Small Transmitting Loop Project
Matt Roberts - matt-at-kk5jy-dot-net
Of the many different antenna projects I have built for HF, the most interesting and rewarding project was the small transmitting loop. After consulting many of the available Internet sources, and by combining ideas, I was able to assemble an antenna that performed well, even under poor band conditions. The experience was so much fun that I built several different ones, all described below.
Thinking About Loops
Having previously spent many years as an apartment-dweller, I have a keen sense of how difficult it is to do effective HF communications from restricted spaces. Even though I now have a small yard in which to experiment with antennas, the idea of a high-performance, small HF antenna still holds my interest.
There are a number of amateurs who have suggested that small loop efficiency and effectiveness can actually be far better than conventional wisdom might suggest. Some have even challenged traditional round loop designs altogether, using different shapes and materials to squeeze more performance out of their antennas. Despite the challenges associated with confronting long-held traditions in design, these amateurs continue to perform some impressive experiments with their creations.
For me, the process of building loops started small, mainly as an experiment driven by idle curiosity. Over the past few years, however, I have slowly developed my loop antennas into fully automated, remotely controlled, high power (500W) antennas for the 80m through 6m bands, becoming a major part of my radio hobby effort. In fact, my experience with low-band (40m and 80m) loops has convinced me to use this type of antenna as a main contesting antenna, even when other larger antennas are available.
As ARRL has noted in their push for relief from CC&R antenna restrictions, the amount of unencumbered available space is becoming increasingly scarce. Additionally, the ever-shrinking lot size for new development is combining with all manner of consumer electronic devices to make our HF bands more noisy than ever. Because of these and other factors, the need for smaller and quieter HF antennas is growing. One of our challenges in the future is to design and build antennas that still have good performance characteristics, both for DX and domestic contacts.
On that note, this project has inspired a couple of related receive-only antenna projects, the loop-on-ground antenna, and the small untuned receive loop. These share many traits with the small transmitting loops, but they also have some important differences for those seeking to optimize receive antnenna performance. A dedicated installation of independent transmitting and receiving loops could be the ultimate small-lot, high-performance HF antenna system, especially for the longer wavelengths.
What follows is a walk-through of my experiences building transmitting loops. I'm not going to include the spreadsheets, calculations, theoretical formulae, etc. I will include links to the more interesting ones at the bottom of the article. What I want to capture here are the more practical experiences, and some of the "Ah ha!" moments of the project.
This document continues to grow, so it's time to add a Table of Contents, to help organize it:
Step 1 - Just the Essentials
Starting out, I wanted to avoid investing any significant amount of money in an experimental antenna until I was convinced that the principles were sound, and that I could make them work for me. People who use small loops often make impressive claims about their performance, but then again, even a light bulb can work the occasional DX station, right? I wanted to prove the concept before committing a lot of cash to the project.
Finding a quality tuning capacitor is the most difficult step in procuring materials, so I started with that. I had quite a bit of success using open-wire feed line for feeding and matching my dipole, and I knew that the voltage handling capacity of such line is quite high. This line is also rather inexpensive, with a 100' roll of 300-ohm window line at around $20.
I decided on a basic and minimal small loop, 3' in diameter, using a stub made from quality window line as the tuning capacitor. Such an antenna would, in theory, readily resonate in the 20m band. This design would also allow me to simply discard the antenna if it didn't work well, without losing a lot of money.
This first loop was tuned for a single frequency, 14,070kHz. I thought digital modes would be a good way to test the antenna, especially since so much digital activity is clustered tightly around a single PSK-31 frequency on each band. That would allow me to find the highest number of stations in close proximity to each other.
In keeping with my cost-saving approach to my experimental antenna, the first mast was made from PVC plumbing pipe. It is non-conductive, and the large-bore PVC pipe is very rigid at short lengths. I keep a surveyor's tripod handy for doing antenna experiments, so between that and the PVC, I had the materials to build the support. The tripod will accept a schedule 40 PVC pipe of nominal 1-1/4" size, so that was the type chosen for the mast. 5' lengths are commonly available, and threaded connectors were used to to join the loop's 5' section with a second 5' section that would slide into the tripod. This allowed a 10' overall height, that could be easily assembled and disassembled.
Some things I learned about using PVC as a mast:
For the loop itself, I chose 5/8" soft copper tubing. This is the type you might use to feed refrigerant to an air conditioner. It is often sold as "refrigeration tubing." The small-loop theory says that larger bore tubing makes the antenna more efficient, but 5/8" seems to be a nice compromise size, and is still in the "cheaper" grade of tubing. Price starts to climb rapidly as you increase the tubing size, and again, I was just trying to prove the theory.
- Conveniently, 1" PVC pipe fits very nicely within 1-1/4" PVC pipe. If you cement the two together, one inside the other, the strength and rigidity of the mast increases substantially. Most of the loops shown here use this arrangement in at least some part of the support structure.
- When using the threaded connectors, it is very wise to apply a small amount (or not-so-small amount) of dielectric (silicone) grease to the threads before trying to mate them. Remember, this is plumbing pipe, and the various connectors are not meant to be disassembled repeatedly. They are meant to glue together and stay glued for decades. The threaded connectors I used had a slight taper, which means they were also meant to thread together tightly, and stay that way. Without some kind of lubricant to prevent this, I would eventually need some large wrenches to twist them back apart.
- Using a high-quality cement to join the pipe to the connectors is a must. Few things will ruin your day faster than watching your beautiful antenna creation come crashing to the ground because a joint worked loose. Cement is cheap. Rebuilding an antenna is not.
- The tripod is a great way to support the antenna, but loop antennas can get very top-heavy. The tripod will easily support the bottom mast by itself. Before threading the loop itself onto the bottom mast section, I made sure to guy the bottom mast section just above the tripod. This is absolutely mandatory. More than once, I had to catch a falling loop because the wind had caught it just right, and caused it to tip over. The tripod wasn't enough to resist the leaning tendencies of the loops under wind load, even though the entire thing was only 10' above ground.
- The green guy lines in the pictures are relatively thick nylon rope. Nylon is not typically UV-resistant, so using it as a long-term guy line for a permanent installation is probably not a good idea. There are inexpensive ropes available that are meant to be used as guy lines for permanent antenna installations, and these ropes are UV-resistant. If you use nylon outside for long periods of time, the sun will eventually make it brittle to the point of failure.
- Speaking of guys, I used cheap aluminum tent stakes from the camping section of a local store. These were were more than adequate to hold the long guys in place. However, there is also a stake in the ground that you cannot see in the photographs. It is directly inside the bottom support PVC pipe segment. This keeps the bottom of the mast from sliding around on the ground. This is also mandatory, because of the top-heavy nature of the loop. Without it, the bottom mast segment could shift, and send the antenna falling.
Soft copper tubing also lends itself to being easily formed into a circular loop. Unlike loops built from copper pipe, the tubing doesn't have to be cut and joined with elbows. Having a long continuous piece of copper seemed ideal for keeping losses low. After all, solder joints increase losses. I have seen some very clever jigs for doing circular bends of piping. I did mine by hand, and the result was almost as good. The trick is to bend the tubing a little at a time, working your way around the length of tubing several times, making very small bends every few inches during each pass. Out of the box, the tubing is already coiled up in a nice circular shape. All you have to do is increase the radius of curvature to get it to the diameter that you want.
For the inner (driven) loop, I chose 1/4" soft copper tubing. An SO-239 connector from Radio Shack was carefully soldered to the ends of the inner loop.
Both types of tubing can be purchased by the foot from local hardware shops for reasonable amounts. I was able to secure both from Lowe's for just over $1/foot.
Some notes about working with copper tubing:
- Handling copper with your bare hands will very quickly cause it to tarnish. The copper content of pipe and tubing is extremely high, and copper loves to react to the natural oils and salts from your skin. If you will wear thin latex gloves while handling the tubing, and especially while bending it, the copper will retain its shiny appearance and you will minimize contaminants on the surface of the inductor.
- On the subject of contaminants, remember that the thickness of the copper is irrelevant for an antenna. The skin effect of RF flowing on any conductor will force all of the current into the top few micrometers of the copper tubing. I have not seen any literature that describes how tarnish, oxidation, and other surface contaminants effect the RF resistance of a conductor, but the cleaner you can keep the surface, the better.
- It is easy to polish the copper loops with a wire wheel, available at any store that sells drills and bits. The coarseness is up to you, but mechanically polishing the imperfections out of the loop is easy and well-advised. If you use a drill or Dremel to work on any part of your loop, make sure to wear eye protection.
Now it was time to tune it.
To figure out how long to make the capacitor stub, I used some existing 300-ohm stubs cut for the dipole project. These were in lengths ranging from 6" to 8', in binary increments. I can combine these into any length of stub, to a resolution of 6". To interconnect them, I soldered PowerPole connectors to the ends. In a very handy coincidence, the spacing between PowerPole contacts is almost exactly the same as the spacing between the wires of 300-ohm window line. This way the stubs could be connected in series quite easily. At the top of the loop, where the copper tubing is split, I soldered in a 2" stub with a PowerPole connector, for attaching to the stub of the stub.
Some thoughts about capacitive stubs:
After some experimentation, I found the length closest to 14,070kHz for the loop. Using a Palstar analyzer, I mixed stubs until I found a length that was close. I then took a spare stub that only had one connector, and started cutting it from one end about 1/8" at a time, until I slowly resonated the antenna at 14,070kHz.
- Using feedline stubs for matching isn't a new idea. People have used open-wire and coaxial feeder stubs for impedance matching purposes for some time. The dipole matching project used both series and shunt stubs between the coax and a 600-ohm feedline to match the two, and was inspired by W5DXP's work on that very subject. His project used series transformer sections exclusively. I just extended the idea by adding a second piece of feedline, open-ended, as a shunt section on the high-impedance side, to further refine the match. That piece served (mostly) as a matching capacitor of very small value. That is the idea here, with the loop. The stub is open-ended, and serves only as a capacitor.
- From an efficiency standpoint, the stub isn't a good permanent solution, because it adds more than capacitance. It serves as a delay line that also contains a non-negligible amount of inductance, that actually adds to the effective length of the large copper loop. For use as a first experimental capacitor it was a wonderful and cheap way to do tests. In the long run, a good design will probably use some kind of lumped-C capacitor, such as a vacuum-variable or an air-variable.
- I have seen some really nice designs for homebrew trombone-style capacitors made out of copper pipe (not tubing). I opted to avoid these as a final solution for two reasons.
- I wanted to operate high-power levels. This means that the dielectric of the capacitor needed to be high-quality and low-loss. A vacuum is hard to beat for this purpose.
- I'm not yet convinced either way with respect to how much additional inductance is introduced by the trombone arms. It may be negligible, but as with the window-line stub, it certainly "looks" substantial, due to the lengths involved.
For the feed loop, I used a single turn of 1/4" tubing, fed directly in a balanced fashion from the coaxial cable. I used an MFJ-915 choke close to the feed point, to ensure that no common mode current flowed on the cable. During later experiments, I found that this is usually not needed, but I didn't want to pollute my test with common mode radiation or reception. I wanted all the power to go into the large loop, whether that mean radiation or loss.
Even before making any contacts, I noticed that the loop Q was quite high. Drifting in frequency more than 15kHz from the center frequency would raise the SWR quickly to 2:1 and beyond. Another 15kHz would take the SWR beyond 10:1, which is the measurement limit of the Palstar device.
Since the high Q is critical to maintaining loop efficiency, I knew I was on the right track. Efficiency and Q are very tightly coupled, and for an electrically small (dare I say, tiny?) antenna, efficiency and Q are directly proportional. Higher Q tends to indicate higher efficiency for a small radiator. If the antenna had a lot of resistive loss, the Q would fall, and the 2:1 bandwidth of the antenna would be wider.
The band conditions on 20m the day of my first tests were terrible, but I still had no problem making coast-to-coast domestic contacts on PSK-31, even in the presence of heavy fade. After spending an afternoon making contacts on the loop, and watching several DX stations come in quite clearly, it was obviously working well enough to justify getting more serious about the loop project.
Step 2 - Vacuum-Variable Capacitor
The next step in improving the loop was to add a variable capacitor, to allow the antenna's frequency to be changed. I wanted to use the loop on at least a couple of different bands, to see how the performance changed as the loop wavelength was changed. A 3' loop is just under 9.5 feet in length. That's about 1/8 wavelength on 20m, almost 1/4 wavelength on 15m, and well over a quarter wavelength on 10m.
Alan Bond over at MaxGain was able to provide me with a couple of used vacuum variable capacitors, 10-60pF, 10kV, for around $100 each, shipped. Vacuum variable capacitor prices only go up from there, so I thought that would be a good starting place. According to the calculators available online, those capacitors would allow me to tune across the frequencies that I cared about, at a peak power level of 500W, which is the limit of my station, anyway.
The capacitor replaced the stub, and I added a shaft made of PVC, to allow for turning the capacitor shaft from the ground. At left is an image of a driveshaft added to a 5' loop, constructed later. At right is a close-up of the capacitor mounting.
You will note that I used wires to connect the ends of the inductor to the capacitor. Although this wasn't optimal from the standpoint of keeping resistance low, the Q of the loop remained quite high after this change. More importantly, I could tune the loop to any frequency from 20m through the CW/data portion of 10m.
The wires were soldered to the tubing using standard PC-board solder. I tried silver solder, but my first attempts didn't work out well. Later, I'll describe how I was able to successfully resolder with silver-bearing solder.
As a side note, most capacitors are rated for maximum voltage, and they are typically marketed that way. While the voltage rating is important applications like this, I found that an equally important capacitor rating is its maximum steady state current rating. The voltage rating only matters once you get close to the limit; anything less than that, and the capacitor's voltage handling is just as good whether you run 100V or 10kV. This contrasts with the current rating, which is the point where the capacitor is no longer able to keep itself properly cool, and heating effects occur. I have seen more than once where the limiting factor for a loop antenna was the capacitor, and it was the current rating that was the limit. As the power level caused the circulating current to approach this value, the capacitor would start to heat, causing thermal drift of the resonant frequency.
Unfortuately, the AA5TB spreadsheet doesn't capture the circulating current value of the loop you are modeling, but it is not difficult to do calculate, since it is included with the ARRL loop formulas. I modified the spreadsheet to include circulating current, which has been very helpful in selecting proper capacitors to use for a given design. I won't publish the updated spreadsheet here, but if anyone would like a copy, please send me an email. I noticed that the MaxGain folks are usually good about documenting the current capacity of their products, so it would be a good idea to compare these ratings with the anticipated value from the ARRL model before selecting a specific capacitor model.
While working with this loop, I noticed some other interesting things that the standard literature didn't seem to mention. I have no explanation for why any of these were true, but my experience was consistent across all of the loops built:
The first point was very helpful, because simply rotating the inner loop didn't always work. By raising or lowering it on the mast, so that the two loops remained coplanar, I could easily reach a 50-ohm point at resonance, regardless of the location details. When mounted outdoors in the clear, the 50-ohm position of the inner loop was several inches up the mast. When used indoors, the 50-ohm position of the inner loop was near the bottom edge of the outer loop. At right, you see what the 3' loop looked like adjusted for use outside.
- Adjusting the inner loop for 50-ohm resonance was much easier if I moved it vertically, within the loop plane, rather than rotating it about the mast. All of the literature I read suggested the latter.
- The proper location of the inner loop for a 50-ohm match was extremely dependent on the loop's surroundings; e.g., its height above ground, whether it was indoors or out, proximity to other objects, etc.
- The range of resonant impedances attainable by moving the inner loop along the mast could also be changed by deforming the inner loop to be oblong, rather than circular. This was another technique suggested by some texts, and it was necessary to get 50-ohm resonant matches when the loop was sited in difficult locations, e.g., indoors.
- The overall loop was also easier to match to 50-ohms if the inner loop was fed at its top, and not at the bottom.
A few QSOs later, it was time to add a motor drive to the capacitor, so that I could remotely tune the loop.
Step 3 - Motor Driven Capacitor
Robotics is a fairly common hobby today, so finding a motor to move the capacitor shaft was easy. I bought a gearhead motor from a robotics wholesale outlet. The gearhead reduced the RPM of the motor from several hundred RPM, to about 3 RPM. Both the motor and the capacitor had 1/4" shafts, so connecting them required only adapting the PVC driveshaft to them. I found a couple of knobs at Radio Shack that did the trick. They were replacement knobs for audio equipment volume controls. The knobs fit tightly inside the 1/2" pipe, and to the shafts.
High-current antennas such as this are capable of generating huge magnetic fields close to the antenna, so I adopted a rule to help keep my test results as trustworthy as possible. I decided not to run any conductors near the outer loop, where the high loop currents exist. That way, the mutual coupling between the outer loop and other conductors was kept to a minimum. The intent was to keep the antenna's radiation pattern as pure and undistorted as possible.
To accomplish this, I did a couple of things that also were not mentioned in any of the small loop literature that I found:
I added a couple of protection items to the motor before using it. First, I placed a 0.05uF capacitor across the motor's DC terminals. This keeps the RF out of the motor windings. Second, I choked the power leads with a common mode snap-on bead, to keep RF from flowing into the motor from the long leads, or back to the power supply from the motor. The motors also had a vinyl cover added, to weatherproof them.
- The coaxial feedline was mounted in such a way to keep several inches between it and the outer loop. This was done by making a large arc from the feed point, over the main loop, then back to the mast.
- The motor drive for the capacitor was not mounted close to the capacitor. Instead, a long "driveshaft" was formed with PVC pipe, and used to connect the motor to the capacitor. The driveshaft was long enough to allow the motor to be placed well outside the outer loop.
Another handy tool I borrowed from the robotics hobby was the PWM motor controller. These devices generate pulses of DC to drive the motor. Using voltage to control a motor's speed can also be done, but it has some disadvantages:
The PWM mostly solves these problems. By pulsing the power, rather than lowering the voltage, the PWM allows the motor to run at full voltage while moving. The PWM generator takes advantage of the rotational inertia of the rotor to provide a natural slow-down of its motion, which allows much more fine-grained control over the motor speed.
- A motor running at a lower voltage develops less torque than one running at full voltage.
- A motor running at a lower voltage can generate more internal heat, especially since it stalls more easily under load.
- A motor running at a lower voltage is less efficient than when it runs at its design voltage.
Adding the PWM to the motor circuit allowed me to more easily find and adjust the resonant frequency of the antenna. I added a DPDT, momentary, center-off switch to the PWM circuit output. This allows me to send normal or inverted voltage pulses to the motor, to rotate it in both directions. Many DC motors are reversible in this way, and the specifications of the motor will tell you for sure. At right is the PWM controller, with the DPDT switch on the output.
The loop was really taking shape, and I was happy with the performance I was getting, but there were still a couple of things I wanted to do to try to squeeze out the last bit of efficiency.
First, I replaced the wire jumpers between the capacitor and the main inductor. Georgia Copper sells nice, polished copper strap in various lengths. I used 1/2-inch strap to make the connections. I also used silver solder the second time. It turns out that my previous attempt failed because I did not properly flux the conductor before applying the solder. Tractor Supply sold me a roll of silver-bearing solder that contained its own flux, and that worked much better.
Note that the copper and solder around the joints was polished after assembly. This removed the discoloration and oxidation that naturally occurs when using a torch for soldering. Again, the skin effect of RF flowing on the surface of a conductor adds enough resistance on its own. I hoped the polish would make sure that the current wasn't flowing through any additional impurities.
Several loop builders also mentioned improvement in performance by adding a fan of short radials underneath the loop on the ground. I added a set of 15 to 18 radials under the loop, each of which was around 6' long. These radials are solid copper, THHN-insulated wire. Next time, I will use stranded wire with short stakes, to make it easier to deploy.
Radiation Pattern Observations
The overall loop pattern was nearly omnidirectional. The nulls that I did find were rather sharp. They were, however, enough to null out some RFI from a local neighbor, when the loop was properly rotated. DX contacts were readily made at angles 60-80 degrees from the loop plane. The theory seems to indicate that this is a typical small-loop pattern.
The three-foot loop has a 2:1 SWR bandwidth of 22kHz on 15m, as measured at the end of a 45' length of RG-213/U.
In the end, six loops were built. These ranged in size from 9 feet down to 17 inches diameter. Each of the new loops was built to emphasize a particular band. The loop described above was approximately 3' in diameter, and is a good choice for multiband operation from 20m through 10m (strongest on 15m) with the capacitor chosen.
One of the loops was a 5' model specifically built for 20m performance. It was a larger diameter, making the overall circumference about a foot less than one quarter wavelength at 14,350 kHz. This maximized the efficiency for that band, but still kept it electrically small. Its measured 2:1 SWR bandwidth on 20m is 18kHz.
This antenna used the second of the two 10-60pF variable capacitors I originally picked up from MGS. This allowed it to tune well outside the 20m band, but I only used it for this band. It does tune into the 30m band, but I have not tried to make any contacts there.
Back in my college years, 6m FM had some fantastic propagation, and I remember some very nice band openings. I have been wanting to get back into 6m, but didn't have an antenna that fit well anywhere at the house. So as an experiment, I also tried a 6m loop. This loop has a diameter of about 17 inches. It used a single 3-30pF capacitor for tuning, which was sized to be usable into the 100W range. This loop has made some domestic CW contacts, but has not seen a lot of testing yet.
Loops that are extremely small electrically are able to maximize other aspects of their operation. For example, lower noise pick-up and deeper nulls. I built a 40m loop to experiment with these properties.
The loop size was chosen to be approximately 4.5 feet in diameter. This makes the circumference of the antenna about 11% of the wavelength at 7,000kHz, and the diameter about 3% of the wavelength. Electrically speaking, that is the definition of "small".
The measured 2:1 SWR bandwidth of the 40m loop is 5.4kHz. At this bandwidth, the antenna is still capable of SSB transmission. However, it reminds me that loops of this size will only be usable for narrow modes (e.g., CW or PSK-31) on lower bands. Antennas large enough for SSB on lower bands will likely not be easily portable. This antenna's Q is high enough that it needs frequent retuning while moving up and down the band, even on CW. Adding an automatic controller eased operation considerably.
This loop was a little different than the others, in that I didn't try to use a single capacitor to tune it. Instead, it used two capacitors arranged in parallel. The first was a vacuum-fixed capacitor, 100pF, to provide most of the 120pF required to bring the resonant frequency down to around 7,500kHz. The second capacitor was a smaller 3-30pF vacuum-variable, used to provide the tuning adjustment to pull the frequency down further into the 40m band.
The maximum current rating for the 100pF vacuum-fixed cap was considerably higher than that of the vacuum-variable. The reason for this is that the current flowing into and out of each capacitor in a parallel arrangement is directly proportional to its value. When the vacuum-variable is adjusted to 20pF, it shoulders roughly 1/6 of the total circulating current within the loop antenna. So the current ratings for the two capacitors were chosen accordingly. This was very helpful, because high-capacity fixed capacitors are far cheaper than high-capacity variables, mostly due to the simplicity of the construction. By using two caps in parallel, I minimized the cost of the overall capacitor bank considerably.
The initial tests of the 40m loop were very promising. During a CW contest, the 40m loop made numerous DX contacts in Europe. When running at 500W, the capacitors showed no signs of heating (SWR drift, physical warmth, etc.).
With the improved conditions on 10m, a dedicated 10m loop seemed to be a good idea. Its construction was very similar to the others, and it showed a measured 2:1 SWR bandwidth of 27kHz.
During a recent 10m contest, I did several A/B tests between the 10m loop and my KIO hexbeam, which is mounted at a height of 23'. The received signal strenth on the loop was about one S-unit less than that of the beam. Given that the difference in expected gain between the two antennas is around 8dB, the signal levels received on the loop were more than satisfactory. The noise level on the loop was also down about one S-unit (6dB). When transmitting, this loop was just as capable of European and domestic contacts as the beam, and I found no stations that could be worked on the beam, but not on the loop.
As you can see in the photo, this loop has been painted with a coat of white enamel. This protects the copper from tarnishing from handling, but it does not seem to have effected the performance in any measurable way. The copper was sanded prior to painting, to make the copper surface as conductive as possible. The other HF loops have been similarly painted, with no adverse effects to performance.
The yard in which I build my "antenna farm" is roughly 64ft square. Even a loaded 80m antenna would take up a lot of room. I modelled a few 80m antennas, and decided to try a loop for this band, as well.
This antenna's construction differed from the others in some significant ways. First, it used flat copper strap, rather than tubing. The 3" strap width was selected so as to give an equivalent surface area to that of tubing roughly 1.9" in diameter. The strap does not have any structural strength of its own, so a "plus"-shaped PVC structure was built from 1.25" schedule-40 PVC. This turned out to be sufficient, but it is still quite flexible under the weight and wind load. A larger-bore pipe would be a better selection.
The antenna is rather large, as compared to the others. The arms of the support structure were each 4.5' long, and each of the four sides are over 6' long, for a total conductor circumference of 26', with about a foot curled up near the tuning capacitor. This means it is possible for the loop to fit through a door, but not easy. So this antenna was built to have some basic protection for the motor and capacitor, so that it could be left outdoors for extended periods of time. The housing around the moving parts is 4" PVC nominal I.D.
This antenna is fed with the capacitor at the bottom of the loop, and the smaller driven loop at the top. This is an inverted configuration from my other loops. I spent some time in EZNEC+, modelling these antennas, and found that for the higher band antennas, the normal (cap-at-the-top) configuration gave the best overall pattern for these bands. However, for a low-band loop, I found that the pattern was slightly better (between 1dB and 2dB) if I inverted the antenna in its resonant state. I can't explain why the models worked out that way, but I suspect it might have something to do with the distance of the antenna from the ground, as measured in wavelengths. Since they are all roughly the same height (5 to 8 feet) from the ground, this is the main difference between them.
Because of the inverted configuration and large size, I moved the location of the motor, as well. While I could have placed the motor below the main loop on a short driveshaft, this would have increased the size of the overall antenna significantly, and it would have placed the motor very close to areas of high RF energy. So this time, I placed the motor near the center of the loop, which should be a near-null area for RF. While the motor is in the center of the area of high flux density, it does not appear to pick up any significant levels of RF on the control lines. Further, the 4kHz square-wave PWM signals that drive the motor during rotation produce only faint RFI to the antenna if the motor is moved while the radio is receiving. Given the coincidence of two areas of high magnetic flux, that of the antenna and that of the motor, I was pleasantly surprised by the effectiveness of placing the motor inside the antenna's null zone at the center of the large loop.
The capacitor selected was a 500pF Jennings, with some impressive power handling specifications. The copper strap was attached directly to the capacitor body, to eliminate any unnecessary mechanical joints in the high-current part of the loop. The ends of the strap were cut to form several "fingers" that fit under the silver clamps on the ends of the cap. The antenna shows no signs of drift due to RF heating, even under 100W continuous key-down. The model suggests that it should be fine through 500W for CW operation, and perhaps higher for SSB duty cycles.
The feed point was made from #16 solid wire, rather than from tubing. This made it easy to shape, and to attach to the weatherproof enclosure housing the coax connector. This was the first antenna that does not have a choke on the coax feed -- and as it turns out, it wasn't needed. The loop balance was quite good, and the broadside nulls were very pronounced. A local neighborhood noise was S-9 end-fire to the loop, but when the loop was turned so that the noise was broadside to loop, it could no longer be heard at all.
This antenna was easily managed with the AutoCap software, using a 400-step/rev stepper motor attached to the capacitor through a 4' PVC driveshaft.
Outdoors, the bandwidth was quite narrow, and it showed a measured 2:1 bandwidth of approximately 3kHz on 80m. The antenna's circumference is less than 1/4 wavelength on 40m, so it is also very usable there, and with higher efficiency. On 40m, the bandwidth was also considerably higher, with both cases' bandwidth roughly as predicted by the ARRL formulae.
My first QSO with this antenna was broadside, to an MFSK-16 station in Missouri. My transmit power was 25W, and we chatted for about an hour. The distance was ~340 miles, and the skip angle was approximately 55 degrees. Later testing over the next few days showed it to be quite capable of domestic contacts at all distances, from coast to coast, as well as within the skip zone at high angles (NVIS). I made contacts on both 40m and 75m SSB, running 500W without any signs of heating or temperature-related drift.
During the 2015 IARU contest, I used this loop as a dual-band antenna, for 40m and 80m, doing CW contacts at 500W+. The loop was oriented with the main lobes pointed NE/SW, and the feedpoint was adjusted for lowest SWR (1:1) on 40m. On both bands, the antenna made numerous contacts at all elevation angles. Once each band's propagation was fully formed, DX stations, NVIS stations, and everything in between arrived with similar signal levels. Working Europe and South America was done with amazing ease, even on 80m. The reception on both bands was exceptional, with generous signal levels.
The nulls appear to be limited to near-zero elevation angles. While the loop can greatly attenuate noise from nearby buildings when turned broadside to the source, it is still able to send and receive skywave signals along the same bearing. If the EZNEC model is anywhere near accurate, the loop should be able to do NVIS and other domestic contacts broadside, although DX signals perpendicular to the loop are probably too close to the null's elevation.
On that subject, it was surprising to me how far off-axis from the main lobes a station could still be worked. NE/SW contacts were not that big of a surprise, but some distant stations were worked with ease at angles exceeding 60 degrees from the main lobes. While the loop is certainly not a gain antenna, on the low bands, the ionosphere is doing most of the heavy-lifting for propagation, so gain doesn't seem to be an issue.
About that feedpoint adjustment... One issue with using an inductively-fed loop for multiple bands is that the 50-ohm feedpoint position for one band is not necessarily the 50-ohm feedpoint position for the others. This effect was more pronounced with the 80m loop than the others, as adjusting for 1:1 on one band meant almost 2:1 SWR on the other. For 2015 IARU, I decided to optimize, and run 1:1 on 40m, and 2:1 on 80m, so I would not have to readjust during the contest. This allowed me to switch back and forth quickly between bands, and it put the 2:1 SWR where it would cause the least coaxial feedline loss.
This brings up a slightly controversial point with respect to loops. It is often said that a loop cannot be used with a tuner. While it is true that a tuner should not be used to adjust a loop antenna, there is no reason why an otherwise resonant loop cannot have its impedance transformed to 50 ohms by a normal "L" or "pi" tuner, if the loop's resonant point is not 50 ohms. As with any other antenna, the tuner and feedline loss will be proportional to the feedline SWR, but at moderate levels, the losses can be kept negligible. See my notes on multiband operation, below for more details on how I do this with my own loops.
Because of the sharp bandwidth on 80m, large movements in frequency would require me to preadjust the tuning point using the controls in the AutoCap software. This wasn't a particular challenge, since it is easy to estimate the correct adjustment by tuning for maximum noise level. A panadapter view makes this procedure even easier, since you can move the noise peak visually, and with more precision. After that, the AutoCap software can do the fine-tuning on its own. The software can do large adjustments, too, but SWR above 2.0 will cause my amplifier to fault before the software can get the antenna tuned. One way to avoid this is to simply avoid large movements, and just work stations in frequency-order. Otherwise, it is only necessary to preadjust as needed to keep the gear happy for the second or two while the software gets the antenna centered up on the new frequency.
With these minor adjustments in the operation of the loop for 80m, it was easily used as a dual-band low-band loop for contesting. Considering that the next step up in antennas for these bands are 1/4-wavelength verticals (with 33' and 67' mast and radials, for 40m and 80m, respectively), a loop antenna with its base 5' above the ground, and its top at 15' is a good option for limited space, and has the benefit of working equally well for DX and domestic contests.
This loop completes the "contest band" set of loop antennas. In hindsight, if I were to set up a limited-space set of permanent outdoor loops, my goal would be to have two: the first would be the 80m loop described above, for use on 40m and 80m; the second would be a 1m (~3ft) diameter loop like the first one described at the top of this article, for the 20m through 10m bands. For now, I am planning to use this antenna for all of my 40m and 80m contesting, while continuing to use the hexbeam for the higher bands.
As the band conditions continue to slide into the solar cycle's "low-band years," I have come to the conclusion that the care and feeding for my hexbeam (and more importantly, the care and feeding of the support underneath it) might not be worth the amount of use I will be getting out of the antenna. As of summer 2016, we are already starting to see days on a regular basis where the MUF in the mid-US is between 20m and 15m. That makes most of the hexbeam quite useless.
I modeled a number of antennas to use for contesting for 20m only, and I realized that a slightly larger version of my existing 20m loop, with an improved mounting structure, would be the best option for me for a long-term installation. When built properly, it would have better low-angle gain than a vertical, but with an efficiency of nearly 95%. In fact, the gain on 20m at elevation angles of less than 10° is actually better than the hexbeam for all installation heights of the hex of less than about 33'. The optimium installation height of the loop is just under two loop diameters, putting the tip-top of the loop at around 15', which is much less of an installation project than a hexbeam at 33'+. So I started a second version of the 20m loop to replace the hexbeam until the next solar peak. This loop is still in progress, but there are a number of design changes that I thought would be worth sharing.
The first change I made for this loop was the support. In order to control the wind-induced torque of the "wings" of the antenna, I used a cross-shaped or plus-shaped PVC frame that supports the copper at four points. I replaced the threaded break-down coupling at the bottom of the loop with an O-ring-bearing union joint. This joint has two nice improvements over a simple threaded joint. First, the strength of the joint isn't on the threads, making it much stronger and resistant to breakage. Second, it is much wider, which forms a nice flange that can be used to hold guy ropes in place. The overall structure is 1.25" schedule 40 PVC, with a 1" piece of schedule 40 PVC telescoped into the vertical portion of the structure for added rigidity and strength.
The second change I made was to replace the tuning capacitor with an air-variable capacitor. This capacitor isn't a butterfly capacitor, but it is a differential capacitor from Palstar, with two stator halves, which I have connected to the inductor ring. Although still a split-stator like a butterfly, this cap has two advantages over a butterfly. First, it allows a larger range of C values for a given size of capacitor, while retaining the butterfly's advantage of not flowing current through wiper connections. Second, the differential cap does not have a uniform rate of change of the C value as the rotor turns. The value changes faster at low C values, and slower at high C values. This is an advantage because at high frequencies (low C), the bandwidth of the antenna is larger, so tuning rate isn't nearly as critical. At lower frequencies (high C values) the bandwidth of the antenna is lower, requiring a slower rate of C change to avoid overshooting the target value. When compared to a vacuum-variable capacitor, the air-variable cap is just aluminum plates, which should make it more durable of shock, and tolerant to temperature oscillations than the ceramic or glass of a vacuum variable. In fact, the air-variable is shaped like a large heatsink, so any heating that does occur should be easier to manage.
The third change is to use a CT-style feed, instead of a simple air-loop wire. I am using a few turns of wire on a large 43-material toroid core from Fair-Rite. The μ values for #43 at 20m were nearly identical to those of #31 and #44 material, so I chose #43, as it also tends to be the most available of the material types. With the loop at its optimal 15' height (10' mast underneath it), a 6:1 turns ratio provides 50 ohms at the feedpoint on 20m. When the antenna is on its 4' test stand mast, the best turns ratio is 4:1 on 20m, so the siting of the loop does have substantial effect on the feedpoint impedance.
Initial testing of the loop suggested that it would have performance on par with the ideal predicted using AA5TB's spreadsheet. The measured -3dB bandwidth was 50kHz at the end of 45' of RG-213, while the 2:1 SWR bandwidth was 35kHz. As an added benefit, the capacitor is large enough at the high end to allow operation on 30m and 40m, albeit with reduced efficiency. I recently used this antenna in the NAQP CW contest, where it performed as expected on 20m. The azimuth and elevation patterns achieved in practice seemed to match that predicted by the model, with peaks and nulls where they were expected. With long CQ runs at 100W, the #43 split-bead showed no signs of heating or stress-related SWR drift. Testing at QRO power levels showed a different result (see below).
I don't expect to need to weld the vanes of the air variable capacitor together to maintain good efficiency. There are two reasons for this. First, the loop already shows near-ideal Q and bandwidth for the conductor size and length used. Second, each bank of stator vanes on an air variable capacitor fed as a butterfly or split-stator can be connected to the inductor lead in either two or four places, since there are two rods holding the stack together. If two of these four points are connected, that means that the current flowing through any stack of spacers is half of what it would be with a single connection, and if all four points are connected, the current for each point is one quarter of the total current, because the current is fed into the stator stack in a distributed fashion. Some commercial capacitor designs add solid bus bars running from each post of each end of the stack to the corresponding post on the far end of the stack, for just this reason -- it keeps I2R losses down by feeding each stack in all four post locations. Similarly, I used copper strap to connect all four stator "corners" for each stator, as shown in the image at right.
One point of consideration with the joints between the vanes of the air variable capacitor is that of water intrusion. Weatherproofing for an outdoor antenna will be a must, to prevent water from seeping into the joints between the vanes if they are not welded together. Alternatively, the careful application of a silicone-based grease to seal these joints would seem to be a good idea. Otherwise, oxidation and/or corrosion may eventually compromise the joints slowly over time, increasing the losses between the plates.
Update: We ended up with warm weather sooner than I expected this year (February 2017), so I went out to test-stand this antenna again, for QRO testing. What I found was rather interesting.
First, the AT2KD capacitor from Palstar is a flop -- at least for QRO operation of an STL. When running anything over 150W CW on 20m, the capacitor arcs. Both the NEC model and ARRL formulas predicted a peak voltage far below the 5kV rating of this capacitor at the 150W level, and further, this capacitor should have been able to handle double that rating because the two stator halves were connected in series. The AT2KD showed great promise, because even in this configuration, it could resonate the antenna from 40m to 17m, but the voltage handling just isn't there for QRO operation. A 100W radio should work fine with this capacitor for 30m through 17m, but for the $150 price tag of this unit, I could have gotten a nice Soviet surplus capacitor with a 25kV rating, so the AT2KD is just not worth it.
That leads to the next experiment I did with this loop, which was to replace the AT2KD capacitor with a 25kV, 50pF Soviet surplus capacitor. This capacitor easily handled power levels up to 750W CW, which is the safe limit of my amplifier. It is actually a very nice device, and I wish I had bought two or three of these instead of just one. When running at these elevated power levels, however, the #43 core I used to couple at the feedpoint gets rather warm. It should be fine for a CW or even a RTTY contest, as the thermal drift is quite slow, even with continuous key-down. Nonetheless, heat dissapated in the ferrite is power that doesn't get radiated, so my next step will be to replace the ferrite transformer feed with a single-turn inductive feed, like I use on my other loop designs. AD5X ran into similar issues with ferrite-core QRO transformers while he was developing his now-famous base-loading matchbox for 43' vertical antennas. In the end, he also settled on a large air-core inductor instead of the compact ferrite-core design, for efficiency reasons.
Despite these challenges, the vacuum-variable capacitor increased the loop Q to the point that it is substantially higher than predicted by the ARRL formulas, when mounted in the clear, and outdoors. This implies that the losses in the antennare lower than predicted by the classical loop models. Even when I recompute the Q value, adjusting the conductor size to account for both the outside and inside conductor surfaces of the tubing, the measured Q is still higher (and the -3dB bandwidth lower) than the formulas predict.
So the Mark-7 was a useful experiment, to show me that my original choices for vacuum-variable capacitors, and single-turn open-air inductive feed were the optimal choices for QRO operation.
Notes on Multiband Operation
I tend to use my loops on single bands, but I have used a few on more than one band. It is easy enough, given sufficient funds, to buy or build a tuning capacitor that has a large enough range that it can resonate a given loop on any frequency across several HF bands. However, the radiation resistance will vary widely as you move from band to band, because the loop circumference is a very different fraction of a wavelength on one band than it is on another. This makes feeding the loop a challenge.
My experience has been that feeding a loop on one band for a 1:1, 50-ohm match, will result in around 1.5:1 match on the two adjacent bands, and a 2:1 match on the two adjacent bands beyond that. For example, if I adjust the Mark-7 loop so that it has a 1:1 match on 20m, the 30m match will show about 1.5:1, and the 40m match will show 2:1. Similarly, the 80m loop can be matched for 1:1 on either 40m or 80m, but once adjusted, the other band will be 2:1, with 60m showing about 1.5:1. I have often used my original 3' loop for both 20m and 15m, but when I move the feed loop to achieve 1:1 on either band, the other band will show about 1.5:1.
So what can a multiband loop user do?
You can adjust the feed loop (or change the number of turns on a CT-style feed) when you change bands, but this isn't terribly convenient. There are probably all kinds of clever ways to motorize the position of the feed loop, or use relays to adjust the number of primary taps on a CT, or to selectively switch in a hairpin matching inductor. And there is nothing wrong with any of these approaches.
There is also nothing wrong with using a common desktop tuner on an otherwise resonant loop. As long as the loop capacitor has been adjusted to cancel the reactive component of the feedpoint impedance, the loop is resonant. If the SWR presented at that point is still reasonable, perhaps 1.5:1 or 2:1, corresponding to a resonant impedance between 25+j0 and 100+j0, using a desktop tuner to pull the real portion of the impedance closer to 50 ohms is perfectly acceptable. The trick is to avoid using the tuner to trim a loop that is off-frequency, even by a small amount. A proper sequence should be something like this:
I have used this sequence for multiband operation of small loops, up to a 2:1 SWR reading at the desktop tuner, and it works very well, even at power levels in excess of 500W. Again, the main idea is that I only use the desktop tuner to do real-valued impedance transformation, with the loop capacitor performing all of the adjustment needed to change frequency within a single band. It is the loop capacitor that does all the work of presenting a real, resonant impedance to the feedline.
- Bypass the tuner, removing its reactive components from the feedline
- Adjust the loop antenna to be resonant on the current frequency; this means that the reactive part of the impedance is zero or as close as possible to zero.
NOTE: This might not be the point of minimum SWR for a 50-ohm system; the target impedance is the point where the loop reactance is zero.
- Put the tuner back in-line, so that the reactive components are connected to the feedline
- Adjust the tuner, or run its automatic tuning sequence, to bring the impedance presented to the transmitter to 50 ohms
- Operate as normal, by adjusting only the loop capacitor as operating frequency changes
- DO NOT ADJUST the desktop tuner until a band change; use the loop capacitor to do all the tuning within a band
- When changing bands, repeat the entire sequence from the top
Some work still needs to be done before I can just put these out in the yard and leave them as permanent installations.
An Improved Control System
- Security - Copper theft is all the rage these days. A yard full of copper loops sticking up in the air might be too much temptation for a thief to resist. Finding a way to prevent this may be tough, since the tubing would be easy to cut from the mast. Height is one tool, getting the loop up high enough in the air to make it difficult to reach. Another thought is to paint the copper with a flat enamel that is a dull gray or green color. That would make the antenna harder to see, as well as making it appear to be just another piece of plastic yard junk. A nice side-effect of painting the antennas with an appropriate paint is that it prevents the copper from tarnishing or oxidizing over time, which is particularly helpful with portable antennas like these, that are handled regularly for set-up and tear-down. Keeping the top layer of copper clean is important to maintain high efficiency.
- Weatherproofing - The capacitor needs to be covered and protected from rain, ice, dirt, debris, birds, insects, etc. Some kind of sealed plastic enclosure would probably be ideal, especially if the plastic is resistant to UV from the sun. The main reason I haven't done this yet is the number of protrusions that would need accommodation. The enclosure would need holes for the mast, the shaft, and the two inductor ends, at a minimum. The 80m loop used a PVC tube as a jacket around the motor and capacitor, and this seems to be a good first draft.
- Mast Alternatives - The PVC mast was cheap, simple and effective. However, not all PVC is made to endure the elements. PVC can deteriorate under UV exposure, not to mention the fact that continued flexing of the mast under wind loading will start to weaken it. Rebuilding the loops on a fiberglass mast would be much better, since fiberglass is also non-conductive, but is also tougher and more rigid. I will probably talk to MaxGain about some mast replacements in the future.
- Motor Stops - There needs to be a way to prevent the motor from running the capacitor shaft all the way to either of its physical limits. This could do some damage to the capacitor, but it is more likely to simply lock the rotor of the motor and damage it. For now, I'm just careful, and I use the Palstar analyzer to make sure the position of the capacitor is still well within its limits while tuning manually.
I have also done some work on an automated control system for these antennas, and that project is described on the AutoCap Software Page. That article is a continuation of this one, describing control system changes. The software-based controller allowed me to convert the loops to use stepper motors to move the capacitor shafts, and achieve some truly impressive tuning speeds.
That said, the simple DC motors described above are more than adequate for loop control, and are extremely easy to run remotely. The AutoCap software supports both types of motors, and satisfactory results can be had with either one. For the casual operator who likes to rag-chew, a simple gearhead motor with a DPDT switch at the control point makes the loop antenna easier to use than a typical tube amplifier.
Closing Thoughts - Possibly Controversial Ones
There are two aspects to loop performance that interest me. The first is receive rejection of certain kinds of interference, and the other is efficiency during transmit.
People who study EM theory point out that a loop antenna's pattern isn't all that "magentic" in a large portion of the near field. They also point out that in the far field, the propagated EM wave has a fixed ratio of E/H components, with the ratio being fixed by the impedance of free space. The latter argument is solid, but the former argument needs some context.
For transmission, the ratio of E/H is variable within the near field, with the ratio being a function of distance from the antenna. As the wave travels away from the antenna, the ratio approaches the fixed ratio that it will hold as it propagates through free space. The small loop antenna does have a mostly magnetic response, very close to the antenna during transmission. However, during transmission, the antenna is driving this field variation. As the current oscillates within the antenna conductor, it forms a strong magnetic field, and a very weak electric field, which generates a wave that transitions to a normal free-space E/H ratio in the far field.
However, during reception, the antenna isn't actively driving the E and H fields in the antenna's near field. EM waves that approach the antenna don't magically start to change their E/H ratio when they cross the imaginary two-wavelength surface surrounding the antenna's near field. These waves maintain their E/H ratio at a natural value, defined by the impedance of free space, until these waves actually strike the antenna, and start to generate a response. Since the loop conductor is essentially a large current propbe suspended in free space, the response of the antenna is driven by the magnetic field crossing the conductor, which induces a small current in the loop. So during reception, it is entirely possible that the antenna really does respond mostly to the magnetic component of an arriving wave.
More important still is the nature of the arriving wave. Remember that a small loop antenna is a high-Q resonant circuit. If an arriving signal is self-similar (i.e., the signal has a high autocorrelation value), wave after wave of energy strikes the antenna, each one adding to the circulating current building up in the loop, producing a signal at the receiver. If the signal isn't self-similar at RF, the amount of circulating current allowed to build within the antenna is limited, which limits the signal level at the receiver. Most ham transmissions (CW, SSB, RTTY, PSK, etc.) are highly autocorrelated, otherwise their spectral purity would be poor. Many pulse-like QRM sources (engine ignition noise, arcing powerline hardware), have poor autocorrelation because they are generated by individual sparks at a rate far less than the receiver's RF frequency. This may be another reason why loop builders report significant S/N ratio improvement from their loops, even when the offending noise source is well within the main lobe of the antenna, and not located in a null. The loop may indeed be less sensitive to some kinds of noise than other antenna types, depending on the autocorrelation value of the noise signal, and the Q of the loop used for reception. If the loop is particularly lossy, this might improve the situation even more, because the required amount of autocorrelation in an arriving signal would be even higher in order to produce a significant signal at the receiver. This "lossy improvement" is likely present even though the loss resistance tends to lower the Q of the antenna.
Another aspect of loop performance that I find curious is efficiency. There is some well-accepted classic theory that describes the efficiency of a small transmitting loop. That theory is documented in the ARRL Antenna Book, among other places. However, people like G3LHZ have done some interesting work trying to account for the losses claimed by the classic theory. Strangely, there are real-world thermodynamic experiments that do not seem to support the traditional loss calculations. For example, if a magnetic loop for 2MHz is constructed so that the classic calculation shows a 5% efficiency, and if we feed that antenna with a 100W carrier, we should be able to find 95W of energy (or something close to it) being dissipated as heat somewhere in the loop. Mr. Underhill's experiments using thermal cameras show this may not be the case. When he accounts for the detectable heat generated by the loop, his experiments suggest typical small-loop efficiencies to be on par with other classic antennas, such as dipoles and verticals. At the very least, they may be no worse than the loaded versions of these antenna types.
I have spent some time thinking about this discrepancy, and how to account for it within the typical ham home-made loop. This is not to say that I am asserting this as correct, but I suspect there are straightforward reasons why the efficiency of a small loop of typical construction could be better than the classic formulae predict.
One simple possibility has to do with construction. Many loop designs, mine included, use open-ended copper tubing for the radiating element. Mechanically, this means that the loop itself actually has two conductors, wired in parallel. One is the outside of the loop conductor, and one is the inside of the loop conductor. The reason for this is skin effect. Anybody who has run high power RF into a coaxial cable that is poorly matched to a balanced antenna is familiar with the "feedline radiation" effect, where the shield of the coaxial cable forms two conductors, with current flowing on both. In the loop case, The outer and inner surfaces of the loop conductor are connected together at the ends, so the two conductor shells carry current in parallel. Depending on the difference in diameter of the two surfaces, the effective increase in surface area can be almost 100%, roughly doubling the surface area of the main element. "But the inner conductor is shielded from the environment by the outer conductor," someone might object. This is true for the electrical field, but not the magnetic field, which just happens to be the largest component of the EM near-field created by this type of antenna. A small loop is driven almost completely by the magnetic field generated by the driven element, and the lines of magnetic flux cut both the inner and outer surfaces of the main (large) loop, inducing current flow into each one, independently, and the two are able to create a combined magnetic field around the antenna.
Many loop builders unknowingly depend on this two-surface behavior, because their designs utilize trombone-style capacitors. These capacitors are often fed current on their outside surface, but the outer "plate" of such a capacitor is actually the inside surface of the outer trombone tube.
If the tubular loop's effective surface area is nearly double that used in the calculations, because it has both an inner and outer surface, the current flowing in each surface is roughly half what is predicted for the loop conductor using the standard formulae. Since power lost in the resistance is proportional to the square of the current passing through the resistance (P = I2R), the heating loss in each surface of a tubular loop could be closer to 25% of that predicted by the model. The two surfaces together, then, have a combined heating effect that is 50% that predicted by the model for a wire of equivalent outer diameter. Put another way, the two surfaces in parallel form a net resistance that is half that for a solid wire with an outer diameter equal to that of the tube. This results in a power loss of one half the amount of a wire of the same outer diameter. This dual-surface feature alone is enough to explain a 3dB discrepancy between the model (which assumes a solid conductor) and an open-ended tubular loop antenna.
Another possibility that applies to loops of any construction has to do with the pattern of current flow on a loop antenna's main conductor. At its core, such a device is a capacitor and an inductor, connected back-to-back. You can think of it as a resonant circuit, where the capacitor and inductor are in series with the abstract "radiation resistance", which is the "load" presented to any antenna, allowing the RF current in the antenna to be transferred into free space.
We want the "radiation resistance" of any antenna to be much larger than the sum of all other losses. This is the heart of antenna efficiency calculations.
Power transferred into the antenna is going to be dissipated in one of two ways -- radiation into space, or heating of the antenna or its immediate surroundings. The copper loops and the metals in the capacitor contain the real resistive components of the antenna. If heating of the antenna is to occur, it must happen here. In addition to the intrinsic real resistance of the copper itself, we must again consider the skin effect, which effectively "thins" the copper conductors for the purposes of conducting RF current.
Copper conductors in a magnetic loop antenna are not simple conductors, however. Even when you factor in skin effect, there is still a component missing. All of the copper conductors in a small transmitting loop are part of one of two inductors. The small loop is a primary winding of a two-winding air-core transformer. The large loop is the secondary. The current flowing through these conductors are operating at varying amounts of phase angle from the voltage at any given point. Inductors delay current changes, capacitors delay voltage changes. Since all of the metal in the antenna is part of a reactive component, the power flowing in the entire loop is subject to voltage-current phase angle shift.
There are two points in the antenna where the phase angle between voltage and current will be zero. These points would be very difficult to locate physically, but they must exist. The large copper loop is an inductor along its entire length. The capacitor is a lumped reactive component, and its leads are, for all practical purposes, part of the inductor. As current circulates in the loop, the current will experience the highest inductive VAR (volts-amps-reactive, or "reactive" power) value at the bottom of the loop, furthest from the capacitor. The highest capacitive VAR value will be within the capacitor itself. Somewhere along the conductive path between each capacitor plate and the bottom of the loop, the capacitive phase angle will cancel the inductive phase angle, and all of the power at that point will be real (i.e., the impedance is completely real, and has no complex components). Remember these points for the moment.
Heat in a circuit is generated as current passes through real resistance. The reactive components of a resistor do not add to the heat generated. Put another way, current cannot do work (including generating heat) unless a voltage potential is also present. The amount of work that can be done is inversely proportional to the phase angle between the voltage and current. This is the whole idea behind power factor -- the voltage and current must overlap to some level to do work. Power companies rely on this principle, and enforce it vigorously in their customer contracts. So heating of any AC circuit component is directly related to the phase angle of the voltage and current within that component.
Now back to the loop. Remember that there are two "loads" within our antenna. The first is the radiation resistance of the antenna, which is its ability to transfer RF current into radio waves in free space. The second load is the loss inherent within the antenna. Remember also that there are two points in the antenna where voltage and current are in-phase. These are the points where the RF energy is able to do real work and heat the antenna conductors. As we move away from these points, there is some amount of phase angle between voltage and current. This angle diminishes the ability of the RF energy to heat the conductors where the angle is not zero. The closer the angle is to 90°, the less heating can occur. By restricting the zero-VAR area of the antenna to two points, and to a lesser extent, the regions immediately around those points, the resistive losses of the antenna are concentrated around those two points. Despite the fact that RF current flows at high levels throughout the antenna, these two points and their immediate surroundings become the focus for resistive losses.
However, remember that there is a second load in the circuit: the radiation resistance. We can't pin a location on this load, but its value is still part of the efficiency equation. If we rethink the loop, and realize that the heating losses don't occur throughout the entire conductor length, but are instead centered at two points in the loop, that realization leads us to the conclusion that the current theory for small transmitting loops is grossly overestimating the contribution of I2R losses contributing to the efficiency calculation. This would go a long way to explain Mr. Underhill's experimental results. The ratio of RF energy being dissipated by the radiation resistance to that of the RF energy being dissipated by the resistive losses of the conductors is likely much higher than predicted by the classic theory. I am increasingly convinced that this is due to the reactive nature of the antenna components, as described above.
If we assume that this is correct, then how might this influence the design and construction of loop antennas? How could we squeeze the highest efficiency out of an antenna if we are correct?
A key improvement would be to focus on the two points of minimum phase angle, and minimize the real resistance of the conductor found there. To do this would require being able to calculate these locations. Given a value for the capacitor, and a length of the attached inductor (that included the leads and plates inside the capacitor itself), it should be possible to estimate their location. Given that the capacitor is a lumped value, and the inductor's reactance is distributed over a relatively large length, it is entirely possible that most real heating occurs close to the capacitor body, possibly within the jumpers between the capacitor leads and the main inductor body. This may explain why heating in G3LHZ's loops appeared to be rather uniform within the inductor body. The maximum heating may have been taking place at spot locations on the capacitor jumpers. Since we tend to expect these connections to be "weak spots" anyway, the extra heating there and its cause may have been overlooked.
It is also possible that the heating effect of loop antennas is just not sufficient to make it necessary to find the two main heating points. Even at these two points, the radiation resistance may sufficiently trump the real losses that the real losses are insignificant. This idea is also supported by the experimentally determined efficiencies of Mr. Underhill's loops.
Devising experiments that would support or discredit these ideas is difficult. However, the current experimental evidence has made me curious, and will continue to encourage me to experiment with these antennas.