withstand and loss are higher priority.

The balun loss data in the article at http://vk1od.net/blog/?p=568 was
obtained by measuring the balun using a VNA, and creating a spreadsheet
that solved the balun + load network for an arbitrary load impedance. The
spreadsheet is revealing, as one can immediately see the broadband
peformance of the balun with extreme loads, R and X in arbitrary
combination.

What I do know is that it is superficial to describe a balun (or unun)
with just two metrics such as 5kW, VSWR1.5... but have a look at
commercial baluns, that is how they are often (mostly) sold. There is the
odd manufacturer that gives a loss and VSWR curve on a nominal load FWIW,
but I have not yet seen any manufacturer publish a set of S parameters
covering the operating range.

I am not naive about magnetics, they are challenging devices, but at
least in the ham radio market, it is more black magic than good sense.

BTW, if you look at the loss graph for this device with a 1000+j0 load,
and assume that it can safely dissipate perhaps 20W continuous, it is
capable of less than 1kW continuous at 30MHz, but some manufacturers
build such a transformer and rate them at 5kW or more. With a load
impedance of 4k+j0 (eg a full wave dipole), the loss is even worse, and
the continous power rating even lower.

Owen

Fishrod anìtennas - transformer and twin-lead
 

On Oct 5, 10:14*am, Owen Duffy wrote:


Non-ideal transformation ratio is not a big issue for an unun used with
an ATU, voltage withstand and loss are higher priority.

Owen,

Agreed. But the "non-ideal transformation" will result in changed
feedline losses and tuner losses. May be better, may be worse :)

I enjoyed reading your balun loss article. "66% of the transmitter
power converted to heat inside the ATU" will be a surprise to many
folk. I can replicate almost the exact set-up you describe: G5RV
half-wave of ladderline4:1 voltage baluntuner; so If I can find
the time I'll try to measure the rate of temperature rise inside the
tuner case when it's handling 100W CW, and then stick a 60W light bulb
in the case and measure the rate of temperature rise again.

73,
Steve G3TXQ

Fishrod anìtennas - transformer and twin-lead
 

Thanks for the numerous comments on the unun / balun, but I read nothing on the
possible convenience to use a 300 ohm flat ribbon in place of coaxial. No
interest for that issue?

73

Tony I0JX

Fishrod anìtennas - transformer and twin-lead
 

On Mon, 5 Oct 2009 17:39:28 +0200, "Antonio Vernucci"
wrote:

but I read nothing on the
possible convenience to use a 300 ohm flat ribbon in place of coaxial.

On Sat, 03 Oct 2009 13:39:12 -0700, Richard Clark
wrote:

If your BalUn has already done the bigger job of turning a High Z to a
modest one, the common logic for the need for twin line has also been
diminished.

73's
Richard Clark, KB7QHC

Fishrod anìtennas - transformer and twin-lead
 

If your BalUn has already done the bigger job of turning a High Z to a
modest one, the common logic for the need for twin line has also been
diminished.

Yes but my question regarded the advantage of twin-lead vs. coaxial in that
particular application where impedance is uncontrolled.

73

Tony I0JX

Fishrod anìtennas - transformer and twin-lead
 

On Mon, 5 Oct 2009 21:17:26 +0200, "Antonio Vernucci"
wrote:

Yes but my question regarded the advantage of twin-lead vs. coaxial in that
particular application where impedance is uncontrolled.

http://www.vk1od.net/calc/tl/twllc.htm

73's
Richard Clark, KB7QHC

Fishrod anìtennas - transformer and twin-lead
 

steveeh131047 wrote in
:

On Oct 5, 10:14*am, Owen Duffy wrote:


Non-ideal transformation ratio is not a big issue for an unun used
with an ATU, voltage withstand and loss are higher priority.

Owen,

Agreed. But the "non-ideal transformation" will result in changed
feedline losses and tuner losses. May be better, may be worse :)

Almost always, but probably more often for the better.

BTW, I gave a brief description of the FT240 #61 12t unun, but didn't
mention the winding details, they are 0.8mm wire spaced (centre to
centre) 3.2mm and permittivity 1.2 which describes a winding with 0.8mm
PTFE insulation for high voltage withstand, an 'ATU unun' in commercial
talk.


I enjoyed reading your balun loss article. "66% of the transmitter
power converted to heat inside the ATU" will be a surprise to many
folk. I can replicate almost the exact set-up you describe: G5RV
half-wave of ladderline4:1 voltage baluntuner; so If I can find
the time I'll try to measure the rate of temperature rise inside the
tuner case when it's handling 100W CW, and then stick a 60W light bulb
in the case and measure the rate of temperature rise again.

Keep in mind that ferrite cores heat (and cool) very slowly. One could
easily be fooled into thinking that there isn't much heat dissipated in
a short test, but after an hour of operation, the core is still heating
at a substantial rate. This is one of the things that saves the bacon of
manufacturers of 5kW and 10kW continuous rated baluns, they are not
usually called upon to operate at high duty cycle for long enough to
reach the Curie point.

Calorimetric measurments are problematic, they sound simple enough, but
latency my mean it takes hours to reach close to maximum operating
temperature.

The greater worry is that this manufacturer, and probably some others,
use thermoplastic insulation to support the coil, which could result in
damage if you operate the ATU long enough to reach operating
temperature. Do so entirely at your own risk.

At one time, I had two identical ATUs, and I attached one with a 600+j0
load to the tx on 1.8Mhz and adjusted for VSWR=1 on the input. I
replaced the load with another ATU backwards and with a 50+j0 load and
adjusted the second ATU for VSWR=1 on the input to the first ATU. I then
read the power into the 50 ohms load and out of the tx using a Bird 43
and calculated the loss. The loss in the first ATU under those
conditions can be approximated by allocating half the total loss. This
test indicated quite high loss, and the case was quite warm near the
balun after just minutes of testing. BTW, this was the same type of ATU
as in the article you mentioned earlier.

In the example article, about 26% of the tx power is radiated on 80m.
That sounds pretty awful, but it should be seen relative to say 80% as a
reasonable system efficiency for a multiband antenna.

Owen

Fishrod anìtennas - transformer and twin-lead
 

"Antonio Vernucci" wrote in
:

If your BalUn has already done the bigger job of turning a High Z to
a modest one, the common logic for the need for twin line has also
been diminished.

Yes but my question regarded the advantage of twin-lead vs. coaxial in
that particular application where impedance is uncontrolled.

Tony, it depends on the details of your scenario, and may be different at
different frequencies.

Unless you believe in the myth that ladder line is *so* low in loss that
you *never* need to consider it, you need to calculate it out to really
know... it is not a no-brainer as we say, in fact it is a quite complex
problem to solve (mainly quantifying the loss and transformation in
transformers which both Roy and I have mentioned in this thread).

BTW, from time to time I see articles that recommend twin line for direct
feeding a ground mounted vertical (ie without using a balun at the feed
point). It is as insane as using a 4:1 voltage balun with coax at the
base of such a vertical, because both types of feed drive substantial
common mode current on the feed line. A review of such an article is at
http://vk1od.net/antenna/multibandun...tical/BSUM.htm , this one
using a magic ingredient, Belden 8222 twin feedline which Belden ceased
manufacturing. But... I am sure some hams have got the QSLs to prove that
it "works real good".

Owen

Fishrod anìtennas - transformer and twin-lead
 

On Mon, 05 Oct 2009 21:30:06 GMT, Owen Duffy wrote:

Calorimetric measurments are problematic, they sound simple enough, but
latency my mean it takes hours to reach close to maximum operating
temperature. ...
and the case was quite warm near the balun after just minutes of testing.

Sounds like the BalUn was doing a superlative job.

Hi Owen,

What you describe (sans the problematic word latent) is specific heat
capacity. And just like any capacitor, charge/heat does not increase
after a source is removed. If it is not removed (which I presume was
the intent of both your statements), then the specific heat capacity
you describe is a design boon.

73's
Richard Clark, KB7QHC

Fishrod anìtennas - transformer and twin-lead
 

Richard Clark wrote in
:

....
What you describe (sans the problematic word latent) is specific heat
capacity.

I used the term latency in the context of time, there is a delay between
commencement of application of steady power to reaching substantially full
operating temperature. Yes, the effect can be predicted using the material
specific heat capacity, subject to the temperature variability of the
ferrite characteristics.

....
the intent of both your statements), then the specific heat capacity
you describe is a design boon.

Yes, but a trap if long term use is envisaged but tested only in the short
term.

Owen

Fishrod anìtennas - transformer and twin-lead
 

To put some numbers around the problem, if one had a FT240 core which has
a mass of around 0.2kg, and specific heat capacity around 800J/kgK, the
energy to raise the core to a Curie point of 130°C to 300°C would be 17kJ
to 44kJ. If the core was well insulated (no heat loss) and dissipating
say 20W, that would take 15 to 40 minutes.

Of course, one would hope that the transformers do lose heat to the
environment, and that would substantially slow the rate of rise of
temperature.

Experience shows that a 5 minute test of a ferrite transformer does not
indicate continuous power handling capability.

Digressing slightly, but on this ferrite heat thing...

Martin questioned my article "A review of the Guanella 4:1 balun on a
shared magnetic circuit" at http://www.vk1od.net/balun/gsc/index.htm . In
particular, his issue was with my proposition that the extent to which
these things "work" is due to flux leakage on low µ cores, the lower the
µ, the more they resemble Guanella's balun.

Martin's inital experiments indicated that the thing did work, but on my
advice he tried prototypes on high and low µ cores and took thermal
pictures of the things after operation. The images showed non-uniform
distribution of heat in the cores which is either due to the main heat
source being the conductor losses, or that magnetic flux is a significant
contribution and not evenly distributed in the toroid. The flux
distribution is a credible explanation for the different patterns for
same winding on the different µ cores.

Again, this is one of those things that lots of hams have QSLs to prove
that they "work real good".

Owen

Fishrod anìtennas - transformer and twin-lead
 

On Tue, 06 Oct 2009 06:25:53 GMT, Owen Duffy wrote:

Of course, one would hope that the transformers do lose heat to the
environment, and that would substantially slow the rate of rise of
temperature.

Hi Owen,

This opens another topic of my study with Thermal Resistance. One
paper that I have filed away that may aid you is W.E. Hord's "Recent
Developments In The Average Power Capacity Of Rotary-Field Ferrite
Phase Shifters." It may lack the specific application discussed here,
but it covers the math and interface relationships. Sorry, but I
don't have any publication details except for author/title.

Hord's work is with ferrites capable of sustaining RF power levels in
multiple KW. My first experience with ferrites (ca. 1972) was with RF
transmission line source/load isolation in the microwaves (the paper
is S-Band), a field that is wholly alien to discussion here.

73's
Richard Clark, KB7QHC

Fishrod anìtennas - transformer and twin-lead
 

Owen Duffy wrote in
:

....
Martin questioned my article "A review of the Guanella 4:1 balun on a
shared magnetic circuit" at http://www.vk1od.net/balun/gsc/index.htm .

Ian (GM3SEK) kindly drew my attention to incorrect reference to two of the
figures in the above article. The error was misleading, it is fixed now. My
apologies to anyone who was confused by the error.

Thanks Ian.

Owen