Wednesday, August 28, 2013

More on Dipole versus Delta Loop

I lied. I'm not done yet with that 20 meters delta loop versus dipole comparison. The reason is that I was not satisfied that I'd properly understood (or explained) the relatively poor DX performance of the delta loop. I'll attempt to do so in this article.

There are a few key factors to understanding DX performance, which I'll address below:
  • Radiation angle (elevation) for the selected propagation path
  • Local terrain
  • Antenna pattern
It is not easy for the individual amateur to determine the radiation angle of a signal to (or from) a particular DX station or region. Thankfully others have done the work for us. While we cannot know the precise figure in every case, there has been enough experimentation to give us a range of angles within which, with high probability, the actual value falls. This is research I've read in the distant past, but since it was so long ago it made sense to do an internet search to find the source material and refresh my memory.

Since the comparison was done for 20 meters, I'll stick with that. Radiation angles depend on many factors, including: frequency; path length; geomagnetic compass direction; season; geomagnetic indices; and more. That's a lot to consider. However, if we stick to paths that do not intersect the polar regions there is ample experimental data that is pretty reliable.

The ARRL summarized some of this data (PDF) for us. Since Ottawa is not too far north of where the measurements were taken this data should be applicable. The ranges of interest for 20 meters are as follows:
  • For short DX paths (Europe) the radiation angles almost all fall between 3° and 20°
  • For long DX paths (Australia and Japan) the radiation angles are always less than 11°
This was the reason why I was so interested in pursuing an antenna that would perform well at the lowest possible radiation angles. This is difficult to achieve for horizontally-polarized antennas up no more than 10 to 15 meters, which is the upper limit for me in my present circumstance.

As already discussed in some detail, the results of the vertically-polarized delta loop did not meet my expectations. Far-field radiation plots are informative but perhaps not ideal for A/B comparisons, unless one is careful. As an alternative I have produced a table of the gains of the two antennas from the EZNEC models. Here we can easily compare their performance versus elevation angle.

20 Meters – Ground(0.002 S, 13 dc) – Gain (dbi) vs. Elevation angle
Dipole up 10.5 meters
Delta Loop, vertical, up 7-13.3 meters
Off Ends
Off Ends

Note that this was modeled using poor ground, which is perhaps typical of the suburban area in which I live. The terrain is mostly flat out to several kilometers in all directions, except for the southeast to southwest quadrant where the land rises to ~20 meters at 0.4 kilometers distance.

For the dipole the broadside compass directions are 70°/250°, and for the delta loop are 40°/220°.

Notice that at prime DX radiation angles, in the broadside direction, the dipole is moderately superior to the delta loop, except at the very lowest angles. Off the ends the delta loop is clearly superior.

This is not what I found, where the dipole outperformed the delta loop in almost all cases, sometimes by a lot. The models are either wrong or something else is going on. My guess is that the ground may be worse that what I modeled, and that metal in the surrounding houses and utilities had more of an effect on the delta loop, the bottom of which is lower and which is also closer to houses and overhead utility lines.

Rather than redo the model with even poor ground I chose to instead try it with good ground, such as one would find in wide-open farm land.

20 Meters – Ground(0.03S, 20 dc) – Gain (dbi) vs. Elevation angle
Dipole up 10.5 meters
Delta Loop, vertical, up 7-13.3 meters
Off Ends
Off Ends

As expected the dipole does not fare much differently -- it does slightly better. Surprisingly the delta loop is not only not better, it actually does worse at DX-favouring angles above 5°. One reason is that there are 2 vertical lobes in the radiation pattern, and the null between them gets deeper with improved ground (see this previous article for the pattern). The null is high, at about 35° elevation, but still impacts gain at somewhat lower elevations. The dipole has just one vertical lobe, peaking at about 30°.

This has me wondering whether the ground quality is actually better than expected, since the measured
DX results come closer to what this table indicates. Well, in truth I don't know and I probably never will. While it is possible to test the ground under the antenna (and even enhance it with a metal screen, if you're ambitious), the distant ground, which is what contributes to the far-field radiation pattern, is less known. It also cannot be changed. I suppose one could move and buy an house outside the city, but that isn't in my future plans.

I'm glad I did these table comparisons since they do give me a better sense of what I measured on the radio. It also shows how fraught with uncertainties and problems vertically-polarized antennas can be.

This all leads me to my next experiment, which will be a mostly-horizontal antenna. The factor I am now focussing on is height. I intend to find out what a few meters can do for low-angle performance. Getting there is taking me a few days longer than expected because getting that height requires some construction. I have to get it installed by Labour Day due to exterior work to be done on my house. Site B, the house-bracketed mast, will be inaccessible for 2 weeks.

Thursday, August 22, 2013

Putting the 20 Delta Loop on 17 and 30 Meters

Antennas that are smaller (shorter) than λ/2 tend toward poor performance. Not only does the SWR increase -- increasing transmission line and matching losses -- the radiation resistance can get so low that ohmic resistance in the antenna can become dominant. You won't notice this (much) for frequencies only a little below that point. But by the time you reach λ/4 it is a critical factor.

On 17 meters a 20 meters delta loop is longer than 1λ, while on 30 meters it is over 0.7λ. I therefore expected reasonable performance in regard to antenna losses and pattern.

As I promised in my final look at the recently-retired 20 meters delta loop, I am following up with my observations of the antenna's performance on both these other bands. The modelled patterns of the antenna on 17 and 30 meters are below.

Notice how on 30 meters the radiation pattern is even more omnidirectional than on 20 meters. It is generally true that the smaller an antenna the more isotropic it becomes. The opposite is true on 17 meters. Just don't become too enamoured of this result since short antennas can have serious performance issues, as mentioned above. However on 30 meters, for this antenna, the impact is small.

The modelled SWR on both 17 and 30 meters is high, and it measures high as well. There are surely substantial losses in the transmission line, which in this instance is approximately 15 meters of RG-213/U plus a λ/4-tranformer made from RG-62/U. Even so the antenna performed reasonably well on both of these non-resonant bands, with the help of a high-power antenna turner on the transmitter end of the coax.

The performance is unlike what I experienced with the TH1vn on 17 and 30 meters. While both tuned well with the same tuner, the losses were noticably higher. It performed so poorly that it was pretty much useless. Exactly why this should be so is not clear to me. It can't simply be the transmission line quality (which works just fine up through 10 meters, on bands where the antenna is resonant). Perhaps the traps are showing a low parallel impedance on those bands. and therefore acting somewhat as resistors. The question while interesting is not important to me at the present. It's enough that I know what the antenna cannot be expected to do.

In operation the delta loop did quite well on 17 meters. I had no trouble working most any DX I heard that was not especially weak. Europe, Siberia (UA9) and South America stations were logged. I even tried to break the E44 pile-up. I didn't succeed, which is no surprise at all. I heard but did not work (or call) stations further afield, including KH6, VK and JA.

On 30 meters I had less success. The lower bands can be deceiving since the noise level is higher. Even an inefficient antenna can hear with similar S/N ratios as better antennas. The real test is whether the DX hears you. I worked a couple of Europe and Caribbean stations, but it wasn't easy. I have to score this antenna as poor on 30 meters. Or use more than 10 watts to compensate for the losses.

With that I will put to bed the discussion of this antenna. However I am not quite done with delta loops, which I still expect to put one or more up for the lower bands where low horizontally-polarized antennas suffer. Who knows, maybe a dipole will do better there as well. I intend to test this at some point.

Tuesday, August 20, 2013

20 Meters Delta Loop - Final Look

Antennas come down easier than they go up. It took all of 45 minutes from the time I picked up the ladder until the 20 meters delta loop antenna was down, disassembled and parts and ladders stowed. The only difficulty was that the pipe shim made of duct tape got a bit sticky in the 30° C heat and did not want to let go of the fibreglass mast. Even with my safety line it was not fun standing at the edge of the roof while using brute force to separate the two.

From this you should be able to guess my final conclusion about the antenna. It is a fine antenna, just not good enough. It's a shame to waste that effort, but then that is what antenna experimentation is all about.

Propagation has been excellent the past few days. This kept the polar paths open and also favoured low-angle radiation paths where those were present. I was able to compare the delta loop to the dipole over many paths, including to Central and South Asia, the Indian Ocean, East Asia, and Australia. These are paths that ought to favour the vertically-polarized delta loop.

However, ought to is not will. The dipole kept winning or at least being equal except in rare cases. Ground losses either in the near field or far field are either greater than expected or the radiation angles on most 20 meters DX paths are not low enough to disadvantage a dipole up only 10.5 meters.

Keep in mind that if you have excellent ground quality in your locale you might very well have more success than I had. Of course that may require moving to the middle of a marsh or a small offshore island, but still.

Above is a recap of the broadside elevation pattern (right) and azimuth pattern at 15° elevation (left). The feed point is 25% up from the bottom corner (λ/4 down from the apex). The model places the antenna bottom 7 meters above typical (poor) suburban ground, but no effort was made to include the effects of metal in the vicinity of the antenna. The picture of the antenna installation is in the previous article.

For comparison, the 20 meters broadside pattern of the TH1vn up 10.5 meter models with a maximum gain that is 7.2 dbi but at an angle of almost 30°. At 15° it is 5.1 dbi, which is 4 db greater than the delta loop. In practice it may be even higher. Off the ends it is a vertical radiator with a gain of -3 dbi at 30° elevation.

If you compare the gain at the full range of elevation angles up to 30° the TH1vn is superior, but only in the broadside directions. Over better ground the delta loop models as the winner. It is also more omnidirectional, which matters for fixed antennas. In other words, the antenna models are arguably ambiguous with regard to declaring a favourite. This is what makes building and testing experimental antennas so interesting to me.

Ok, that's a lot of preamble. Now let me supplement my first look with two more days of observation:
  • To Central Asia and Japan  the antennas were roughly equal. While trying to work a UN (Kazakhstan) station I tried switching between antennas but without any tangible effect on either transmit or receive -- he had QRM and I had QRP. I did finally work him. I had the very same results with an EX station. At another time I listened for about 10 minutes to an EA6 running JAs. I toggled between antennas while listening. It was close, though more often slightly favouring the dipole.
  • VU and VK were consistently stronger on the dipole. Both should be low angle paths and, paradoxically, the path to VU is not much different than that to UN and EX.
  • The dipole was the clear favourite to 3B9 and three 3B8 stations.
  • All the findings in the previous article were confirmed.
I thought that perhaps with the quieter geomagnetic activity these past few days that the delta loop would perform better. My reasoning is that absorption in lower ionospheric layers can be higher during disturbed conditions. This would favour higher angles (shorter distance through the D and E layers). I had no such luck so scrap that hypothesis.

Rather than make this article any longer I will follow up with another on the delta loop's performance on other bands. It did better than expected on 17 and 30 meters, especially on the former. This is the only real loss I am suffering after dismantling the delta loop -- for now I have nothing else for these bands.

I have another experiment planned that should prove interesting. I'll say more about it after I finish with the delta loop in the next article. I also have some planning and construction work to do in preparation for that experiment. Of course I must also find the time. The weekend beckons.

Saturday, August 17, 2013

20 Meters Delta Loop - First Look

I finally freed up a few uninterrupted hours during calm, clear weather to install the 20 meters delta loop (described and shown on the ground here) on top of the Site-B mast. As you can see in the picture below it is not too high -- the bottom is about 7 meters above ground, with the apex a little over 13 meters up. The dipole (TH1vn) height on the Site-C tower is centred on this range (10.5 meters). Rope stays stabilize the fibreglass mast. You should be able to spot the RG-62/U ¼-wave transformer connected λ/4 down from the apex, complete with coax common-mode choke.

I had intended to raise it one further 4' section of fibreglass mast, but I had to abandon that plan. The reason was one of personal safety due to lifting an unwieldy structure while standing at the edge of the roof. I was not at risk of falling! I rigged up a safety harness that allowed me to move fairly freely along the roof line without being able to go over the edge. (Safety first!) I was more in danger of dropping the antenna and damaging both the shingles and the antenna.

As installed, the northwest corner is close to the roof. This is not ideal. There is RF noise emanating from household and neighbour's computers, and the bottom is closer to the eaves trough than is ideal. Coupling to the eaves trough, soffit and house wiring will detune the antenna. However the pattern is unlikely to change much in comparison to a slightly-greater height. For an experiment it'll do.

I had great hopes for high-band delta loops. This experiment was designed to minimize cost and labour should the antenna not meet expectations. If the experiment has a positive result I will proceed to add more bands to it and weather-harden the structure.

Before I talk about how it performs, let me first recap my hopes for the delta loop:
  • Omnidirectional, low-angle pattern
  • Low-angle (DX) radiation at modest height
  • Broadband, low-SWR match
  • Inexpensive and physically robust
There is ample discussion (and endless argument) about the relative merits of full-wave loops versus dipoles, including directional arrays of both (quads and yagis, respectively). However few actually do real-world comparisons. I do not expect large differences, but I hope to be able to make a clear choice. Models are nice, though never definitive. In the past I've tried both styles of antennas, both single and multi-element, just never at the same time that would allow A/B direct comparison. Now I can. Consider these points:
  • Height has a strong influence of antenna performance, regardless of polarization. While low-angle radiation angle does not appreciably improve for higher vertically-polarized antennas, all antenna gain an advantage by getting above the local environment. There is a lot of metal in houses and utilities that can degrade the antenna pattern, especially at low angles.
  • Performance of vertically-polarized antennas is very sensitive to ground quality. The poorer the ground the higher the near-field losses and absorption of low-angle radiation in the far field. EZNEC and other modelling software can estimate the effect but despite your best effort what you will encounter in the field can be quite different.
So...with 24 hours of use how do the antennas compare? Is there a clear winner? What does it even mean to say that one antenna wins?

First, the antenna works. I've worked a number of stations with it. The resonant frequency is much lower than designed, almost certainly due to nearby metal. The SWR dips to 1.0 around 13.5 MHz, well outside the band. Even so it only rises as high as 2.0 at 14.350 MHz. Despite being 92Ω, the ¼-wave transformer is working.

Note: All the following comparisons were done on receive. I did not bother any contacted stations to help me with transmit A/B tests. Each comparison took the time to allow for the vagaries of multi-path and Faraday rotation due to the different position and polarization of the antennas. All quantities were "eye-balled" on the S meter, not measured with any instrument.

There are a few areas where the delta loop is a clear winner over the TH1vn comparison dipole:
  • Closer stations are attenuated. Stations in the eastern half of North America are often 1 or 2 S-units weaker, and sometimes as much as 4 S-units weaker. This makes DX'ing more pleasurable, and would be a benefit during DX contests.
  • With a tuner in line it performs very well on 17 and 30 meters, much better than the TH1vn.
  • Very broadband, as noted above.
  • Omnidirectional, though not as pronounced as expected. It is not always the better antenna for DX off the ends of the dipole (South America and Asia).
Now let's talk about the important comparison. Which is the better DX performer?
  • The dipole wins on almost all near and medium-distance DX. I did not expect this. This includes DX off the ends of the dipole. Recall that dipoles do not really have nulls off the ends, just at very-low angles. At higher angles there is substantial vertically-polarized radiation.
  • The dipole is superior to the delta loop into Europe, the Middle East, west Asia, west Africa, Central America and northern South America. Into western Europe (EA, F) the dipole is up to 3 S-units better.
  • The antennas are roughly equivalent into Siberia (UA9), Brazil and (surprisingly) VK.
  • The delta loop is better into southern South America (CX and LU), Japan and UA0.
During these tests the K-index was 3 or 4, so there was some geomagnetic activity. I mention this since it could cause higher absorption at low angles. If true this would favour the dipole. Testing will continue to determine if this is the case when propagation improves.

If first impressions tell me anything it is that this antenna is not going to pass the test. It is not only the DX performance but also the susceptibility to EMI from home electronics. Even when the delta loop is better, if the DX is weak it is sometimes hard to copy due to the noise. The dipole, being farther away, is much quieter.

Regardless of the outcome I am pleased with this experiment. I'm learning new things. I am already thinking about alternatives that would meet my needs. Summer is wearing away and with it the remainder of antenna-raising weather. I have some work ahead of me.

Tuesday, August 13, 2013

Luck and the Pile-up

While I was making a ¼-wave transformer out of RG-62/U last evening I had the rig on. Band conditions were very good and there was some good DX on tap. In addition to working TT8 and 3B8 among other less-rare stations I was attracted to the pile-up on HV0A. All of this was on 20 meters CW.

Late last week I spent a few minutes trying to work this station, though without success. QRP (10 watts) plus dipole versus the maddening hordes is not a recipe for easy success. Back in town after the weekend I tried again. This time I got through, and rather quickly. The pile-up seemed thinner than last week but was still plenty big -- wide and loud.

Was I just lucky?

HV0A was planted on 14.027 MHz for hours, working stations at a good clip. Evening here is middle of the night in Europe, so it is unsurprising that, despite any propagation-related reasons, most of the callers were in North America. Aside from the usual nonsense on his transmit frequency the pile-up ranged from 14.029 up as high as 14.037 MHz.

If you think about it for a moment this makes no sense. The DX station is only listening on one frequency at a time. This can usually be discovered within a QSO or two (or three). HV0A was not randomly flipping his receiver around between contacts so why were stations calling all over the place? Were they hoping he'd eventually stumble across them? Was this a secondary activity while they read a long novel, stopping only to press a memory key every 20 seconds or so? Or were they just lazy? Inquiring minds want to know.

My objective was to either work him or determine in short order that my quest was futile. I've got other things to do. It was therefore in my interest to figure out how to work him quickly. I followed a time-honoured procedure that was so well described by W9KNI many, many years ago in his book "The Complete DX'er".

I did not make my first call until after the first minute or two of listening. It was more important to find who he was working -- and therefore where he was listening -- and determining his pattern over the course of a few contacts. He didn't change listening frequency much between contacts, usually shifting up or down less than a kHz between contacts.

With the pattern established I cranked up all 10 of my watts and entered the fray.

QSK ensured I did not waste precious opportunities to listen when he transmitted. I stopped and used the RIT to find who he was working instead. If his listening frequency had moved up I quickly jumped higher again by a similar amount. This was usually no more than 500 Hz. I did the same in the reverse direction if he chose to listen down in frequency. This is more work than calling blind and hoping for the best. Hope, however, is not a strategy in DXing. It's easy but not terribly effective.

Speed is of the essence. It takes little time for the lucky DXer to send "R 599 TU" at 20 or 25 words-per-minute. In those 2 seconds you need to find that station, calculate the frequency offset, predict where the DX will listen next, then adjust the VFO in preparation to call and flip back to the DX to time your call. The operator at HV0A was good, so it was easy to settle into a rhythm of listen, shift frequency and call.

I didn't count exactly how many times I called. My transmit frequency was different each time, per the above procedure. But it was only 6 or 8 QSOs later that my little signal scored the contact, putting HV into the log.

I was not the only one following this procedure of hunting, VFO-setting and calling. It is just that we seemed to be a minority. What was everyone else thinking?

Early on in this blog I speculated as to what -- after having been QRT for 20 years -- in this new era with new and powerful tools at everyone's disposal would give the modern DXer a competitive edge. Maybe it's nothing more than what has always worked: being smart and working hard. Then getting lucky.
I am a great believer in luck. The harder I work, the more of it I seem to have.
-- Coleman Cox (1922)

Monday, August 12, 2013

RG-6U Warning

In my previous posting on ¼-wave transformer accuracy I mentioned that I'd bought a small roll of RG-6U 75Ω coax with which I planned to build the transformer for my experimental delta loop. Impedance transformation is needed since the loop radiation resistance is well over 100Ω. Today I cut into the cable to see how I might attach a UHF connector on one end and make a pigtail connection at the other.

What I discovered is not good. The attached picture is not particularly good (curse those auto-focusing smart phone cameras!) though I think you'll be able to see the important bits.

As with most RG-6 cables I've read about there are a few features that I found:
  • Foam insulation between the inner and outer conductors
  • Primary outer conductor is foil
  • Braid surrounds the foil
There's nothing wrong with that, though as I mentioned before I had some concern with making the needed connections at either end.

The problems are with the details of the cable construction. To be blunt, this cable was designed to be used as-is, complete with connectors at both ends. The connector I cut off is shown in the picture. The cable is made by a major manufacturer and was bought in a local big-box store.

Here are the difficulties with this cable:
  • The braid is no more than 10% coverage and made from easily-broken strands. What you see in the picture is a fair representation of it. There is nothing to connect to. I don't even see the point to its presence. Well, ok, there is one: as one side of the "sandwich" for the machine-driven connector insertion to form a bond to the outer conductor.
  • The foil is bonded to the polyethylene foam. It cannot be separated from the foam without damaging both. If that had been possible I might have been able to at least made a pigtail of some type, or soldered to it.
  • I tried to solder to the foil. No go. The attempt also melts the foam.
  • An RG-58 adapter for a male UHF connector is not a friction fit for the outer conductors. If it had been I could have probably made a workable connection. The F-connector the cable comes with is fine, but I have nothing compatible. I don't want to spend more money purchasing female connectors. Besides, that does not really solve the problems with this cable.
With enough time and ingenuity I could eventually make this cable useful. However my time is worth more than the small amount I paid for it.

The lesson here is that if you do go for some variety of RG-6 when you require 75Ω coax you should first ensure that it can be put to use without excessive effort. There is no RG-6 standard to rely on; every manufacturer's product is different. I suggest it is worth paying a few dollars more for RG-59 or RG-11.

For the purpose of this one antenna experiment I will use RG-62. Since it is 92Ω cable the SWR of the delta loop models at 1.5, which is good enough. Using 50Ω cable all the way puts the SWR above 2, and that could effect the results of the experiment. If all goes well with the antenna I'll purchase some RG-59.

Baluns also work but the 1:2 ratio required is not commonly available and would have to be built. That is another item for consideration, but not now.

Thursday, August 8, 2013

Quarter-wave Transformer Accuracy

I built the experimental delta loop for 20 meters over a few hours this past weekend. It now rests up against the house and mast on which it is to be mounted. As you can see in the picture it stands taller than the eaves of the house! I expect the neighbours will be...impressed when it goes up.

Although large it is actually quite light and can be carried around, lifted and put down without much effort. The heaviest part is the fibreglass mast, consisting of 6 x 4' nesting 1.75" OD tubes. I could get by with lighter-weight fibreglass, except I don't have it and this is good enough for an experiment.

The horizontal arm of the loop is the boom of an ancient Cushcraft 32-19 long-boom yagi for 2 meters, slightly extended. The wire is 12 AWG stranded THHN copper wire. Each leg of the loop has been cut to 7.3 meters, which should resonate at 14.075 MHz when mounted 7 meters above ground.

You should be able to see the feed point (white insulator) on the left arm, 25% of the way up the bottom. This is ¼-wave down from the apex, which is what makes this antenna vertically-polarized and omnidirectional.

What is missing from the antenna is the transmission line. This will consist of a ¼-wave of 75Ω coax, complete with common-mode coax choke. Loops have an impedance that can range anywhere from 100Ω to 200Ω, depending on height, shape and position of the feed point. For this antenna, with the bottom leg at around 7 to 8 meters off the ground, the use of 75Ω for the transformer results in an SWR of about 1.1 at resonance (modelled in EZNEC). The primary line to the rig will be RG-213.

Digging through endless rolls and hunks of coax in my basement I was not successful in finding much in the way of usable 75Ω coax. The only RG-59 was in short patch cord. There is a roll of RG-11 but I know it is in questionable condition. I did eventually find one good section of RG-11 which happened to have connectors and was already in line with a longer length of RG-213. That puzzled me for a moment until I realized it was the transmission line to my old delta loop for 40 meters.

Not wanting to destroy that perfectly good ¼-wave transformer I decided to buy some RG-6. This 75Ω coax is widely available and cheap. It is harder to work with than RG-59 (though about the same diameter) since there is a foil layer underneath the outer braid and the centre insulator is foam. This can be challenging since one has to be certain the foil, the inside of which is the "true" RF conductor, is electrically connected to the pigtail or PL-259 termination. Soldering must be carefully done so as to not melt the foam. The foam also increases the minimum bend radius, which is important when winding the coax choke.

Assuming that all of this is taken care of, the next challenge is calculating the length of the transformer. This requires knowing the velocity factor (VF) of the cable. There are a couple of issues. First, RG-6 from different manufacturers has been found to vary in the insulator construction so that the VF can range from 0.75 to 0.9. This is a wide range! In comparison, cables with solid polyethylene center insulators are pretty consistent in having a VF of 0.66.

The wavelength at 14.150 MHz is 21.19 meters. One quarter of this is 5.3 meters. The transformer will be shorter in proportion to the VF. Foam PE has a nominal VF of 0.83, so that is what I started with in my design. This works out to 4.4 meters. However, because of the VF uncertainty the true length could be anywhere between 3.9 and 4.8 meters.

It is possible to test the cable with suitable equipment to measure the reflection time or impedance transformation to determine the exact VF of any length of coaxial cable. But that's a lot of work, and in any case I don't have the needed equipment.

What I did instead was to do a sensitivity analysis with EZNEC. This is very simple and quick. First I set the transformer length to 4.4 meters and the VF to 0.83 (see above). Next I generated the SWR curve across the band. Here is the result:

The SWR has a minimum value of 1.1 at 14.050 MHz (recall that my major operating interest is CW).

I then repeated the exercise with the lowest and highest VF values I might encounter in typical RG-6 cable. The first is for 0.75 and the second if for 0.9 VF.

The SWR didn't change much but the frequency where it dipped did change. For a VF of 0.75 the SWR minimum is ~14.140 MHz and for a VF of 0.9 it is at or just below bottom of the band.

The single-element delta loop is known as a reasonably broadband antenna. Even in the worst case (VF of 0.9) the SWR stays below 2 even near the top of the band.

This sensitivity analysis tells me I have little to worry about in regard to VF of precision measurement of the transformer length. This might not be true for antennas with a smaller bandwidth, which includes any directive array and antennas for 160 and 80 meters.

I will almost certainly have to adjust the antenna length in any case due to environmental factors that are not in the model. The affect of VF is just one more factor, and one that I could not distinguish from any other. Further, should the experiment succeed and I go ahead and add more bands the interactions will affect both resonance and impedance.

This is just a lengthy way of saying that the VF of the coax is not much of a concern: the SWR should end up being good enough. Regardless of the impedance match, the pattern will be unaffected.

Now if I can only find the time to get to prepare the transmission line and raise the antenna. It may have to wait until at least next week.