For a general introduction to Small Transmitting Loop antennas (STL, a.k.a. "Magnetic Loops"), incl. coupling methods, please see my 80-20 STL page.
- [Bending a copper tube loop]
- [Initial measurements - without capacitor]
- [Tuning capacitor]
- [General construction]
- [Coupling loop]
- [Motor drive for the tuning capacitor]
- [Initial measurements - with capacitor]
- [Linear actuator for coupling loop]
- [Comparison vs. 1-turn loop]
- [Antenna simulation / modeling]
Latest page update: 16 January 2022
©2021-2022 F. Dörenberg, unless stated otherwise. All rights reserved worldwide. No part of this publication may be used without permission from the author.
I started this page in July of 2021 and hope to finish it by
My motivation for adding this page. My 1-turn loop antenna (ca. 2 m diameter ) actually works quite well. Though electrically small, it is physically large (compared to my own size). It is also quite heavy, and therefore awkward to handle. To maximize performance in the direction that I am interested in, I have to lift the antenna above the roof line with the telescopic mast on my terrace. I cannot leave this antenna permanently installed on the mast. Installing the antenna requires me to get up on a step ladder and maneuver the antenna. On several occasions, I have almost fallen of the ladder, or of my pergola, with the antenna! This antenna also has a significant wind load.
A 2-turn antenna with the same total conductor length, would be significantly smaller, and easier to handle. However... conventional antenna theory implies that a loop's radiation resistance (simply put: the part of the loop impedance that radiates rather than dissipates) is proportional to the square of the surface area that is enclosed by the loop - independent of the actual shape. Going from a 1-turn to a 2-turn loop with the same "copper length" would reduce the radiation resistance by a factor of four. So, the already very small radiation resistance (several dozen milliohms) would become even smaller. At the same time, the loss resistance would actually increase due to coupling between the two turns and "more copper near ground". Combined, this would significantly reduce the loop's efficiency, and therefore the performance.
The conventional formula for "radiation resistance" (Rrad) includes a factor N2, where N is the loop turns number. Suggesting 4x increase of Rrad for N = 2. However, two turns with same total radiator length --> diameter D is halved, which - via the term D4 - implies a reduction of Rrad by a factor of 16, or an overal reduction of Rrad by a factor of 16 / 4 = 4.
Vs. increased losses, e.g., due to proximity of the loop turns?
How / to what extent is main loops self-inductance affected by N (conventional N2 formula does not take into account all sorts of effects such as proximity between adjacent turns and RF frequency - use the "RF Inductance Calculator" by ON4AA for my N=1 and N=2 loops at 80-40-30). Implication for capacitor size? Confirmed by measurement? Can the current around the two loop turns still be considered constant, as in same-inductor-length STL? Q and voltage across the capacitor? For lossless loop, Q = SQRT(L/C) / Rrad --> if L 4x larger (not realistic per ON4AA calculator), hence C 4x smaller (TBC) for a partuclar fres, and Rrad 4x smaller, then Q increases 32x --> BW 32x smaller????
This is quite discouraging for conventionally minded people. It is also consistent with one of the most important fundamental laws of nature: Conservation of Misery!
Nonetheless, I would like to be able to weigh the actual reduction in performance against the improvement in compactness, weight, wind load! I am primarily interested in "DX" performance, not NVIS and local ragchew. An extensive web etc. search on this topic basically came up with not much practical evidence, in particular no side-by-side comparisons of actual antennas. Also, a 2-turn loop should be less expensive: it has a higher self-inductance, which should require a smaller (in terms of pF, size, weight, cost) vacuum capacitor for tuning down to 80m.
This is why I am going through the trouble of building and testing a 2-turn loop - without cannibalizing my 1-turn loop. So I can make comparative performance measurements. Construction and test results are / will be documented on this page.
Fig. 1: This is what it is about: my 1-turn and 2-turn loop antennas side by side - with myself as size reference
(I am about 1.8m = 5 ft 9 inch tall)
The bottom line conclusion of my build-and-compare efforts is quite positive. It reminds me of the more than 100 years old encouraging saying: "That may work in practice, but not in theory!". But getting to that point has not been a smooth path...
BENDING COPPER TUBING INTO A 2-TURN LOOP
Let's jump straight into te construction. A couple of years ago, I bought a standard 20 feet "copper coil" at a large Do-It-Yourself store - for a future project. Total length 20 ft = 6.1 m. I used another such coil for my 1-turn loop. The tubing has an inner diameter (ID) of 1/2 inch (12.5 mm) and an OD of 5/8 inch (16 mm). It weighs 5.75 lbs (2.6 kg). It is made of soft copper. This is also called "annealed" tubing, as it is heat-treated after the tubing is drawn in the factory. This relaxes the stress that is caused by the tube-drawing process. This is very important. You can almost bend soft copper tubing by hand, if it has a reasonably small OD. For hard-drawn copper, you need a heavy manual pipe bender, or - for a clean job - a professional hydraulic bender.
To make a nice, round loop without professional bending tools, you need a bending jig. It has to be somewhat smaller than the specific loop diameter that you want. I reserved 6 inch (15 cm) at each end of the 20 ft tubing, for a bent 90° connection to my tuning capacitor. This leaves 19 ft (5.8 m) for the actual loop, or 9½ ft (2.9 m) per loop turn. I.e., a loop with an inner diameter of about 3 ft (92 cm). Upon bending, tubing tends to spring back a little, so I designed my jig for an inner diameter that is about 2 inches (5 cm) smaller than that.
Note: if your copper tubing is new and nice & shiny, and you want to keep it that way (at least for a while): don't touch it with your bare hands (I use very thin touchscreen / smartphone gloves)! Otherwise the copper will get tarnished very quickly. Contrary to popular belief in some circles, this does not affect performance of a loop below VHF frequencies, as long as the contact surfaces between the loop and the tuning capacitor are corrosion-free. See here.
The photo below shows the tools that I used to make my wooden jig. At the far right in the photo is a standard "manual rotary draw bender" (F: "cintreuse de tuyau", "pince à cintrer", D: "Rohrbieger"). It has a so-called "die" that matches the outside diameter of the tubing or pipe - 16 mm in my case. As stated above, I will bend the ends of the tubing 90°. I want nice bends with a relatively small radius. This can only be done cleanly with a pipe bender. It clamps the straight tubing against a concave bender-die, and pulls the tubing around the die - while maintaining a constant tube diameter. I.e., without collapsing or wrinkling the tube. You cannot do this by simply pulling the tube around a small round shape small by hand!
Fig. 1: The basic tools I used to make my jig (variable speed power drill, jigsaw, vise-grip clamps) and a "household" pipe bender
I made the loop bending jig with pieces of scrap wood that was left over from a project around the house. The jig must have a "channel" that holds the tubing. My tubing has an OD of 16 mm, so I used 18 mm thick particle board. The pieces are fixed together with about two dozen 5x35 mm self-tapping drywall screws ( = self-drilling plasterboard screws). Note that the screw length is just less than twice the board thickness, so the screws will not poke out the bottom of the jig base plate, and damage whatever is underneath (such as the table).
Fig. 2: Pieces of the wooden bending jig (left) and the assembled jig (right)
Fig. 3: The jig is clamped onto a heavy table
Jigs and benders are normally used with straight tubing or pipe. My copper tubing was rolled up into a small tight coil - yes, much easier to transport than 20 ft / 6m straight tubing! The ends of such coils are normally straight - which is good - because the coil was made of straight tubing. I first carefully uncoiled about 1½-2 ft (≈50 cm) of the coil. It doesn't have to be straight - just straighter than the curvature of the jig!
Fig. 4: The 16 mm wide starting end of the jig (left) and the "groove" (channel) that holds down the tubing while pulling it around
The straight(ened) end of the tubing is inserted into the starting end of the wooden jig (from the top-left in the left-hand photo in Fig. 4 above), until about 6 inch (15 cm) sticks out. This piece will later be bent 90° to attach the capacitor. The uncoiled part of the tubing is then pulled completely into the channel of the jig, all the way around the entire jig. Then, the now curved part of the tubing is loosened a bit from the jig channel, and pulled through the feed-end of the jig. Then, the next section of tubing is carefully straightened a bit, and pulled all the way into the entire curved jig channel. This is repeated until the entire coil has been reshaped. The resulting loop looks quite nice, see Fig. 5 below. It would have been entirely impossible to make it this round without a jig (or paying a professional machine shop too much money to do the work for me). Bending the 90° turns at the ends of the loop did require some fiddling, and learning how to set up the pipe bender for making the bend at the right spot.
Fig. 5: The soft copper coil - reshaped into a 2-turn loop with bent ends
INITIAL MEASUREMENTS - WITHOUT THE TUNING CAPACITOR
Fig. 6: My 2-turn loop without the tuning capacitor, suspended for measurements
Before making the attachment brackets for the vacuum capacitor, I was anxious to take some simple measurements with my miniVNA antenna analyzer. In particular the self-resonance frequency. Without the tuning capacitor, this is inherently the highest possible fundamental (i.e., non-harmonic) resonance frequency that can be obtained with this loop - at the specific installation location and height. Adding a tuning capacitor will always result in a lower resonance frequency: the capacitor has a non-zero minimum capacitance - at least several pF - and mounting it onto the loop-ends probably also adds some stray/parasitic capacitance.
I did not change the pitch of the loop turns from when it came out of the jig: about 3-4 inch (8-10 cm). Note: coil "pitch" is normally defined as the on-center distance between two adjacent conductor turns. However, sometimes the separation distance between two adjacent conductor turns is meant. This is not always explicitly stated in coil inductance calculators and in antenna simulation tools that support definition of a helix.
Fig. 7: Coil dimension parameters, including "pitch"
I used simple unshielded coupling loops, like the one I use with my 1-turn loop antenna - which has with the same overall circumference as this 2-turn loop. Coupling loop #1 had a circumference of 123 cm (4.4 ft), i.e., a diameter of 39 cm (1.28 ft). Coupling loop #2 was slightly smaller: circumference of 100 cm (3.4 ft), i.e., a diameter of 32 cm (1.04 ft). These experimental coupling loops were made of stiff solid household installation wire, mounted directly onto the BNC connector of the antenna analyzer - no coax. In both cases, the self-resonance frequency was around 17950 kHz. The coupling loops were suspended between the two turns of the main loop, see Fig. 6 above. Their position could easily be adjusted for a minimum SWR of 1.14, which is excellent. With the smaller coupling loop, this best SWR was obtained with the coupling loop coplanar with the main loop. The larger loop had to be rotated about 45° out of the plane of the main loop. This means that it is a bit too large.
My 1-turn loop also has a circumference of 20 ft (6.1 m), i.e., a diameter of 6.37 ft (194 cm). A standard 1/5 size coupling loop would have a diameter of 1.2 ft (37 cm). My simple measurement shows that the coupling loop of a 2-turn loop should basically have the same size as a standard size coupling loop of a 1-turn loop with the same overall circumference.
What is the optimal pitch of a 2-turn loop, or a multi-turn loop in general? I have not been able to find any theoretical basis in available literature. In the few documented implementations that I have come across, the pitch is based on "size of standard tube-clamping spacers", "visually pleasing proportions of the pitch vs. the loop diameter", "at least 5x conductor diameter" (which would be 5x16 mm = 8 cm in my case), and 7.5x conductor diameter (ref. 1A). Of course, a multi-turn loop is just a single-layer cylindrical solenoid air-core inductor. And "optimal" has to be defined first. Factors: stray capacitance (primarily between adjacent turns), proximity effects, loss...
Expecting loop inductance to be at least 2x that of my "same circumference" 1-turn loop --> need only half the tuning capa range of --> 5-250 pF. So, I acquired one. It is about half the size of the big "bottle" of my 1-turn loop, and 1/3 the weight of the latter:
Fig. 7: My vacuum capacitors: (top) 10-500 pF, 10 kV, 36 revs, 2.2 kg; (bottom) 5-250 pF, 5 kV, 24 revs, 0.73 kg
Fig. 8: Capacitance vs. shaft revs of my 10-500 pf / 10 kV and 5-250 pF / 5 kV vacuum capacitor
Curve is perfectly linear between min & max capacitance; remember that resonance frequency of an LC-circuit (such as loop + tuning capacitor) is proportional to the reciprocal of the square root of the capacitance. So, the resonance freq does not vary linearly with the capa revs! The capacitor shaft can make 24 revs, but the capacitance effectively only changes over 15 revs. So, the motor drive for this capacitor should also be able to make at least 15 revs.
Copper tape mounting brackets. For connecting the cylindrical ends/electrodes of the vacuum capa to the ends of the copper tube loop - same approach that I used for my 1-turn 80-20 STL (link; Fig. 75, 76.).
Diameter of vacuum cap ends/electrodes: 52 mm -- > circumf 163 mm, add ca. 2 cm at each end for taps --> need 20 cm (8 inch) strips. Soft Cu strips: 200x15x0.8 mm. They are a tad thin, would have preferred 1.0 mm, as for my large vacuum cap. 2x2 rectangular steel washers ["stretchers"], customized (18x15x2, offset hole --> 2 hole-to-edge choices, cut out of a 2 mm thick flat bracket from the junkbox ). 2x stainless steel bolt 6x20 mm, with hexhead for adjustable or socket wrench, + 2x stainless lock nut
Fig. 9: Capacitor mounting brackets - drilled & preshaped strips + rectangular washers, M6 bolts, M6 lock nuts
For pinching the ends of the loop, I use locking pliers (trade names include Vise-Grip™ and Mole-Grip™) because you can exert very large force with them. Drilling 6 mm holes, deburr, ensure completely flat (smoothing/filing if necessary).
The inside of the copper brackets and the pinched ends of the copper loop must be cleaned until they are shiny. I either use standard household copper/brass cleaning cream and a cloth, or - what I actually prefer - a small piece of kitchen scrub sponge and some.... toothpaste! Then rinse thoroughly. Sometimes I also boil them in water for a couple of minutes. Once the surfaces are clean: no more touching the inside surface of the brackets! I clean the silver-plated electrodes of the vacuum capacitor with standard household silver polish (you may have to repeat this several times to get all the oxide off), then thoroughly clean with a sponge and water. Again, do not touch the cleaned electrode surfaces anymore!
Made 4 spacers. Copper diameter 16 mm, used some 20 mm diam OD PVC conduit, left over from another project. Number of spacers is to be minimized, to minimize inter-turn effects / Q during high humidity, rain, etc.; already have 2 spacers: the vacuum cap and the attachment to the PVC mast. Used standard tie-wraps - black ones, because white ones do not last very long in sunlight.
Spacers are dimensioned for 8 cm = 5x diameter of the Cu tubing. Why?
Components / material for the mast & loop support:
- Mast (that slides onto my heavy umbrella stand and onto the mast insert of my telescopic mast): standard PVC tubing, 63 mm OD, length 125 cm (loop diameter + 30 cm)
- Loop support "gallows": thick-wall PVC tubing, USA type "Schedule 40 - above ground / underground non-metallic conduit" (0.84 inch OD (21.5 mm) and 0.622 inch ID (5.8 mm), length 1 ft (30 cm).
- Due to its 3 mm wall thickness, this tubing is very stiff - which is exactly what I want for suspending the loop on the side of the mast.
- With the capacitor at the bottom, the copper tubing at the top of the loop is at 1/2 and 1-1/2 x inter-turn spacing + 1 tube diameter from the mast. Add mast diameter + a couple of cm --> support tube length has to be > mast OD + 2x Cu tubing OD + 1-1/2 inter-tube spacing = 63 + 2x16 + (3/2)x80 = 215 mm --> 25 cm incl. some margin.
- PVC tube clamps, 3 for clamping the loop to the "gallows" and to the mast.
- I use standard clamps intended for 14/15 mm OD tubing. They fit very snugly onto the 16 mm OD copper tubing of my loop.
- The clamps have an integrated M6 nut, so I need two M6x30 bolts + 6 mm lock washers for attaching two clamps to the "gallows", and one M6x80 bolts + lock washer for the attaching the bottom of the loop to the mast.
- Inter-turn spacers (at least 2, distributed around the loop)
- Thin wall PVC tubing, 20 mm OD, length: 4 inch (10 cm) each
- Black tie-wraps (white ones are not UV-resistant and become brittle very quickly outdoors), 2 per spacer
Fig. X: Top end of the PVC mast with PVC support "gallows" for the loop
Fig. X: Tube clamps + lock washers + bolts
Fig. X: The 2-turn loop attached to the support
Choice: clamps upward on top or downward below the PVC "gallows" ???
Mast: my standard (fits snugly on my umbrella stand and the custom insert of my telescopic mast.
The on-center spacing of the capacitor electrodes is 10 cm (2 inch). So, I decided to go with a 5 cm (2 inch) pitch. Two clamps at the top, capacitor across the tube ends --> decided to add two spacers
THE COUPLING LOOP
Standard coupling loop has appr. 1/5 the diam of the main loop, some use 1/6. But what is the standard for a 2-urn loop? 1/5 or 1/6 of the diameter that i shalf that of the 1-turn loop)? To be able to quickly explore various CL diameters, I got a couple of 1 m sections of thin straight brass tubing at the local do-it-yourself store. 4mm OD 3 mm ID. "female-BNC to banana plugs" adapter, ca 10 cm section of ca 23 mm diam broomstick – to place the CL between the 2 turns of the main loop, PVC clamp for standard 63 mm OD PVC tube (like I use as my mast). Note: the brass tube ID is 3.0 mm, the tip of the banana jacks has 3.1 mm OD; I increased the tubing ID to 3.1 mm by carefully drilling with a 3.1 mm drill. The jack tips can then be inserted a coupel of m into the tubing and soldered. This is rigid enough for experimenta purposes. I made 4 exchangable brass loops with 16, 19, 24, and 31 cm diameter (compared to the 95 cm diameter of the 2-turn loop and ca. 195 cm diam of my 1-turn loop). Note: the . BNC adapter rigidly fixed to the broomstick stub with two cable ties. Note: for the CL, contact/loss resistance (e.g., between the between the banana plugs of the BNC adapter and the banana jacks soldered to the brass tubing) is not critical (compared to losses in the main loop).
Fig. X: Experimental CLs
Fig. X: Experimental CLs
Which one did I select? Ca. 1/5 of the loop diameter, "best" = SWR close to 1 possible and not too finicky; general: must be placed within the volume of the turns.
I used the the banana plug and BNC-adapter approach for the final version of an easily-removable coupling loop. A "bird house" made of pieces of PVC L-profile provides weather protection. A small insert made of three sandwiched-and-glued pieces of PVC closes the slit on the mast side of the birdhouse.
Fig. X: The
The optimum position of the coupling loop is sensitive to installation height. I need the flexibility of using the antenna at different positions on my terrace and above my telescopic mast. Absolutely need motorization of the coupling loop. See this section.
I also tried a ferrite ring transformer coupling, instead of a coupling loop. Ferrite ring: FT-240-31, i.e., OD = 2.4 inch (6.1 cm), made of "31" material. With the loop in my umbrella stand on the terrace, the loop bottom about 1 m above the terrace floor, rthe ing installed half way around the loop, i.e., between the loop end, exactly between the capcitor connections ( = equivalent to the neutral point, opposite the tuning capacitor of the 1-turn loop), standard 1.5 mm2 solid copper household installation wire with PVC insulation (European type H07V-U). With 17 wire turns, evenly spread around the ring, I got SWR = 1.53 around 3590 kHz and SWR = 1.03 around 7080 kHz. With 19 turns, I got and SWR = 1.53 and 1.23, respectively. With 21 turns, I got SWR = 1.1 and 1.47, respectively. So: no single number of turns to cover both bands. The required number of turns is sensitive to loop installation hight / position. Note that this is very similar to the results obtained for my large 1-turn loop with ferrite ring transformers: only useable over a frequency range of about 750 kHz, i.e., for single band operation. See here. To cover the 80 & 40 m bands for experimental purposes (at least the portions of those bands that I am interested in), I put 17 + 4 wire turns on the ferrite ring, and used a simple household terminal block to select the 17 vs. 21 turns:
Fig. ##: Selecting 17 vs. 21 wire turns with a terminal block and a BNC adapter
(shown with 17 + 4 = 21 turns connected to the BNC adapter)
MOTOR DRIVE FOR THE CAPACITOR
Drive folded back, parallel to longitudinal axis of varicap; more compact than fully in-line, as I built for my 1-turn 80-20 loop.
Diagram. Design / parts list. Slide(r) potentiometer with linear taper instead of 10-turn potentiometer - no need for motor gearbox with 2 output shafts. Retain POM isolation shaft. End-stop protection (though the capa may be able to handle the motor torque at the ends of its travel).
- Motor: 12 volt DC, with integrated down-gearing to 20 rpm, Ø 6 mm output shaft, torque rating not specified.
- The 20 rpm speed is the unloaded speed for a 12 VDC supply. I use a standard "amateur radio" commercial power supply, so it outputs 13.8 VDC. This increases the unloaded motor speed to 24 rpm.
- My varicap has a 24 revs range, of which 15 revs actually change the capacitance, see Fig. 9 above. I would like traversing the 15 rev effective range to take about 45-60 sec. Based on this, I decided to go with a 15:20 down-gearing ratio between motor and capacitor.
- Choice of drive speed (motor + down gearing): effective capa rev range (see Fig) + cover that range in about 1 min.
- Note: the output shaft of this motor is not centered on the round surface of the gearing (see Fig. XX). This makes it a bit awkward to install the motor on an L-bracket such that the shaft is aligned with lead-screw. To adjust the height of the shaft, either the height of the bracket has to be changed, or the motor housing has to be rotated. This is a bit of a hassle. With a centered shaft, only the height of the mounting holes has to be adjusted straight up or down.
- Backlash is "play" when changing direction. This undesirable in high-precision positioning systems. I have measured a backlash of 4° shaft rotation at the output shaft of the gear box. The gear box has a very large gearing ratio, to get down from several 1000 rpm to 20 rpm. This requires a multi-stage gear box, and each gear stage adds backlash. Only very expensive gear boxes have anti-backlash (ABL) gearing, which is beyond the typical amateur radio budget.
- Isolation shaft between motor and capacitor not needed if using a timing belt between the two gear pulleys that does not have embedded steel reinforcement cords (Kevlar is OK; polyurethane belts usually have steel, which will lead to arcing with high voltage across the tuning capacitor, see Fig. 100 on the 80-20 page).
- Flexible shaft coupler, 6 mm / 8 mm bores, 19x25 mm LxD; connects motor shaft to isolation shaft. Of course, a ceramic shaft works fine too.
- Isolation shaft, Ø 8 mm POM (acetal, polyoxymethylene; this is very strong polymeric resin with trade names such as Delrin, Celcon, Duracon), xxx cm long. has a high dielectric strength. A 20 mm long piece of clean, smooth, dry POM should easily provide well over 10 kV isolation.
- Flexible shaft coupler, 8 mm / 8 mm bores, 19x25 mm LxD; connects isolation shaft to lead screw
- Lead screw assembly:
- Lead screw: stainless steel, Ø 8 mm, 2 mm pitch, length: standard 200 mm (8 inch), reduced to 115 mm (≈ 4.5 inch); eBay "linear lead rod shaft".
- Brass lead-screw nut (typ. comes packaged with the lead-screw)
- The flange of the nut has four non-threaded holes. I threaded the holes with an M4 tap
- M4 screws, for fixing flange of leads-screw nut to the slider block.
- Two pillow-block ball bearings with Ø 8 mm bore, to support the lead screw.
- Spacers (for raising pillow blocks, if necessary) - TBC
- Slider block (PPE, 45x30 mm WxH; width the same as the length of the OD of the lead screw bushing), to be mounted onto the lead screw bushing.
- Hole for bushing not drilled until after confirming final height of the pillow-blocks and, hence, of the lead screw
- ACTUALLY: Some (1-2 mm max) extra height below the holes, bottom of the block to be adjusted with rasp & file for low-friction slide without creating a gap that adds any significant rotational backlash/play of the lead screw.
- Two micro-switches, to detect reaching the end of the travel of the slider block. The micro-switches must be "single pole, double throw" (SPDT) types. I.e., with three contacts: common, "normally open" (NO), and "normally closed" (NC). The switches are not only used to interrupt power to the motor, but also to enable changing the motor direction away from the end-stop (which is rather practical).
- Two general-purpose diodes, used in combination with the micro-switches, to enable changing motor direction after reaching an end-stop. They should have sufficient forward-current capability to handle the max motor current (1 Amp in this case). I use 1N4007 diodes, as I have plenty of those in my junk box.
- Additional 15:20 down-gearing of the 20 rpm nominal motor speed to 15 rpm at the capacitor shaft (yes, I could have used a 15 or 10 rpm motor and 1:1 gearing).
- Gear (pulley), aluminium, 8 mm Ø bore, 24 mm OD, 15 teeth, 0.2 inch pitch (5.08 mm), 11 mm between the flanges. To be mounted on the 8 mm Ø lead screw.
- Gear (pulley), aluminium, 10 mm Ø bore, 20 teeth, 0.2 inch pitch (5.08 mm), 11 mm between the flanges; 45 gram (1.6 oz). To be mounted on the 10 mm Ø shaft of the capacitor.
- After arc damage & large freq shift & Q reduction: got polycarbonate timing pulleys (15T, 30T) with aluminum insert. Solved the problem???
- Timing belt (a.k.a. toothed belt, synchronous belt),10 mm width, 0.2 inch pitch (5.08 mm), 41 teeth, i.e., "82 XL".
- My measurements suggested I needed either a 40 of a 41 teeth belt. A slightly long belt could be accommodated by the height of the varicap support cradles (see next item). A slightly short belt would not work. The 41 teeth belt turned out to be perfect.
- Use a belt that does not have embedded steel reinforcement cords - Kevlar and fiberglass! Many polyurethane belts have steel cords, which will lead to arcing when high voltage across the tuning capacitor occurs (i.e., at the antenna's resonance frequency), see Fig. 100 on the 80-20 page.
- change 15:20 --> 15:30 gear ratio = factor 1.5 change --> capa drive speed & range reduced by factor 1.5 (easier precis tuning) but freq range by factor SQRT(1.5) = 1.22 from 3.5-11 MHz --> 3.5-9 MHz --> antenna from “ 80-30” to “80-40”.
- Two support cradles for the capacitor. I made them out of a piece of PPE. See Fig. ??? below.
- I used a Ø 55 mm hole saw - slightly smaller than the 58 mm diameter of the capacitor's black end-cups of my capacitor's glass cylinder. Next, I used a large so-called "half-round" rasp, to increase the hole diameter to a tight fit on the end-cups. Then I cut the PPE piece in half, to get two cradles. Final adjustment of the cradle height was made after selecting the length of the timing belt.
- Note: do not use a hole saw at high rpm with PPE - it melts the PPE, which fills the cut back in, and makes the saw appear "dull".
- Mounting plate: 250x100x11 mm PPE material (polyphenylene ether, a stiff polymer "plastic"), cut out of an inexpensive PPE kitchen cutting board.
- Two tie-wraps, black (white ones are not UV resistant!), width x length ????. For fixing capacitor to the support cradles.
- Ethernet chassis connector, for the ethernet cable to the remote control box.
- Slide(r) potentiometer (for position feedback to the remote-control box), must have a linear taper - i.e., absolutely not a logarithmic "audio" taper !!!)
- The lever must have a sliding range/travel of at least that of the lead screw nut for the effective rev range of the capacitor. In my case: 2 mm pitch x 16 revs x 15:20 down-gearing + width of the sliding block (??? + width of nut flange?) + margin = 43 mm + ???? = 1.7 ??? inch, plus margin. I used a mono ALPS brand model with 60 mm travel.
- Resistance: at least 10 kΩ. The one that I use is 20 kΩ.
- I soldered small copper L-brackets to the ends of the potmeter housing, to be able to mount the potmeter onto the base plate with countersunk M3 screws.
- Note: the potmeter that I got, has a small bump on one of the long sides, to mark the center-detent position of the lever. This side of the potmeter has to be "up", otherwise the potmeter cannot lie flat on the base plate. Of course, the small copper brackets have to be oriented accordingly.
- In the 36 revs motor drive of my 1-turn 80-20 STL, I used a 10-turn rotary potentiometer. This required a motor with 2 output shafts and additional gearing. Here, I used the alternative: attaching the lever of a slide potentiometer directly to the lead-screw nut slider block.
Fig. X: Mechanical components of the motor drive
(the actual belt used has more teeth; slider block not shown; micro-switches & diodes not shown, aluminum L-bracket to be adapted to motor)
I do not have a workshop with bench tools. OK, I have a bench vise, but no drill press, bench saw or table saw, ... - only hand tools: electric hand drill, a thin-blade Japanese-style "pull" hand saw (which makes much more accurate & straight cuts than any EU/US "push" saw), a rasp and a file, a thread tapping set, an L-shaped straightedge, and a sliding vernier caliper. Be careful when countersinking a hole in a PPE plate with an electric hand drill instead of a drill press: the drill will tend to suddenly "grab" (especially if the drill bit is still new & sharp) and drill completely through the PPE before you know what is happening!
Fig. X: The pre-drilled PPE sliding block, brass lead-screw nut, and M4 screws
(note: the narrow side in the far right image has a hole for the lever of the slide potentiometer)
PPE, 10 mm hole for the bushing part of the brass lead-screw nut; countersunk holes for two M4 screws, and a hole in one side - for the lever of the slide potentiometer.
Fig. X: Both sides of the base plate - before installing the parts
Fig. X: The cradles for the vacuum capacitor - made of PPE
(the hole is cut with a hole saw and electric drill, height of the cradle is adjusted for belt length, mounting holes are threaded with an M5 tap)
PIX: top & bottom view of populated base plate + 1 image with detail views vs. two full angle views. HOOKUP CONTROL ETHERNET CABLE
The complete drive unit - without the weather protection hood - weighs 1.5 kg (≈ 3.3 lbs). About half of this is the capacitor. After final adjustments, the drive has a range of 24 lead-screw revs between the end-stop switches. I.e., 24 x (15 / 20) = 18 capacitor shaft revs. This is 20% more than the minimum required 15 revs (which is the effective shaft rev range of my capacitor, see Fig. 9).
Fig. X: Top view of the assembled capacitor motor drive
Fig. X: Bottom view of the assembled capacitor motor drive
Fig. X: Angled views of the assembled capacitor motor drive
Fig. X: View of both ends of the drive unit
I re-use the control box of my 1-turn 80-20 loop and the 15 m long "twisted shield pair" ethernet cable to the motor drive. TBC if current limiting resistor (in the motor-stall LED circuit) is correct for this motor's stall current.
Video clip: end-stop to end-stop motion of my capacitor motor drive
©2021 Frank Dörenberg (N4SPP)
Fig. X: Capacitor and drive installed on the ends of the loop
As visibile in the right-hand photo above ( = left-hand below), the initial copper strip bracket was not mounted tightly enough around the front electrode of the capacitor. The one in the rear was OK. This did not appear to affect the contact resistance and, hence, the Q and bandwidth of the loop. At least not yet! Better to fix this right away! So, I made two new rectangular washers. This time I made them longer then necessary. As we all know: "It is easier to cut/file/saw something off, then to cut/file/saw something on". I reduced the length in two fit-and-file steps to their final size. Nice and tight, as shown in the right-hand photo below:
Fig. ##: The initial and final rectangular washers
You may ask: "Why mount the capacitor inside the 2-turn loop instead of on the outside?" Well: 1) overall, it is more compact, 2) to protect the capacitor, 3) ease of adding weatherization (no need for slits in the sides of the removable hood for the copper tubing). Note that the field strength near the loop conductor is basically the same inside and outside the loop, so that makes no difference. Yes, the motor control cable now has to go inside the loop, but that is just like the coax of the coupling loop - the control cable will be guided upward, mid between two adjacent loop turns.
I made a customized clear polycarbonate box for weather protection. See below.
No motor drive for coupling loop. TBC: loop diameter too small to mount the sliding coupling-loop drive of my 1-turn 80-20 STL with its 10 cm ( = 4 inch) stroke.
INITIAL MEASUREMENTS - WITH LINEAR MOTOR DRIVE FOR THE COUPLING LOOP
Needed because coupling different loop position required for positioning at the middle of my terrace vs 1+ m above my steel pergola. Same type of drive as successully used with my 1-turn STL. Added same motor selection relay to the vacuum capacitor motor drive, so 100% compatible with the remote control box of that I made for my 1-turn loop.
Support for loop: made screw-and glue PVC tubing adapter.
Fig. ##: Linear actuator with custom PVC elbow and BNC to male banana adapter
(BNC adapter attached with two cable ties)
Fig. ##: Motor drive assembly of the vacuum capacitor - expanded with motor selection relay and DC power jack
(two 5 VDC SPST relays with solenoids in series, as in my 1-turn STL drive); linear actuator power plug is inserted from below)
My miniVNA measurements (with 0 dBm power, i.e., 1 mW into 50 ohms) show that the coupling loop motor drive has no impact on BW / Q compared to manually adjustable coupling loop. Also, transmission with 80 W shows no undesirable effects either.
Add pix of "bird-house" weather protection.
Fig. ##: "Bird house" for weather protection of the BNC adapter of the coupling loop
INITIAL MEASUREMENTS - WITH THE TUNING CAPACITOR AND MOTOR DRIVE
Graph: resonance freq vs capa revs, in umbrella stand, on telescopic mast @ 2m and 4m above ground, telescopic mast @ 1m above pergola.
Conclusions regarding tuning range for used varicap, also compared to 1-turn loop.
Tuning range with 5-250 pF cap: INDOORS in umbrella stand, bottom of loop 1m above floor: 3.44 - 12.8 MHz, compared to the self-resonance frequency of 17.95 MHz (= without the capacitor). I.e., for the given tuning capacitor, the antenna covers the 80-40-30 m bands. To cover 20 m: make loop smaller, and use a larger capacitor (because the low end of the tuning range will also move up). --> validated my decision to go for a varicap with 250 pF max, i.e., half the max of the varicap of my 1-turn loop.
SWR= 2.618 = - 3dB = half-power bandwith: Q is about 1325 around 3590 kHz. Compare this to my 1-turn loop: BW = 4.3 kHz around 3580 kHz --> Q = 845.
TERRACE in umbrella stand, bottom of loop 1m above floor:
80-30 without changing the coupling loop position?
TX/RX directivity: like Fig. 86B on 80-20 STL page.
Without the two PVC spacers between the loop turns, the resonance frequency increased about 35 kHz in the 80m band (3620 --> 3655 kHz). No signifcant difference in bandwidth.
80m: SWR 1.1 with 34 cm diam coupling loop halfway between top & center of loop and turned 45° out of main loop plane. SWR 1.1 with 19 cm diam coupling loop coplanar with main loop, 10 cm spacing wrt main loop.
80m: SWR=2 bandwidth ≈2 kHz, vs ≈3.2 kHz for my 1-turn loop. You don't want less than that vs B/W of modulation and need to be able to very finely tune. 0KDF theoretical prediction for BW?
Effect of adding/removing hood?
I thought that the neoprene belt that I used initially, did not have steel cords, but alas... Effects: at 80 W: key-down, SWR increased rapidly and was then limited by power reduction by transmitter's protection circuit. This suggested heating due to eddy currents somewhere, but I no parts got hot or even warm to the touch. Then I systematically disassembled the capacitor+motor drive (first the cable ties - that were actually very close to the end electrodes of the varicap = high voltage). This slowed down the SWR increase significantly. Now the power stayed high enough long enough to feel and smell heating: the gear belt:
Fig. ##: The original neoprene timing belt - discoloration and other clear signs of arcing and heating ( = dissipation)
(neoprene belt with steel cords)
Same issue as what I encountered with the first capacitor drive (with a stepper motor) of my first large 1-turn loop. Removed the belt and problem gone - but of course: no motor drive capability. I thought that a rubber belt with fiberglass, polyester, or polyurethane cords would do the job. So, I bought a such a replacement belt: rubber/neoprene, but now with fiberglass cords. The impact on SWR and Q was worse than with the original belt:
Fig. ##: Effect of timing belt material on resonance frequency, SWR, and "Q"
I did not even bother to run tests under power. "Loading" the pulley on the capacitor shaft with a rubber/neoprene belt kills the "Q". Note that the DC-motor drive of my 1-turn loop does not have a belt (other than for connecting a position-feedback rotary potentiometer). Instead, is has a short section of POM-material isolation shaft.
Next, and hopefully final, solution: polycarbonate pulleys instead of aluminum pulleys, and a 80XL037 polyurethane belt with fiberglass cords and 84XL037 rubber with fiberglass (rubber should hopefully/actually be OK with polycarbonate pulleys). EXPECT TO RECEIVE ALL PARTS IN FEB 2022.
Obviously, any movement of the turns with respect to each other changes the loops self-inductance, which causes a shift in the resonance frequency and SWR. The lowest point of the loop turn that is nearest the mast is already attached to the mast. The top of the two turns are attached to the "gallows". At the bottom, the ends of the loop's tubing are attached to each other with the vacuum capacitor. The next Figure shows the effect of just a smal breeze, when the movement of the windings is not restricted any further:
Fig. ##: No spacers installed - effect of varying loop-turns interdistance due to a light breeze
Clearly, the movement of the loop-tuns must be limited. So I installed two spacers between the loop turns:
Fig. X: Adding spacers to limit movement of the loop turns
I decided to place them at the 3 and 9 o’clock position. Placing them lower would put them closer to the capacitor and the associated high voltage. However, I did not experiment with this.
Fig. X: Two pairs of PVC spacers - for two different coil pitches
Installing the two spacers caused no significant change in SWR or Q (at miniVNA power level), but the resonance frequency shifted 22 kHz downward. This implies an increase in the loop's self-inductance. This is not surprising when introducing a dielectric between the windings. I have not yet systematically checked the effect on SWR, Q, and resonance frequency during rain and fog!
In order to minimize the frequency shift, and any other potential effects, I minimized the amount of spacer material by drilling a hole in the spacers - vertically, to minimize water collecting in the spacer:
Fig. ##: Making 15 mm Ø hole in each spacer increased the resonance frequency by about 1/4 kHz, but no change in "Q"
WEATHER PROTECTION FOR THE CAPACITOR DRIVE
Make a new clear polycarbonate hood, similar to the large one that I made for my 1-turn 80-20 STL. Simple rectangular box, open at the bottom [easier than with the capa installed on the outside of the bottom of the main loop]. Plate thickness: 4 mm. Five plates: top, long side x 2, short side x 2. Plus 4 narrow 4 mm strips, same length as the inside of the 4 side plates, to support the hood onto the PPE motor drive base plate.
Hood high enough to fully cover capa + connections, even when not installed horizontally (i.e., loop rotated about 30° max), but not sticking out below the main loop.
It is made of clear, colorless polycarbonate (PC, e.g., Lexan™). This material is harder and stronger than acrylics such as plexiglass (with trade names such as Plexiglas (with one "s"), Acrylite, Lucite, Perspex). It is also easier to drill and cut than plexiglass - without breaking or cracking it. It is also available with UV protection (plexiglass is inherently more UV-resistant). On the downside: it is about 35% more expensive than same-dimensions plexiglass sheet. Another issue is bonding sections of polycarbonate. You absolutely can not use (and do not want to use) cyanoacrylate glue (a.k.a. "Super-Glue"). PC requires a special one- or two-component "glue", in general a Methyl Methacrylate Adhesive (MMA) solvent. The good stuff is toxic!, so you have to do the gluing outdoors or in a very well ventilated area! I used SCIGRIP® 16 glue. Note that some MMAs are colored when cured - not what I want! SCIGRIP 16 is still available (2021) at do-it-yourself stores and on-line shops in the US (but is not for sale in southern California) and the UK. It is on the "hazardous material" list in mainland Europe, and basically not allowed to be shipped to there (and only via surface-mail within the US).
I re-used my very simple wooden jig that I made to glue-up the polycarb plates of the motor-drive hood of my 1-turn loop.
Fig. X: My design for the hood
Fig. X: The custom-cut pieces of polycarbonate sheet - white protective film on both sides
(the two narrow strips without white film on them are cut from left over pieces of another hood)
Fig. X: The various pieces of the hood - all glued up
(the 30 cm / 1 ft ruler is shown as size reference)
Fig. X: The installed hood
The hood weighs 725 grams (≈ 1.7 lbs). This is about half the weight of the motor-capacitor assembly (1.5 kg). Total weight of my 2-turn STL is 5.9 kg (≈ 13 lbs).
Compare this to my 1-turn STL: the hood of its capacitor drive unit is more than twice as long and weighs 2.5 kg (≈ 5.5 lbs), the capacitor drive unit itself weighs 4.2 kg (≈ 9.3 lbs), including the large 2.2 kg (≈4.9 lbs) vacuum capacitor (10 kV, 500 pF). Total weight of the 1-turn STL is 12.3 kg (≈ 27 lbs) = more than twice that of the equivalent 2-turn STL.
COMPARISON WITH MY 1-TURN LOOP WITH THE SAME OVERALL CIRCUMFERENCE
This section is what it is all about: how does this 2-turn STL compare to my 1-turn STL with the same total circumference, in particular regarding "performance"?
Compared against my 1-turn 80-20 STL with the same total circumference= conductor length. Under near-identical installation conditions and loop-bottom clearance/height above ground, at close to the same time (propagation conditions). Repeated several times.
Fig. X: My 1-turn and 2-turn loop antennas - size & weight comparison summary
Issue + troubleshooting of SWR increase / power-foldback by TX protection function.
"Performance": for me, I am only interested in DX, so I determine performance by recording signal strength at several remote Web-SDRs (or Kiwi-SDRs) - I can do that by myself 24/7, without having to make scheds with other stations. On DATE-MONTH-2021, I ran transmission tests in the 80 m band during a 15 minute period shortly after local sunset (no 80 m DX until sunset). I normally use Web-SDR receivers (available 24/7) for such tests, to see my own signal in their respective waterfall diagram and on their S-meter. To get the cleanest S-meter readings, I minimize the Web-SDR's adjustable bandwidth. This time I used four Web-SDR receivers simultaneously:
Figure 86E: Map with the four Web-SDR locations relative to my QTH in the south of France
(most Web-SDR's world-wide are here: www.websdr.org)
Add symbol for Bordeaux for 80, Andorra for 40.
Test side by side with A-B coax switch - only if de-tuning the deactivated antenna away from resonance on test QRG (e.g., jump-wire across large loop or short jump-wire across 2-turns, to avoid coupling that would otherwise completely falsify the test results.
ATTENTION: when comparing two High-Q resonant antennas - such as STLs - at the same location, make sure that they are NOT tuned to the same frequency (or close to the same frequency, with overlapping bandwidths)! They will couple and distort measurements and operation! Rather than de-tuning and re-tuning with the capacitor drives, I simply de-tune the STL that is not used, by bridging the capacitor or the main loop (e.g., with a lightweight car battery jumper cable).
My transmitter output power was around 100 watt. The plane of the loop was aligned with the location of each Web-SDR station. I recorded S-meter signal strength of each Web-SDR for three configurations: 1) antenna mast installed in the umbrella stand, bottom of the loop 60 cm (2 ft) above the terrace floor, 2) antenna installed on my telescopic mast, poking up between the steel I beams of my pergola, bottom of the loop 90 cm (3 ft) above the pergola, and 3) same, but bottom of the loop 200 cm (6.5 ft) above the pergola. Note that when my antenna is installed in the umbrella stand, the pergola blocks the "view" of the antenna in the direction of all Web-SDR's that I used.
Comparison for both 80 AND 40 m.
Bordeaux does not cover 40M. Andorra (117 km, 173° E, 1400m altitude vs 140 m @ QTH) covers 80 & 40. Use different color map symbol.
TRY Andorra for radiation pattern (far field but not DX, so hopefully more stable radings / no QSB) .
Figure 86F: signal levels at five Web-SDR's for three different antenna positions & heights
Figure 86G: signal levels at five Web-SDR's for three different antenna positions & heights
Fig. X: My 1-turn and 2-turn loop antennas - DX performance comparison summary
Conclusions: any significant difference in DX and radiation pattern shape (in particular depth of "nulls")?
Effect & performance when short-circuiting one turn (across bottom center and one capacitor end)?
ANTENNA SIMULATION / MODELING
"Models are always wrong, but some are useful" (George E.P. Box, statistician, 1976)
TO BE ADDED: antenna radiation pattern simulations with the excellent 4NEC2 freeware simulation package.
Add caveats about NEC-based simulations have significant limitations regarding accounting for proximity effects of conductors. Ref. to be added.
Use the convenient "helix" shape creator in the Geometry Builder function of 4NEC2, for the basic 2-turn loop:
Fig. X: 4NEC2 modeling of the basic 2-turn loop
Note: in the Helix Geometry Builder, entry of values for loop length/height, loop radius, and conductor radius is in m, cm, and mm, respectively! The loop is oriented vertically and in the XZ plane by entering "90 90 0" for "Rotate X, Y, Z" in the "Helix" window. Then add the 15 cm long capa connection stubs ( = 90° bent ends of the loop tube), add capa across these stubs. Add coupling loop (also as helix?). Caveats, segment errors. In the Source/load" tab of the 4NEC2 editor, the "Show loads" box is checked and in "Load(s)" line item 1, "Wire-conduc" is selected in the "Type" column, and "Copper" is selected in the "Cond(s) column. All other column field remain blank.
Fig. X: 4NEC2 modeling of the complete 2-turn loop - with capacitor and coupling loop
Fig. X: Radiation pattern and current distribution of the modeled 2-turn loop
(capacitance zero & TBD? height above ground?, frequency?, ground type?)
Compare against similar simulation of 1-turn loop - also construct model with "Helix" builder function of 4NEC2.
Fig. X: 4NEC2 modeling of the basic 1-turn loop
(note the tiny gap between the ends of the loop (at the bottom of the loop) - the helix tool does not allow zero pitch "length")
Per this very detailed and comprehensive on-line coil RF-inductance calculator, this 2-turn coil - by itself - has an inductance of ≈4.1 μH (at 3.6 MHz), compared to ≈2.7 μH for the same-tube-length 1-turn coil. Due to numerous non-trivial effects, this calculated RF inductance varies with RF frequency: ≈3 μH vs. ≈2.3 μH (at 7 MHz), and ≈3.5 μH vs. ≈2.5 μH (at 10 MHz).
- Ref. 1: general
- Ref. 1A: "Some thoughts on a two turn small transmitting loop", Owen Duffy (VK1OD, VK2OMD), 7 March 2017, owenduffy.net blog page 7217. Accessed 15 July 2021. [pdf]
- Ref. 1B: "A 160/80 Metre Transmitting Magnetic Loop Antenna Design", Steve Adler (VK5SFA). Accessed 23 July 2021. [pdf]
- Ref. 1C: "The impedance and efficiency of multiturn loop antennas", T.L. Flaig, Ohio State University, Electroscience Laboratory Report 2235-2, April 1968, 44 pp. Source: dtic.mil, retrieved 2 August 2021.
- Ref. 1D: "Optimal design of single-layer solenoid air-core applications for High Frequency applications", G. Grandi, U. Reggiani, M.K. Kazimierczuk, A. Massarini, Proc. 40th Midwest Symposium on Circuits and Systems, Sacramento, CA/USA, August 1997, pp. 358-361. Source: unibo.it, accessed 2 August 2021.
- Ref. 1E: "An introduction to the art of solenoid inductance calculation with emphasis on radio-frequency applications", David W. knight, V2.0, February 2016, 97 pp. Retrieved 2 August 2021 [pdf]
- Ref. 1F: "A Two Turn Magnetic Loop Antenna for 30 through 10 Meters", Wayne Openlander (W9NZB), in "QEX", March/April 2013, pp. 3-6. Source: archive.org, accessed 22 October 2021. [pdf]
- Ref. 1G: "An update on compact transmitting loops", John S. Belrose (VE2CV, VY9CRC), in "QST", November 1993, pp. 37-40.
- Ref. 1H: "Performance of Electrically Small Transmitting Loop Antennas: Part I", John S. Belrose (VE2CV, VY9CRC), in "RadCom", Radio Society of Great Britain (RSGB), June 2004, pp. 64-67; "Part II", in "RadCom", July 2004, pp. 88-98; and "Technical Feedback", in "RadCom", June 2005, p. 78, and "RadCom", August, 2006, pp. 74-76.
- Ref. 1J: "Small Transmitting Loop Antennas - A different perspective on determining Q and efficiency", Milton E. Cram (W8NUE), 5 June 2017, 14 pp. Accessed 22 October 2021. [pdf]
- Ref. 2: NEC / 4NEC2 simulation models for 2-turn STLs
- Ref. 2A: to be added. Can NEC modeling even account for proximity affects related to the closely spaced turns?
- Ref. 3: commercial 2-turn STLs - note: I am not endorsing any listed products, as I have not been offered any for testing and, hence, have not tested any.
- Ref. 3A: MLA-M (2-turn, loop Ø 62cm, 80-10m coverage, 10W/QRP, manual tuning, tabletop / not weatherized, price built/kit €440/€400 + S&H), MLA-T (4-turn, loop Ø 80cm, radiator Ø 23mm copper tubing, 160/80/40m coverage, 100W max, motorized tuning, 12 kg, price €940 + S&H), manufacturer: B PLUS TV a.s., accessed 7 October 2021.
- Ref. 3B: "MLA-M - Kleine Loop für QRP" ["Small loop for QRP", in German; description, indoor & outdoor tests], Carsten Hausdorf (DF2DD), in "CQ-DL", nr. 10 (October) 2013, pp. 722-724, source: doczz.net, accessed 4 October 2021. [pdf]
- Ref. 3C: "MLA-T: Magnetantenne für 100 W auf 160, 80 und 40 m", Harald Kuhl (DL1ABJ), in "Funkamateur", 10/2013, pp.1062-1063. [pdf]
External links last checked: July 2021 unless noted otherwise.