This page provides a top-level description of Small Transmitting Loop (STL) antennas (a.k.a. "Magnetic Loop Antenna", MLA), and my two versions of such an antenna for 80 mtrs and up. My smaller 40-20 loop is described here. My helically wound "Slinky" loop is described here.
- [Coupling methods]
- [Some antenna simulation modeling]
- [My first STL]
- [My second STL]
- [Placement of the antenna]
- [Effects of corrosion]
- [DC- & stepper-motor drives for the tuning capacitor]
- [DC-motor drive - weather protection]
- [DC-motor drive - remote control box]
- [DC-motor drive for the coupling loop]
- [Next project]
Latest page update: January-May 2021 (expanded the coupling loop motorization section with a linear actuator drive;
added new motor drive weather-protection design; added Fig. 86B-86D, added
section on modeling; expanded ref. 4B, added Figs: 86E-86G + text; expanded Fig.
Previous page updates: December 2020 (expanded text around Fig. 24C, added Fig. 2B with text); June-August 2020 (expanded "Effects of corrosion" section, expanded "air variable capcitor in oil" paragraph); January-February 2020 (added Fig. 28A/B and 34A/B + text, Fig. 83B & text, Fig. 24F & text); December 2019 (added Fig 24C); August 2019 (expanded the shielded coupling loop section with Fig. 24D and text)
©1999-2021 F. Dörenberg, unless stated otherwise. All rights reserved worldwide. No part of this publication may be used without permission from the author.
I wanted a small transmitting loop (STL) antenna that covers at least the 80 and 40 meter bands (preferable 80 - 20). Why?
- I want to do 80 mtrs DX, but I have no room for a decent 80 m wire-antenna, nor would I be able to install such an antenna high enough above ground. I have had some success with short, loaded vertical antennas with a single elevated radial, see here and here. But I cannot install those permanently at my QTH.
- Below 10 MHz, our apartment building generates a large amount of "electro-smog" QRM. An STL tends to be less sensitive to picking up electrical noise in the near-field (< 1 λ), which appears to be the reason why this type of antenna is also referred to as a "magnetic loop antenna".
- STLs have a radiation pattern with directivity. They are also small enough to rotate with a small motor, or TV-antenna rotor.
- They are less conspicuous (to my friends of the home-owners association "police") than a wire antenna that is strung along the outside of the building.
- I don't want to have to mess with radials, counterpoises, RF-grounds, etc. Loops are inherently symmetrical, like dipoles.
- Can be installed close to the ground (vertically oriented), without significantly losing efficiency. Yes, higher is better.
A loop antenna is generally considered "small", if its circumference is less than 10% of the operating wavelength. So in my case (for 80 mtrs), "small" would be a circumference of less than 8 mtrs, e.g., a circular loop with a diameter less than 2.5 mtrs (≈ 8.2 ft). To be more precise, we are talking about a small resonant loop. Note that a multi-band loop that is "small" in the lowest band, is not necessarily "small" in the higher bands ( = higher frequency).
Clearly, as with all antennas, "radiation resistance" is very important parameter. As the graph below shows, the radiation resistance of an STL is very small - we are talking milliohms here! The radiated RF power is determined by the radiation resistance (ref. 2J), multiplied by the square of the circulating RF loop current. As the radiation resistance is very small, a large loop current is required to get practical levels of radiated power. This implies that all losses (e.g., capacitor losses, contact resistance due to loop construction, losses due to coupling with the environment), even if only a couple of milliohms, are important in STLs!
Fig. 1: Radiation resistance of a Small Transmitting Loop antenna
The radiation pattern of a Small Transmitting Loop antenna is shown below. The kidney-shape of the horizontal pattern (top view) becomes more pronounced ( = deeper minimums) as the antenna circumference becomes a larger fraction of the wavelength. This is the case when operating a multi-band STL on the higher band(s). For large loops, the maximums of the horizontal pattern are actually in the directions perpendicular to the surface of the loop! See the "Some antenna simulation modeling" section for a more detailed analysis.
Fig. 2: approximate radiation pattern of a vertically oriented Small Transmitting Loop close to ground
(circumference = 0.15 λ, installed 0.08 λ above ground)
Due to the closed-loop shape, this type of antenna can be considered an extreme case of a "terminated folded dipole". A standard loop has a circular single-turn inductor. Of course, other shapes are possible: square, rectangular, octagonal, etc. There are variations such as multiple turns and configurations such as "figure-eight". As with dipoles, single-band directivity and gain can be increased by adding passive reflector and director loops, as in so-called multi-element "Yagi" beam antennas. This is all beyond the scope of this discussion.
Just to get a feel for some basic parameters, I have calculated the characteristics for a circular loop with a circumference of 5 m (diameter =1.6 m, ≈ 5.2 ft), made of copper tubing with a standard 16 mm outside diameter (5/8"). Input power is 100 watt (the limit of my transmitter).
Fig. 3: Calculated antenna characteristics for the given copper loop
(KI6GD calculator, ref. 2A; no additional losses assumed in the calculation - note: read ref. 2F for caveats about loop antenna calculators!!!)
Fig. 4: Calculated antenna characteristics for the given copper loop
(AA5TB calculator, ref. 2B; no additional losses assumed in the calculation - note: read ref. 2F for caveats about calculators!)
If the input power is increased by a factor of N, then the maximum voltage across the capacitor is increased by a factor √N. E.g., doubling the power increases the capacitor voltage by ≈1.4. Conversely, the voltage is reduced by a factor of 1.4 when the input power is reduced by a factor 2.
Fig. 5: Capacitor voltage as a function of frequency (1.6 mtr Ø loop made of 16 mm OD copper tubing)
(calculated with ref. 2B; assumes 5 milliohm loss resistance - note: read ref. 2F for caveats about calculators!)
"Efficiency" can be defined as "total power radiated by the antenna" divided by "net power accepted the antenna" [IEEE Std 145-2013 "Standard for Definitions of Terms for Antennas"]. The tables above show that the calculated / predicted efficiency for 80 mtrs is rather low (no surprise), but my other antennas for 80 mtr are (very) short verticals. I do not know what their efficiency is, but I am sure that it is very low. In the end, what counts is performance at my location, for the available space, for the prevailing conditions (proximity to the building, QRM levels, etc), and with respect to other antennas that I can (afford to) install there. The efficiency of STL antennas remains controversial (ref. 3).
As a rule of thumb, the optimum circumference of a multi-band STL is about 0.15 λ of the lowest operating frequency. With an appropriate variable capacitor, the resonance frequency of an STL can be tuned over a frequency range that covers at least two octaves ( = factor 4x). However, from an antenna efficiency point of view, a factor of 2-3 is probably the practical limit. E.g., 80-40, 40-20, 30-10.
I have not looked into the assumptions that the calculators make, regarding installation height (free space?), coupling method, etc. As in all high-Q resonant circuits, calculated and actual performance is highly dependent on the losses in all components (loop, capacitor) and all interconnections. Losses in the milli-ohm range may be significant! In general, increasing the diameter of the tubing will reduce the (inductor) losses - up to a point.
Instead of the standard tubular conductor, loops can be made of a wide, flat conductor strip such as copper "flashing" or foil. The strip can be straight (ref. 4), or helically wound (hence, helically loaded, ref. 5A/B). Of course, helical/spiral "hula hoop" antennas can also be made of a Slinky™ coil, as I did late 2016. Ref 5C, 5F. Another option is a meandering or fractal loop circumference.
Figure 6A: Flat conductor loop (helically wound/loaded, shown without capacitor) and Slinky™ coil loop
(sources: ref. 5A/B and 5C)
Figure 6B: Flat conductor loop and meandering "fractal" loop
(source: ref. 4 and www.radioworld.co.uk)
Even on VHF (2 m band), the size of standard antennas such as HB9CV and Quads can still be sizeable or akward for portable operation. VHF loops can be made with the same construction techniques as for HF. However, for the 2m band, a 0.1 λ STL only takes an area of about 10x10 cm (4x4 inch). The main loop, and even the coupling loop, can be etched on a printed circuit board (PCB). This is what Thomas Schiller (DC7GB) did. Fixed capacitors can also be made of 2-sided PCB. However, Thomas' extensive experiments concluded that the dielectric properties of standard PCB material (e.g., FR4) varies too much (and on-linearly) with the main loop's E-field, even at low transmit power levels. At VHF, FR4 also has a large loss tangent δ. So he used a 4.7 pF 500V mica capacitor (yellow arrow in Fig. 7 below). That capacitance is too small to make variable for tuning. The latter is done by shaping a small (2-3 turn) coil (at the red arrow), placed in series with the coupling loop. A kit version is sold commercially, with a 1.6-8 pF trimmer capacitor (ref. 4B). Loop performance is supposedly close to that of a full-size dipole.
Figure 7: Printed circuit board loop for the 2m band
(source: ref. 4B; the PCB of the kit version measures 9x11 cm ≈3.6x4.3 inch)
Figures 3-5 above show that there is a very high voltage across the capacitor at resonance, even at QRP levels! This is not only important when choosing a suitable capacitor, it is also a SAFETY issue! When transmitting, NEVER touch the capacitor or the loop, and do not let any other person or animal touch it! RF burns do not heal well!
Exposure to RF radiation is also a health hazard to humans and (other) animals! Legal limits and guidelines for such exposure generally vary by country. The table below shows the minimum estimated safe distance for various transmit power levels. Ref. 14A, 14B, 14C.
Table 1: Estimated minimum safety distances for Small Transmitting Loop antennas
(sources: ref. 14A, 14B; distance is measured from the center of the loop)
TUNING THE LOOP'S RESONANCE FREQUENCY
The loop antenna is basically an LC-circuit that has to be tuned to resonance on the desired operating frequency. The loop by itself is an inductor that has the shape of a closed-loop. The generic formula for the resonance frequency of an LC-circuit is shown in Fig. 8 below. Note the duality of the "L" and the "C" in this formula. Based on this, the resonance frequency can be changed in two basic ways:
- by adding "C" to the circuit. This is typically done by opening the loop, and connecting a variable capacitor across the open ends of the loop. This is the standard way to "tune" the resonance frequency of a loop antenna.
- by adding "L" to the circuit. This can be done by opening the loop, and connecting a variable inductor across the open ends of the loop. Continuously variable inductors with a large value range, a high power rating, and low loss are rare. Also, a fixed-value capacitor may also have to be added to the loop, based on the value range of the inductor. This is why there are very few practical examples. The only example known to me, is described in ref. 13A. It uses a ferrite rod that is inserted into a 2-turn coil. This tuning method is not discussed in the rest of this article.
- The "L" of the loop can also be changed, by changing the size of the loop. However, this is not very a practical method for tuing the resonance frequency - other than for a single-frequency application.
Figure 8: The duality of L and C in changing the loop's resonance frequency
Note that when "L" or "C" is increased, the loop's resonance frequency is always reduced. Also, the loop not only has inductance, but also stray ( = parasitic) capacitance. This means that the loop has a self-resonance frequency, even without a tuning capacitor.
A simplified lumped-element diagram of a tunable LC-loop is shown below. The tuning capacitor is modeled as "non ideal", with equivalent series resistance (ESR) and inductance (ESL). Likewise, the loop's self-inductance includes loss resistance that represents skin-effect losses, construction losses (e.g., solder joints), etc. A "single-turn coil" loop is assumed, so no turn-to-turn stray capacitance is modeled. The model does contain parasitic capacitance, to represent coupling to ground below the antenna and to nearby objects. The "radiation resistance" is a fictitious conceptual resistance that relates the power that is radiated by the antenna, to the current flowing in the antenna. So it is directly related to antenna efficiency. It can be modeled, but unfortunately, it cannot be measured directly.
Fig. 9: Simplified equivalent lumped-element electrical circuit of an STL with tuning capacitor
(coupling to ground and objects near antenna is not shown; see Fig. 17 for tuning capacitor with dielectric other than air or vacuum)
"Tuning" the antenna is done by keying the transmitter (at low power setting) and observing the SWR-meter (or antenna-current meter) while adjusting the tuning capacitor. Alternatively, by tuning for maximum receiver noise level: there should be a sharp increase in the noise level when the antenna becomes tuned to the desired operating frequency.
An other important aspect to keep in mind, is the voltage and the current distribution along the loop - at resonance. As shown in the figure below, the voltage is highest at the capacitor, and zero at the point diametrically opposed (in a perfectly symmetrical loop + capacitor + capacitor connections + environment). In some coupling methods, the braid ( = shield) of the coax feedline is actually connected to that neutral point.
Figure 10A: Voltage distribution around a loop antenna
The current is highest at the point opposite the capacitor, and lowest at the capacitor. See ref. 1 for an illustration. Note that the minimum current is not zero! Unlike the voltage distribution, the current distribution depends on the size of the loop (circumference), as a fraction of the wavelength. For a small transmitting loop (circumference < 0.1 λ), the current distribution is nearly constant (uniform) around the loop. Both the voltage and the current distribution are symmetrical.
Figure 10B: Current distribution around a loop antenna
(note: a circumference > 0.1 λ is not "small")
Figure 10C: first-order approximation of the amplitude of relative current around the loop - in free space
(source: adapted from ref. 8G)
The diagrams above shows that the largest current occurs at the point opposite the capacitor. This part of the antenna radiates the most. Some operators therefore install their loop with the capacitor at the bottom. Furthermore, placing the part with the highest voltage closest to the ground, increases losses due to parasitic capacitance to ground...
Based on the voltage and the current distributions, the impedance (Z = V / I) varies around the circumference of the loop. It is highest near the capacitor, and lowest at the point opposite the capacitor. E.g., there are two points, left and right of the neutral point opposite the capacitor, where the impedance is 50 ohm points with respect to that neutral point. This property is used in coupling methods such as Gamma Match and Delta Match.
THE TUNING CAPACITOR
A loop with a fixed-value capacitor is resonant at a single, fixed frequency. A well-constructed small loop antenna has a bandwidth that requires re-tuning when changing frequency across a band. Also, the resonance frequency will vary with temperature changes (sunshine/weather). In order to change the resonance frequency to the desired operating frequency, we need a variable capacitor.
The basic choice is between "air variable" capacitor and "vacuum variable" capacitor. Clean air has a dielectric strength of 0.8 kV per mm (at 20 °C and standard humidity). So, an "air variable capacitor" for 5 kV would need an air gap of 6.25 mm (1/4 inch) between the plates. High-vacuum has a dielectric strength at least 10x as high.
A typical air-variable capacitor is "rotary variable". It consists of a stack of stator plates ( = stationary), and a stack of plates that are mounted on a rotor shaft. The rotor plates intermesh with the stator plates. Ideally, the rotor plate "vanes" are welded to the rotor shaft (rather than clamped) to reduce loss resistance. Connection to the rotor is either done via a sliding contact, and via a bearing to the frame of the capacitor. This always causes losses (series resistance)! Such moving contacts also tend to make tuning a bit "jumpy", cause receiver noise when changing rotor position, and limit transmit power during rotor movement. Such capacitors are generally to be avoided in "high Q" STL antennas. A discussion of losses in air variable capacitors is given in ref. 12M.
There are several basic types of air variable tuning capacitors:
- Single-section: a single rotor-stator section.
- Multi-section: basically two (or more) variable capacitors that are ganged (mounted side-by-side), with a single conductive rotor shaft. Hence, the rotor vanes of all capacitor sections are electrically connected. The losses of the wiper contact can be eliminated by putting two capacitor sections in series: the rotor contact is not used, only the two stator contacts. This doubles the voltage rating, but at the same time halves the total capacitance. However, note that parasitic capacitance of the capacitor is not cut in half, so neither is the smallest achievable capacitance!
- Broadcast-band: typically used in early AM/FM receivers. The rotational range (rotor "swing") is limited, typically to around 140°. This mechanical limitation makes motorized tuning more complicated. Plate distance is small, so only suitable for low power (QRP) transmission. As the plates and spacing are small, the sections are separated by a shielding wall.
- Split-stator: a 2-section arrangement in which the two sets of rotor plates are mounted on opposite sides of the rotor shaft. Likewise for the two sets of stator plates.
- "Butterfly". The rotor vanes are typically shaped like a bow-tie ("butterfly wings"). There are two rotor/stator stacks. However, they not arranged side-by-side, but diametrically opposite of each other. Note that the full capacitance range is covered by 90° turn of the shaft. There is not always a rotor contact. The RF current passes through the two "wings" of each rotor plate, rather than through the rotor shaft. This reduces losses compared to split-stator and a regular 2-section capacitors.
Figure 11: Single-section and dual-section capacitor
Figure 12: Broadcast receiver capacitor, split-stator capacitor, and butterfly trimmer
The dielectric strength ( = voltage rating, breakdown voltage) of pure, clean, mineral oil is at least 10 kV/mm, as compared to 3 kV/mm for standard air. So, immersing an air variable capacitor in such oil more than triples the voltage rating (dielectric strength, breakdown voltage). Also, the dielectric constant ( = relative permittivity) of oil is about 2, i.e., twice that of air. So an air-variable capacitor may be immersed in oil to double its capacitance. Of course, this also doubles the minimum capacitance of an air-variable capacitor, i.e., reduces the maximum tunable operating frequency of a loop by a factor of SQRT(2) = 1.4. Use an oil-tight non-metal container, and pure clean mineral oil (a.k.a. paraffin oil), synthetic motor oil, or similar. I.e., not transformer oil, which is expensive and often toxic. Make sure that the capacitor plates are completely immersed!
Figure 13: Air-variable capacitor immersed in oil - doubles capacitance and voltage rating
(source: ref. 12A)
Rather than meshing stacks of rotor and stator plates, a variable capacitor can also consist of "trombone-style" coaxial tubes: one tube is slid in and out of a slightly larger "stator" tube. This principle is also used in variable vacuum capacitors, see below.
On 15 June 1896, Nicola Tesla filed US Patent Nr. 567,818A (awarded three months later) for an “Electrical condenser”, with increased efficiency that is obtained by “practically complete exclusion of air or gas from the dielectric”. I.e., the vacuum capacitor! Nowadays, such capacitors typically use two sets of plates that are concentric thin-wall cylinders. In a vacuum variable capacitor, one of the two sets can be slid in or out of the opposing set of cylinders ("sleeve and plunger/piston"). The same concept is used in old fashioned air trimmer-capacitors that were made by Philips for several decades since the 1930s (a.k.a. "beehive" trimmer; German: "Tauchtrimmer"). Instead of intermeshing concentric cups, the electrodes may also consist of a continuous spiral (with a fixed pitch).
Figure 14: Philips tubular-piston "beehive" trimmer capacitors (5-30 pF, 0.3 mm plate distance)
(due to their shape, they are called "toltrimmers" in Philips-country (i.e., The Netherlands), meaning "spinning-top trimmer")
In the vacuum capacitor, spacing between opposing cylinders is several mm. The plates are sealed inside of a non-conductive envelope such as a glass or ceramic "bottle", and placed under a high vacuum. The movable part (plunger) is mounted on top of a flexible metal membrane (harmonica-style bellows). The membrane seals and maintains the vacuum. A screw-shaft is attached to the plunger. When the shaft is turned, the plunger moves in or out of the sleeve, and the value of the capacitor changes. The vacuum dielectric significantly increases the voltage rating of the capacitor, compared to an air-variable capacitor of the same dimensions and construction.
The tables in the previous section show that the assumed loop should be tunable from 80-20 mtrs with a 15-500 pF high-voltage variable capacitor. Note: a commercial air-variable capacitor for 15-500 pF and 5-10 kV is not necessarily smaller or less expensive than an equivalent vacuum variable capacitor! In 2010, I purchased a Russian-made capacitor. It is marked "10 kV,10-500 pF". I measured 15-510 pF with a simple LCR-meter. This "bottle" is quite heavy: 2.2 kg (≈ 4.8 lbs). It takes 36 revs of the shaft to go from minimum to maximum capacitance. In 2021, I acquired a second vacuum capacitor, for some experiments. It is also Russian made and is marked "5 kV, 5-250 pF". It is significantly smaller and lighter: 730 grams (≈ 1.6 lbs).
Figure 15: My vacuum capacitors
Capacitors have two limits that are important in STLantenna applications:
- Voltage rating, which is the dielectric breakdown voltage (with some margin).
- Current rating, which is driven by losses that cause dissipation ( = heating).
BREAKDOWN VOLTAGE. Dielectric strength is the maximum voltage that can be applied across a dielectric, without electrical breakdown occurring. Simply put, at the breakdown field strength, the dielectric becomes (locally) conductive: sufficient electrons are knocked out of the dielectric and/or electrode material, are sufficiently accelerated, and set free additional electrons via collisions. In capacitors with gaseous dielectric (such as air), the breakdown peak voltage as a function of plate spacing gas pressure is a non-linear relationship. It is critically affected by factors such as the geometry of the capacitor conductive parts, smoothness of edges, surface finish of the plates, ultraviolet illumination of the electrodes, etc. Breakdown results in a discharge, and can be limited to a luminous corona glow (low-current, high-voltage) around plate edges, or take the form of a "spark" (high-current, low-voltage). It is modeled by Paschen's law and associated curves.
Note that dielectric strength of practical vacuum is not infinite! Even deep space is not a perfect absolute vacuum. Ref. 12K. In vacuum electronic components, the vacuum level is typically on the order of 10-7 Torricelli ≈ 0.0133 mPa. The breakdown field strength of air is often given as VS = 30 kV/cm = 3 kV/mm = 3 MV/m. Note that this only applies for electrode (plate) spacing of about 2 cm = 20 mm! For smaller spacings, it is actually larger! E.g., for a spacing D around 1 mm, the following Townsend’s formula is used in standard atmosphere: VS = (30xD + 1.35) kV, where D is spacing in cm. For 1 mm (D = 0.1 cm), this yields VS = 4.35 kV, i.e., ca. 43 kV/cm = 4.3 kV/mm = 4.3 MV/m. The breakdown field strength of air is actually on the order of 2-5 MV/m. Note: if a vacuum capacitor is kept in storage for a long time, or is only exposed to low peak voltage levels for a long time, some gas may be released into the vacuum. This reduces the breakdown voltage below the capacitor’s specified test voltage rating. The capacitor may have to be reconditioned (treated with an increasing DC voltage).
Figure 16: A vacuum capacitor with typical over-voltage arcing damage
(the round damage spots are about 4 mm (≈1/6 inch) in diameter)
The following lumped-element equivalent circuit diagram shows that a practical capacitor is quite a bit more than just an ideal, pure capacitance:
Figure 17: lumped-element equivalent circuit diagram of a capacitor
C = ideal, lossless capacitance
Rseries = equivalent series resistance (ESR, loss)
Lseries = equivalent series inductance (ESL)
Rparallel = insulation resistance
RDA = resistive component of the dielectric absorption
CDA = capacitive component of the dielectric absorption
When transmitting, the loop's tuning capacitor will heat up due dissipation in the capacitor's loss resistances. The latter can be summed into the Equivalent Loss Resistance, ESR. The dissipated power is:
ESR consists of metallic losses in the capacitor's electrodes and connecting leads, as well as dielectric losses. In a vacuum capacitor, the dielectric is "vacuum". Hence, the dielectric loss is negligible. At HF frequencies, the ESR of vacuum capacitors varies over a range of about 2 milliohms (at low HF frequencies) to about 20 milliohms (high HF). Ref.12G. The loss-resistance is primarily caused by the capacitor plates, the bellows and the structure that connects the movable electrode to its external mounting flange (in variable vacuum capacitors), and the transition between the rotor shaft and the rotor terminal (in air variable capacitor types, other than "butterfly" and "split-stator" with the stators interconnected). ESR is inversely related to the capacitor’s (frequency dependent) Q. Manufacturers of vacuum capacitors typically provide a nomogram chart of max allowable IRMS as a function of operating frequency at the specified peak operating voltage and max capacitance ( = largest ESR). Ref. 12B shows the example of a particular vacuum capacitor with a temperature rise of about 40°C when operated at 6 MHz, 7.5 kV peak, and 10 amps RMS. Glass vacuum capacitors typ. have a max operating temperature around 90 °C ( = 195 °F). Ceramic vacuum capacitors typically have a higher maximum: around 120°C ( = 250°F).
Note that near resonance, a small transmitting loop may have a circulating RF current of several dozen Amps when transmitting at 100 W!
Some manufacturers of vacuum capacitors issue data sheets that include an RMS current rating graph. It typicaly shows a "continuous RMS current (amps) vs. frequency" curve for a fixed operating voltage (often the voltage rating). For variable vacuum capacitors, there may be two or more such curves, where the rating for lower capacitance values is lower than for higher capacitance values. The rating-curves normally increase (linearly on a logarithmic scale) with frequency, up to a certain frequency. For higher frequencies, convective heat-sinking capability becomes the limiting factor, and the curve(s) go down with frequency. The voltage rating is not frequency dependent.
Dielectric absorption is the effect by which a capacitor that has been charged for a long time, does not discharge completely when briefly discharged. In air capacitors and vacuum capacitors, this effect is typically too small to be measurable. The insulation resistance Rparallel accounts for leakage current through the dielectric. For variable vacuum capacitors, the latter is typically less than 10 microamps. This is extremely small, compared to the capacitor current when the loop is tuned to resonance.
The series self-inductance Lseries of an air variable capacitor typically ranges from about 6 to 50 nH. For fixed vacuum capacitors, it ranges from about 2 to 10 nH. Variable vacuum capacitors have a bellows and a structure to connect the movable electrode to the external mounting flange. This increases the self-inductance to about 6 - 20 nH, and this inductance changes with the capacitance. The capacitor's self-resonance frequency that results from this series inductance, is normally well above HF.
EFFECTS OF TEMPERATURE, ATMOSPHERIC HUMIDITY & PRESSURE
(this section still needs some work...)
Have you ever noticed that the resonance frequency of your “Mag Loop” STL drifts when the capacitor’s temperature changes? The temperature change may be due to loss-dissipation in the capacitor when transmitting, the sun shining on the capacitor, or change in ambient temperature. Likewise, have you noticed a frequency drift when the relative humidity of the air changes significantly (foggy weather, temperature near the dew point)? Or you have noticed a change in the maximum transmit power you can apply, before a luminous corona discharge appears at the capacitor plates, or arcing occurs?
There is surprisingly little literature (including university textbooks) that discusses the effects of parameters such as humidity, atmospheric pressure, and temperature on the performance of tuning capacitors. General literature often considers the effects as “minimal” or “negligible”, and uses simplistic, approximate models such as that of an ideal capacitor that consists of two flat parallel plates or concentric cylindrical plates:
C = capacitance in Farad
ε0 = absolute permittivity of free space ("pure vacuum"); ε0 = 8.85x10-12 F/m
εr = relative permittivity of the dielectric (a.k.a. dielectric constant)
A = area of plate overlap in square meters ("active area")
d between plates in meters ( = dielectric thickness)
l = length of overlap between the electrodes in meters
r1 = inner radius of the outer electrode in meters
r2 = outer radius of the inner electrode in meters
These formulas ignore edge effects, and suggests that the capacitance C is a constant. However, the capacitance does change with temperature, as well as humidity and barometric pressure (air capacitors). Ref. 12B, 12C.
TEMPERATURE. The capacitance of a decent “glass bottle” vacuum variable capacitor typically varies no more than about 100 ppm/°C = 0.01%/°C (ref. 12G). Ceramic vacuum capacitors only drift about half as much, but an air capacitor may drift three times as much. That’s still not much, right? Well, in a “low-Q” filter application this may well be the case. But in a well-constructed “high-Q” loop? Let’s take a marginal vacuum variable capacitor and assume a temperature increase of only 10 °C ( = 18 °F). Worst-case (!), the capacitance will change by 10 x 0.01% = +0.1%. What does this mean for the resonance frequency of a loop antenna?
where L = loop inductance, and C0 = capacitance of the tuning capacitor at a particular temperature T0. Note that, for the sake of simplicity, we are ignoring the stray (parasitic) capacitance of the loop inductance here. Based on the above formula, we can derive the change of the resonance frequency for a given shift in the capacitor temperature :
where m = capacitance change-factor due to temperature change from T0 to T1. Hence, m = 1 + drift percentage. For ΔT = +10 °C, m = 1+0.01% = 1.01. Hence:
I.e., a change of -0.5%: temperature increase causes a frequency decrease. For instance, at 28 MHz , the resulting frequency drift would be 28 MHz x -0.005 = -14 kHz. At 3.6 MHz, the resulting frequency drift would be 3.6 MHz x -0.005 = -1.8 kHz. This much drift is quite noticeable! Note that there are even small hysteresis effects associated with large temperature changes (ref. 12C).
In the discussion above, we used the standard equation for the resonance frequency of an LC circuit and approximate models for capacitance. Per the resonance frequency equation, a relative change in C clearly has the same effect as the same relative change in L. The standard approximate model for an inductance coil is given below. Instead of the capacitor’s permittivity ε of the medium between the plates, we now have the magnetic permeability μ of the medium inside the coil winding(s). For a cylindrical coil with N turns (N = 1 for a standard STL antenna), the inductance is approximately:
L = inductance in Henry
μ0 = absolute permeability of free space ("pure vacuum"); μ0 = 4π x 10-6 H/m
μr = relative permittivity of the dielectric
N = the number of turns of the coil-winding
A = area of plate overlap in square meters ("active area")
l = average length of the coil in meters ( = dielectric thickness)
A standard "Mag Loop" STL antenna is a 1-turn air-core inductor. Like a capacitor's relative permittivity, a coil's relative permeability depends on the operating frequency, and the temperature, pressure, and humidity of the dielectric ( = "air" for a loop antenna)!
Before I bought my used vacuum capacitor, did a quick test to verify integrity of the vacuum: I put the capacitor in the refrigerator for about an hour. There should be no formation of condensation on the inside of the glass when in the fridge, or after taking it back out (on outside is OK). If the vacuum seal is compromised, the shiny copper will turn dull eventually. As heavy as the capacitor is, the glass is actually rather thin. I found this out when my first vacuum capacitor imploded when it rolled around on the tiles of my terrace floor.
HUMIDITY. Yes, the capacitance of vacuum capacitors is not affected by humidity: moisture can only affect the outside surface of such capacitors. But high ambient humidity may cause a small leakage current across the outside of the capacitor. However, for air capacitors, the capacitance change as a function of relative humidity of the air is actually so large, that such a capacitor can be used as a relative-humidity sensor (ref. 12D)! Note that air capacitors also exhibit small hysteresis effects associated with long exposure to high humidity (ref. 12F). Relative permittivity εr = 1 for vacuum. Dry air has an εr ≈ 1.0006 (at standard temperature and pressure of 1 atm). This “constant” changes 2 ppm/°C for dry air, and 7 ppm/°C for moist air. Ref. 12H. Dry air has a relative permittivity μr ≈ 1.000000037. I’m still trying to dig up data on the relative permittivity of air as a function of temperature, humidity, and partial vacuum. With my own helical loop antenna with air variable capacitor, I have observed a frequency drift of 0.5% (20 kHz around 3.6 MHz) when fog moved in, while temperature only changed 0.5 °C.
COUPLING A LOOP TO THE FEEDLINE
The loop antenna will be connected to my transceiver via a coax feed-line. This means that the coax needs to be coupled to the loop, and the coupling must be wide-band enough to cover the tuning range of my antenna. As with other types of antennas, there are several ways to do this:
- [Inductive coupling (coupling loop)]
- [Capacitive coupling]
- [Magnetic transformer coupling (ferrite ring)]
- [Auto-transformer coupling (Gamma Match, etc.)]
Note: this is only a overview of the most common methods. The list is not exhaustive.
The most common coupling method is using a small inductive coupling loop (a.k.a. matching loop). The main loop and the coupling loop form a (rather) loosely coupled transformer:
Fig. 18: Simplified equivalent lumped-element electrical circuit of an STL with inductive coupling
(coupling to ground and objects near antenna is not shown)
The turns ratio of this is inherently fixed (1:1), but there are several coupling loop parameters that affect the coupling:
- The size of the coupling loop. Its standard diameter is 1/5 that of the main loop. However, I have seen designs with 1/3 to 1/8 the diameter of the main loop.
- The shape of the loop. The standard shape is circular. Obviously, like the main loop, other shapes can be used (square, octagonal, ..). To obtain the desired coupling, the coupling loop can be squashed or stretched into a vertical oval or egg-shape. This changes the aperture of the loop (area of the "opening"), as well as the distance to the main loop, see Fig. 21 below.
- Placement along the main loop. Standard is opposite the tuning capacitor. However, to adjust the coupling, it can be moved off-center, along the main loop.
- Proximity to the main loop. Normally, the coupling loop is placed opposite the tuning capacitor, close to the main loop.
- Alignment with the main loop. That is: whether the plane of the coupling loop coincides with that of the main loop. The coupling with the main loop can be varied by turning the coupling loop about its vertical axis (from where the coax is connected to the point at the top of the loop), such that it sticks through the main loop. Instead of turning, it can also be bent.
- The gauge of the conductor - as with all coils / inductors.
- The operating/resonance frequency of the antenna: with increasing frequency, the optimal spacing (in terms of SWR) between coupling loop and main loop decreases.
A distinction is made between "un-shielded" and "shielded" coupling loops.
Unshielded coupling loops are very simple:
- A heavy gauge wire or small diameter copper tubing; the conductor need not be heavier gauge than the center-conductor of the feed-line coax. However, heavier conductor will help retain shape of loop, and make it self-supporting.
- I have used "extra heavy" single-strand (solid) installation wire of 2.5 mm2, but these days I use standard soft copper tubing of about 1/4 inch (6.35 mm) diameter in my large loop (see Fig. 79 below, and Fig. 139 & 140 for my "new and much improved" version), and thin brass tubing (see Fig. 9 of my small STL project). This is mechanically quite stable.
- With such a simple coupling loop, I obtain very good SWR (better than 1.1) over a frequency range of at least 1:2.5.
- The shield of a section of coax cable. The center conductor is left unconnected, or both ends of it are connected to the shield.
- The center conductor of coax, with outer insulation and braid fully removed. The dielectric material of the coax is kept, and provides rigidity.
Figure 19: Un-shielded coupling loops
(solid wire, braid of coax, center-conductor of coax)
One variation of this is a "tuned coupling loop", but is does not appear to be popular:
Figure 20: Un-shielded coupling loop with a tuning and a loading capacitor
Note that with the standard round coupling loop, the main loop and the coupling loop are close to each other, but only over a small part of the circumference of the coupling loop. Depending on the size of the coupling loop, better coupling (“lower SWR”) can sometimes be obtained when the coupling loop is stretched or compressed into a more oval shape:
Fig. 21: Stretching or compressing a round coupling loop to change the coupling with the main loop
A variation of this method is what I call the "coat hanger" coupling loop. It consists of insulated wire (e.g., installation wire, or even heavy enameled copper wire). The overall wire length is a little more than the diameter of the main loop. The coupling loop is symmetrically placed onto (and affixed to) the main loop, over a distance equal to 1/2 the main loop's diameter (i.e., ≈ 1/6 the loop's circumference). Rather than connecting the coax at the bottom, it is connected at the top of the feed loop. I.e., an upside-down wire loop. The wire ends are folded towards each other, joined and twisted over a distance of about 10-12 cm (4-5"; not critical), and connected to the coax. A current choke "balun" is placed near the coupling. The point where the wire ends are twisted, is moved up or down, to obtain the desired matching.
I have only briefly played with this coupling method. The antenna's resonance frequency varied quite a bit when the twisted connection to the coax was moved up and down. SWR was relatively flat over a significant frequency range - about 200 kHz, quite a bit wider than with a regular coupling loop.
This is similar to the triangular feed-loop of my (mono-band) spiral loop antennas, where the coupling loop has a circumference that is 1/8 that of the spirally-wound 1/4 λ main loop.
Figure 22: "Coat hanger" coupling loop
The coupling between the triangular coupling loop and the main loop can be made tighter, by winding the insulated wire of the coupling loop around the main loop, like Jo Lourenço (CT1ECW) has done for his 7-21 MHz loop (ref. 6M). This looks like a "twisted" delta-match. The same technique is used in the "twisted" gamma-match that is shown further below. Note that in the photo below, the turn-direction of the spiral changes at the midpoint (i.e., where the spiral passes through the wooden "mast"). This may be be counterintuitive, but is based on Jo's experiments...
Figure 23: Spiral coupling
(photo: ©Jo Lourenço (CT1ECW), used with permission)
The second type of inductive coupling loop is the shielded ( = screened) loop, often referred to as a "Faraday Loop". As with the unshielded coupling loop, the typical diameter is 1/5 that of the main loop (though some people have better results with a coupling loop as small as 1/8 the size of the main loop). For ease of construction, this coupling loop is typically made of a section of coax cable. In my experience, it is difficult to make such a coax loop mechanically stable, especially with thin coax (RG58, RG8,...) and a "Faraday" configuration ( = interrupted coax braid and center conductor).
There is number of variations that differ with regard to:
- whether the coax braid (= shield) is interrupted at the point half way around the loop,
- whether the center conductor is interrupted at that same point,
- how the braid and center conductor are connected at the starting point of the loop.
Figure 24A: Variations of shielded coupling loops
Figure 24B: Variations of shielded coupling loops (continued)
Let's have a closer look at variation D. The shield of the coax loop envelopes the flux that is created by the 1-turn coil formed by the center conductor of that coax. This induces a voltage across the looped shield. The maximum voltage occurs at the point where the shield ends. At the mid-point of the coax loop (i.e., at the top of that loop in the diagram), half of this maximum voltage is present. Hence, the loop as a whole, also has an average Vmax/2 with respect to ground. This coupling loop generates an electrical field that is primarily vertically polarized (assuming the coupling loop is installed vertically), This is coupled into the shield of the feedline. Conversely, this loop "receives" vertically polarized E-fields, incl. from the feedline (which may carry any disturbances that the transmitter passes to ground from its power supply and main power). This problem is solved in variation B (which is actually a half-shielded loop). Here, the left-hand and right-hand half of the coupling loop generate opposite ( = cancelling) voltages. In the vertical direction, the average is now zero. This eliminates receiving and generation of vertically polarized E-fields. Clearly, there still is reception and generation of horizontally polarized E-fields. In principle, both polarizations can be suppressed by opening the coax loop at the 3 o'clock and the 9 o'clock position, instead of only at the 12 o'clock position. See variation F. Ref. 6R.
CAUTION: the following configuration may be easy to build, but it does NOT work! There is no gap anywhere in the shield. It cannot be used to generate or receive an EM field! Some commercially sold loop antennas appear to use exactly this coupling loop configuration. However, on close inspection, they are constructed per, e.g., configuration B in Fig. 24A above. The shield gap, cross-over between coax shield and center conductor, and center conductor opening are hidden in the back of the coax connectors. This construction method significantly weakens the coax rigidity at those connectors. Which is why the coax entry into the connectors is typically reinforced with crimping, potting, and/or some type of glue.
Figure 24C: this configuration does not work!
The next two shielded loops are inherently balanced. Note that unbalanced coupling loops cause an asymmetrical radiation pattern of the main loop, even if positioned symmetrically with respectto the latter. Configuration G is another conventional "split loop". In configuration H, the center conductor of the coupling loop crosses-over to the shield on the opposite side of the gap. If you trace one of the terminal wires, it is clear that the signal goes around the coupling loop twice. Start, e.g., with the red terminal wire. Follow it via the first cross-over, then all the way around the shield, then another cross-over, and via the blue wire to the second terminal. This resembles a so-called "Möbius" strip. It is named after the 19th century German mathematician August Ferdinand Möbius (equivalently spelled as "Moebius"). This strip is a surface with only one side! In it simplest form, it is a strip of material, one end of which is twisted 180 degrees and then attached to the opposite end of the strip. The result is a loop with a twist. Hence, loop configuration H is also referred to a "Möbius (strip) loop". Note that the two-turn signal path doubles the (very small) path delay time. As a reception loop, the voltage across the terminals is double that of configuration G. See ref. 15A-15G.
Figure 24D: Balanced shielded coupling loops
To connect the above balanced coupling loops to a coax feedline, a 1:1 balanced-to-unbalanced (Bal-Un) transformer must be used. The one shown in Fig. 24D comprises 11+11 bifilar turns on an FT-240-43 ferrite ring (an FT-140-43 should be fine upto 100 W or so - once the main loop is tuned!). I used 2x0.75mm2 twin-lead wire (≈ 18 AWG) with relatively thin insulation, to maximize the number of turns. The green wire in Fig. 24D connects the shield of the coupling loop to the shield of the feedline coax.
Note that a coupling loop is not used anywhere near its own resonance frequency - which is much higher than the maximum resonance ( = operating) frequency of the main loop. Due to its particular configuration, the resonance frequency of a Möbius loop is half that of a same-size conventional loop. In an STL, this is irrelevant.
Figure 24E: Balanced shielded coupling loop - fed by (unbalanced) coax via a 1:1 BalUn
I made this coupling loop with 7 mm coax cable. This cable is fairly stiff, but the gap at the top and the feed point must absolutely be stabilized and fixed in place. I cut the required pieces out of section of a rigid PVC angle profile. A strip of 3 x 20 mm of PVC provides the vertical support to retain the round shape of the loop. The gap area is fixed to a small angle piece with cable ties (tywrap). See Fig. 24F. At the feed point, the cable is also fixed to an angle piece, with 2x2 cable ties. This loop could be weatherized by brushing generous amounts of "liquid electrical tape" on the stripped coax parts at the gap and the feed point.
Figure 24F: Construction details of my experimental balanced feed loop
I tested the above coupling loop configuration (with and without the green wire) early December of 2019, using my standard unshielded loop as a reference. I could achieve the same low SWR (close to 1) with both. However, I did have to re-tune the loop with the tuning capacitor. When receiving, I could not detect a difference in the background noise level. When transmitting (using a Web-SDR as a remote receiver), I could not detect a difference in signal strength.
For the same diameter, the unshielded and the various shielded coupling loops all have a different self-resonance frequency (easily measured when not coupled to the main loop).
Jochen Huebl (DG1SFJ) has done some interesting comparative measurements with an unshielded coupling loop, and with shielded coupling loop variations D and E (ref. 6A). The coupling loop (in his case: 16.5cm (6.5"), 1/5 the diameter of the main loop) was placed in the same plane as the main loop, opposite the tuning capacitor. He then varied the distance d between the two loops: starting with the coupling loop against the main loop (with some insulation between them), then moving the coupling loop closer to the center of the main loop (max 10 cm / 4 inch). See the figure below:
Figure 25: The experiment of Jochen Huebl (DG1SFJ)
As the induced magnetic field decreases with distance, the coupling between the two loops becomes weaker when the distance is increased. Note that it basically makes no difference whether the coupling loop is inside the main loop or outside. Jochen's observations are:
- SWR increased linearly with the distance between the coupling and main loop (from close to 1:1 to ca. 5:1).
- Lowest SWR was obtained with the coupling loop closest to the main loop.
- The shielded coupling loops had slightly better SWR than the unshielded coupling loop.
- Network parameter S11 is the magnitude of the Reflection Coefficient, expressed in dB. That is, S11 = +20 x log(abs(Γ)), where Γ is a complex number (a vector entity). It has a magnitude that is commonly denoted ρ, and a phase angle θ. S11 is 0 for a full reflection and negative for everything else. "Return-loss" is simply that same dB value of S11, but with the opposite sign (at least for passive devices such as antenna systems). "Return loss" does not mean loss due to reflection ( = "return"), but rather means loss of reflection! Jochen observed that S11 increased rapidly when the distance was increased from 0 to 2-3 cm (1"), then became more flat with further increase in distance. Over the initial distance increase, his shielded coupling loops had better coupling: S11 was more negative by about 6 dB ( = return-loss decreased by 6 dB). See the figure below.
Figure 26: Return-loss S11 as a function of distance between coupling loop and main loop - for a given frequency
(source: ref. 6A)
The main loop and the coupling loop basically form an air-core transformer. Some literature claims that the transformation ratio only depends on the ratio of the surface area of these two loops. As shown above, this is simply not true - unless the two loops are round, concentric, and co-planar ( = lie in the same plane), and the loop-current is uniform around the loop's circumference. Ref. 6Q.
Note that if the coupling loop is too large, moving it away from the main loop may improve the SWR. Likewise, if the loop is too large, coupling may be improved ( = SWR lowered), by turning the coupling loop about its vertical axis, such that it no longer lies in the same plane as the main loop:
Figure 27: Turning the coupling loop about its vertical axis to change the coupling with the main loop
This rotation can actually be motorized with remote control (see this section further below), to maintain low SWR over a larger frequency range than is possible with a fixed-angle coupling loop. Assuming that the radiation pattern of the antenna is symmetrical, then the motor drive only has to be able to rotate the coupling loop about its vertical axis over 90° max, Actually, the required rotational range will be a lot less than 90°: when the two loops are close to perpendicular, the coupling will not be good. Note that asymmetrical coupling methods such as the Gamma Match make the radiation pattern somewhat asymmetrical. Objects close to the antenna may have the same effect.
The SWR changes, if the installation height of the STL is changed. The next diagram shows SWR curves for my 80-20 STL, with a shielded coupling loop and with an unshielded coupling loop. The shielded coupling loop is made of generic "5D-2V" 50 Ω coax with a 7.3 mm outer diameter and shield configuration "E" in Fig. 24B above. The unshielded loop is made of 1/4 inch (6.35 mm) diameter soft copper tubing. Both coupling loops have the standard 1:5 size of the main loop. As use this antenna primarily for 80m, the position of the coupling loop was adjusted for that band. I measured SWR curves for both coupling loop types, with the bottom of the main loop at 75 cm (3.5 ft) above ground level (AGL). In my case, "ground" is my tiled terrace. The shielded coupling loop appeared to offer no advantage regarding SWR, and I also could not detect a reduction in received noise level. So, curves taken at 2m (6.5 ft) and 4m (13 ft) are only for the unshielded loop.
Figure 28A: SWR plot of my second STL antenna (80-20), with shielded and unshielded coupling loop
When going from 75 cm to 2m AGL, the coupling loop had to be slightly adjusted ( = rotated a couple of degrees more out of the plane of the main loop). Again, when going from 2m to 4m AGL. Also note that - for this size & type of coupling loop - the minimum achievable SWR increased slightly, when increasing the installation height.
The next diagram zooms-in on the 80-40 mtr part of the above diagram:
Figure 28B: SWR plot of my second STL antenna (80-20), with shielded and unshielded coupling loop
The capacitive coupling methods basically consist of one or two tuning capacitors, and one or two loading capacitors. This suggests that there are several configurations, as is indeed the case. This type of coupling is much "tighter" than with the coupling loops described above. This may make the antenna system more effective, even though the "Q" of the loop is reduced.
Figure 29: Capacitive coupling methods
Configuration B in the figure above is referred to as the "Patterson loop" (ref. 6B, 6P) or "Army loop". It was used in overseas adventures of the US army in the 1960s. The octagonal loop for 2-5 MHz consisted of 5 ft (1.5 m) sections of aluminium tubing (diameter: 1.75 ", 4.5 cm). The ends of the tubes were gold plated, to reduce contact resistance.
Figure 30: The tuning & matching unit of the "Patterson" Loop
(source: ref. 6B; note that tuning is done based on maximizing the antenna current, not minimizing SWR)
MAGNETIC TRANSFORMER COUPLING (FERRITE OR IRON-POWDER RING)
A simple transformer coupling can be made, by passing the antenna loop through a ferrite or iron-powder ring (toroidal core). The secondary side of the transformer is then formed by one or more turns of insulated wire. The coax cable is connected across the secondary winding. There are no adjustments or other manipulations required.
This coupling method only has a few simple variables:
- The type of ferrite or iron-powder core material.
- The size of the core.
- The number of stacked cores.
- the number of secondary turns.
There are many different ferrite material mixes. Most commonly used in STL transformers are Amidon / Fair-Rite / Micro Metals mixes nr. 31, 43, and 61 (or equivalents from another manufacturer). Important parameters from the data sheets (ref. 7) are "Initial Permeability and Loss Factor vs. Frequency" and "Core Loss vs. AC Flux Density" curves. Note that the permeability of ferrites varies with the magnetic flux level. Hence inductance of a coil or transformer made of such material will change with the power level. Power handling of a loop with transformer coupling is often limited by core losses, rather than the voltage rating of the tuning capacitor. These core losses (primarily hysteresis loss and eddy-current loss) roughly increase with the square of the flux density in the core, at any frequency. Some recommendations:
- Mix 43 becomes quite lossy above about 7 MHz. Use this material mix for 80-40 mtrs, possibly 80-30.
- Below 5 MHz, Mix 31 (a manganese-zinc mix) is probably a better choice than type 43 (nickel-zinc mix).
- To cover 20 mtrs and above, use material Mix 61 (nickel-zinc-iron mix).
Note that properties of ferrite cores may vary as much as 30% from the nominal values in the data sheets! Also, there are not homogeneity specs for ferrite material, and hot-spots may occur at power levels below the maximum.
Obviously, the ferrite core must be large enough for the ring to be slid over the loop tubing and accommodate the required number of secondary turns. More importantly, ferrite RF transformers must be operated at a core flux-density level that is commensurate with the volume and cross-sectional area of the ferrite ring. Conversely, the core dimensions should be adequate for the power level and frequency. The maximum allowed flux level is driven by the loss-tangent ( = dissipation hysteresis loss factor) of the ferrite mix. If that flux density limit is exceeded, then a runaway effect causes the core temperature to rise very quickly and ultimately (and possibly violently) destroy the core! Note that mix "61" has a Curie temperature (above which the ferrite properties are permanently destroyed) that is much higher than that of type "43": 350 °C (660 °F ) vs. 150 °C (300 °F). Two or more cores can be stacked to increase power handling capability. However, stacking cores also increases the total inductance of the transformer. Furthermore, a larger core also results in larger inductance, compared to a smaller core of the same material. E.g., a T-240-43 toroid (2.4 inch outer diameter, material type 43) has a higher AL value ( inductance in μH per 1000 turns) than an FT-140-43 (1.4 inch OD): 1075 vs. 885. Experiment! Very small cores such as T-82 or T-130 are basically limited to QRP operation.
As it is a 1:N transformer for voltage and current, N (the number of secondary turns) has to be chosen such that 50 / N2 = impedance of the loop at the point where the transformer is installed on the loop. N is typically determined empirically, by trial-and-error: start with a number that is too high, measure SWR at resonance, then reduce by one or two turns at a time. In a small transmitting loop, the current is basically constant around the loop circumference. This is illustrated in the introduction section at the top of this page. So it does not make much of a difference where the transformer is placed around the loop. However, if the loop size is increased to, say 0.2 - 0.25 λ, the loop is no longer "small", and the current through the capacitor is significantly smaller than the current at the point opposite the capacitor. This means that the coupling with a ferrite core transformer then does depend on where the transformer is placed along the loop. The turns of the secondary winding should be spread out evenly around the ferrite ring, to minimize parasitic capacitance.
One of my first experiments with the transformer coupling was with an 1:1 transformer comprising an T-140-43 ferrite core and a single-turn coax loop. See the figure below. This configuration puts the 50 ohm impedance of the coax feed line in series with the very small loop impedance. This results in significant mismatch. I tried this, and found a low SWR over the entire frequency range of interest, but a bandwidth that was at least an order of magnitude larger than when using multiple wire windings. Still to be explained...
Figure 31: A 1:1 ferrite transformer-coupling with coax loop as secondary winding
Figure 32: A 1:N transformer coupling with a ferrite core
The two graphs below show my measurements for my three STLs, with ferrite material mix nr. 43 and 31 transformer cores:
Figure 33: SWR plot of my first STL antenna (80-20), with a ferrite transformer core FT-140-43
The next diagrams shows SWR-sweeps of my second STL antenna (80-20) with an T-240 ferrite ring of matarial mix #31 and with 8-18 turns of heavy insulated copper installation wire (1.5 mm2 cross-sectional area, 16 AWG):
Figure 34A: SWR plot of my second STL antenna (80-20), with a ferrite core FT-240-31
I use this antenna almost exclusively on 80 mtrs, so I settled on 17 turns of wire. "Key down" with 100 watts for 1 minute did not cause the ferrite to heat up at all, for resonance frequencies where SWR is better than 1.2. For 40 mtrs, I use 9 turns. The next diagram zooms-in on the 80-40 mtr part of the above diagram:
Figure 34B: SWR plot of my second STL antenna (80-20), with a ferrite core FT-240-31
Note that in Fig. 34A/B, the resonance frequency range with an SWR < 1.15 is (only) about 750 kHz wide: single-band. Also, the curves were recorded with the bottom of the big loop about 75 cm above the terrace floor. When increasing the height of the loop, the position of the curves changes and the number of turns may have to be adjusted (+1 or -1).
Of course, I also tried a ferrite transformer coupling with my small STL (40-10 m):
Figure 35: SWR plot of my third STL antenna (40-10), with ferrite cores FT-140-43 and FT-240-31
Lásló Rusvai (DL2JTE/HA7HN) has done extensive testing with the transformer coupling (ref. 6C/D). One of his initial loops has a diameter of 1.2 m (4 ft) and is made of 20 mm (3/4") OD copper tubing. Using a T200-2 iron powder core and 2 secondary turns, he obtained SWR = 1.01 over a frequency range of 3.5 - 10.1 MHz. He also confirmed that with an STL antenna, the position of the transformer along the loop circumference makes no difference - for this size loop and frequency range. Note: I ran a very quick test with an T-200-2 core on my second STL, but with less than 10 turns, SWR was at least 20!
An other 80-and-up loop that he tested, has a diameter of nearly 3 m (10 ft) and is made of thin copper wire (0.4 mm Ø, AWG #26). With a single ferrite core, he could not get SWR below 1.2. He obtained wide-band coupling (SWR < 1.1) with a stack of 9 ferrite cores of type T-240-61 cores (size FT-140 OK when not QRO). Eight of the cores are tightly stacked on the loop, the 9th core is only on the two secondary turns. See the diagram below. Note that he furthermore attaches a dipole across the tuning capacitor.
Figure 36: Transformer-coupling per Lásló (DL2JT/HA7HN)
(source: ref. 6C/D)
Another variation on the toroidal transformer coupling is using a small number of primary windings, instead of just a single one. I.e., an N:M transformer. This requires the loop to be opened and the primary windings to be connected across the gap. For a loop made of copper tubing, the transition to wiring may not be great. But I have no experience with this, nor references regarding its performance. Joe (W9SCXH) used 2 primary and 5 secondary turns on a small ( = QRP) T-50-2 (iron powder) core in his 30-15 mtrs square wire loop (ref. 6F).
Figure 37: N:M transformer coupling with a ferrite core
WARNING: if you are experimenting with various forms of coupling, do NOT leave a ferrite ring on the loop and transmit via another coupling (e.g., a coupling loop, Gamma rod, or ferrite transformer). Any unused ferrite ring will act like a current choke, and will get fried if you transmit with more than QRP (you will see the SWR increase when that begins to happen). Another clear symptom is that the SWR=2 bandwidth will be much larger.
AUTO-TRANSFORMER COUPLING (GAMMA MATCH, ETC.)
Recall the voltage and current distribution of an STL antenna, as discussed at the top of this page:
Figure 38: Voltage and current distribution of an STL antenna
Clearly, the voltage distribution is symmetrical with respect to the neutral point (V = 0) that is located opposite the tuning capacitor. In an STL antenna, the current distribution is basically constant. Resistance (impedance) is voltage divided by current. Hence, an STL has a resistance "distribution" that looks like the voltage distribution. The neutral point is a convenient reference point. If we move along the loop circumference, away from that reference point, we will find a point at which the resistance is 25 Ω with respect to the reference point. There is a similar 25 Ω point on the opposite side of the reference point, at the same distance from that point. Moving further away, we will find a symmetrical pair of 50 Ω points. This (admittedly simplistic) description suggests some simple methods for coupling the loop to an asymmetrical/unbalanced feedline (i.e., coax) or to a symmetrical/balanced feedline (twin-lead, ladder line).
When using a coax cable as feedline, we need an asymmetrical tap on the loop. The shield of the coax is connected to the neutral point of the loop. The conductor of the coax is connected to a so-called Gamma Rod. The rod is installed parallel to the loop. At some distance from the neutral point, the rod is connected to the loop. The tap is typically made adjustable, to be able to tune the effective length of the rod. This method also does not have the operating power limitations that are typically inherent to components of the transformer and capacitive coupling methods. This coupling method is wide-band: reportedly as much as 10:1, if the antenna installed sufficiently clear (15-20 ft, 5-6 m) from any objects and at least 1/2 loop diameter above ground). but the exact location of the tap point does depend on the frequency. In my own experiments, I have not obtained acceptable SWR ( less than 1.5) over more than a 2:1 frequency range.
- The Gamma Rod adds inductance to the coupling. In a Gamma Match coupling, there normally is a variable capacitor in series with the rod, to cancel out that inductance. Ref. 6G, GH, 6J. In "magetic loop" applications, this compensation capacitor is typically omitted. However, a small series capacitor (several pF) may significantly increase the frequency range over which low SWR is obtained.
- As the Gamma Rod configuration is asymmetrical, the radiation pattern is slightly skewed, causing a front-to-back ratio that slightly favors the direction of the Gamma Rod mount.
- Contrary to the inductive coupling and transformer coupling methods discussed above, this coupling is galvanically connected to the antenna loop.
Figure 39: Gamma Rod coupling
In my first loop, I decided to insert a copper T-piece at the neutral point, just in case I ever wanted to play with a Gamma Rod. The T-piece is for 16 mm OD copper tubing (my loop), whereas the side connection is for 10 mm OD copper tubing. The latter is perfect for a female BNC chassis-mount jack. I drilled a hole opposite the BNC connector. A 1 m (3ft) section of heavy, insulated household installation wire is soldered to the BNC connector and passed through the hole that I drilled. That serves as Gamma Rod. A hose clamp (UK: "jubilee clip") can be used to fix the end of the wire in place at the tap point.
Figure 40: Copper T-piece - inserted into the main loop at the neutral point - with BNC connector
Ref. 6N provides following nominal dimensions for the rod and the tap point:
Figure 41: Nominal dimensions for the Gamma Rod coupling
(source: adapted from ref. 6N)
Instructions for adjusting/tuning a Gamma Rod/Match are deceivingly simple:
"Change the size, shape, material, position with respect to the loop, and the tap point of the Gamma Rod
along the loop, until the desired impedance matching is obtained"
This is not all that surprising, as the position tap point depends on characteristics of the Rod: length of the bar/wire/tubing, diameter of the rod, shape of the loop formed by the rod and the loop, center-to-center spacing between the Rod and the loop, etc. See ref. 6H and 6J, considering the main loop as a circular folded dipole that is terminated with the tuning capacitor. The position of the tap point also depends on the loop and its construction. In general, the lower the Q of the loop is (e.g., due to losses in solder joints), the farther away from the neutral point the tap point will be. Converesely, the higher the Q, the closer the tap point will be to the neutral point, and the more sensitive the position of the tap point will be: moving the tap just a couple of mm (≈ 1/8 inch) may make a difference!
This basically means that finding the "sweet spot" for the tap point is pretty much 100% empirical. This is why there appear to be as many settings as there are antenna builders, and settings vary widely. Here are some examples that I have collected from designs posted on the internet (only very few indicate sufficient details to reconstruct the actual design):
- Some literature suggests the tap point at "main loop circumference / 10" from the center point, and the rod at a distance of "main loop circumference / 200".
- Tap point at "loop circumference divided by 15.8" from center point; rod is 1/4" diam. copper tube, 2⅜" (6 cm) distance from the loop(diam. 3½ ft); started half-way up the loop (i.e., 1/4 circumference from the neutral point), final tap at 8.375" (≈ 21 cm).
- Tap point at "loop circumference divided by 10" from the neutral point; rod at distance of 0.5% λ from the loop.
- Tap point at "loop circumference divided by 10" from the neutral point; rod at distance of 20 cm (8") from the loop. Loop circumference 2.4m (8 ft), rod length 23 cm (10"); 20m loop.
- Tap point at "loop circumference divided by 8" from the neutral point.
- Tap point at "loop circumference divided by 11.4" from the neutral point ; rod at distance of 7.6 cm (3") from the loop with 20 ft (6 m) circumference..
- Tap point at "loop circumference divided by 7" from the neutral point; rod is 12" of 1/8" wire, spaced 1" (2.5 cm) from the loop made of 5/16" (8 mm) copper tubing.
- Tap point at "loop circumference divided by 4.3" from the neutral point.
- Tap point at "loop circumference divided by 10" from the neutral point; rod is 12" log, parallel to main loop at 1" distance
- Tap point at "loop circumference divided by 4" from the neutral point; rod is 9"
- Loop diameter 1 meter, rod length 31 cm, rod spacing 11 cm
- Tap point at "loop circumference divided by 10" from the neutral point. Loop circumference 4m (13 ft), rod of 8 mm Ø copper tubing, parallel to main loop at 8 cm (3.25") distance.
The Gamma Rod construction itself can also be considered as a kind of loop. If the end of tap point is chosen relatively close to center point (where the coax braid is attached) but we retain the size (area) of the loop, we end up with the Hairpin (stub) Match (a.k.a. Beta Match).
Figure 42: Hairpin coupling
Yet an other variation is the "Twisted" Gamma Match (a.k.a. "Mu-Gamma" or "G3LHZ-Gamma", ref. 3B (pp. 12, 13, 20) and 6K). I have no suggestions regarding the total length of the wire and the number of turns.
Figure 43: Twisted-Gamma coupling
If a Gamma Rod is installed on both sides of the neutral point, we have a T-Match It can be used with a 2-wire feedline.
Figure 44: T-match coupling
The T-match can also be used in combination with an N:M transformer, to connect to a coax cable. But this should actually not be necessary, if the T-Match dimensions are adjusted correctly...
Figure 45: T-Match coupling combined with N:M transformer
SOME ANTENNA SIMULATION MODELING
"Models are always wrong, but some are useful" (George E.P. Box, statistician, 1976)
Out of curiosity and for fun, I ran some antenna radiation pattern simulations with the excellent 4NEC2 freeware simulation package. Simulations were done for a generic loop with a diameter of 2 m (6 ft 7 in), with a standard coupling loop that is 1/5 the size of the main loop. Simulations were repeated for various configurations of a vertically oriented loop: tuning capacitor at the top vs. bottom, coupling loop opposite the capacitor vs. next to it, and feed-point of the coupling loop towards the center of the main loop vs. right next to the main loop. No optimizations of the coupling loop position were done. In these models, the loops are modeled as 18-side polygones. It is also possible to model loops as a 1-turn helix with a pitch that is slightly larger than the diameter of the loop conductor. I did not run tests to compare the various approaches and modeling techniques
The simulation models that I used, were adapted from the ones created by Carol Milazzo (KP4MD), ref. 16A. Adaptations include 1) making installation height a variable parameter, and 2) using conductor diameters as used in my own antenna: 12 mm (≈1/2 inch) copper main loop, 6.35 mm (1/4 inch) copper coupling loop, rather than 2 mm diameter default wire. My adapted NEC files are provided as ref. 16B.
NOTE 1: the simulations are without any objects anywhere - just the antenna at a certain height above ground that has standard average conductivity and dielectric constant. This is absolutely not the case at my QTH, as shown in the "Placement of the antenna" section. The simulation also does not account for coupling between the capacitor and the environment, etc.
NOTE 2: I ran into error messages for the coupling loop, when running the model for the 80 m band. This is due to the tool's minimum segmentation length limit of λ/1000 (≈ 8 cm ≈ 3 inch in the 80 m band). There are also models floating around that do not simulate a coupling loop, but simply define a voltage source point that is located somewhere around the main loop.
Fig. 46A: 3D radiation patterns for Antenna Configuration #1
Upto an installation height of around 1/4 λ, the radiation pattern does not change a lot. Of course, this is not the case when buildings, trees, and other objects are near the antenna location!!!
Configuration #2 is simply Configuration #1 upside-down. The radiation patterns are similar, but not identical!
Fig. 46B: 3D radiation pattern for Antenna Configuration #2
As always, dimensions and spacing relative to wavelength are of prime importance. An interesting thing happens with the simulation model of Configuration #2, when the main & coupling loop conductor diameter is reduced to the 2 mm (radius = 1 mm) of the original model. With this reduction, the 3D radiation pattern for 28 MHz at 1.5 m is then aligned with the plane of the main loop, instead of at 90° to it! It flips 90°, when the loop-center height parameter is increased to around 2 m, which happens to be the loop diameter. I have no explanation (yet) for this behavior... In Fig. 46A, antenna configuration #1 has the coupling loop at the top, where it is already above 2 m when the loop-center height is still at 1.5 m.
This is all just playing with the model... The results are not all that different from my (short) dipole simulations for various operating frequencies ( = dipole size vs. wavelength) and installation heights.
MY FIRST SMALL TRANSMITTING LOOP
As with all antennas, the efficiency depends on the radiation resistance. For an STL, the radiation resistance at a given frequency is proportional to the square of the surface area. So, bigger is better. For a given circumference ( = total length of copper tubing), a circular loop has the largest surface area of all shapes. However, I have no access to a tube/pipe bender, and annealed (heat treated) copper tubing is quite hard and stiff. So I decided to build an octagonal loop instead of a circular loop. But as derived below, a circular loop has a surface area that is only about 5% larger than an octagonal loop with the same circumference ( = linear length of the required material such as wire or tubing). For a square loop, the difference is larger: for the same circumference, a circular loop has a surface area that is about 27% larger ( = factor 4 / π ) than that of a square loop.
For a circle with radius R and diameter D:
For an octagon with side L:
After some basic manipulations, we can derive that for equal circumferences ( = total length of the copper tubing), the circular and octagonal loops basically have the same surface area:
Note that the radiation resistance of an STL increases with the square of the loop area surface. For the same circumference, a round loop has a radiation resistance that is 1.0552 = 11% larger ( = better) than the octagon!
However, that is not the entire story. Clearly, maximizing the surface area is rather important. Typically, we have room for a "loop" with a certain width and height. Let's take the simple case where "maximum width" and "maximum height" are the same. In this case, a square loop will have the largest possible surface area. Obviously this is not the shape with the smallest circumference - that would be a round loop. However, a square with a standard construction has soldered, braised or welded elbow-joints at the four corners, which may introduce loss resistance that a single-piece round loop does not have. For a given width = height = D, and all else remaining equal, we obtain the following surface areas and relative radiation resistances.
Based on that, the square loop would have the largest radiation resistance (but the loss resistance mentioned above does factor into effciency...). Just to keep in mind.
Anyway, I decided to make a loop with a circumference of about 5 mtrs (16 ft). The resulting octagon is then 1.5 mtrs tall and wide (5 ft). This size is quite manageable, but the circumference is sub-optimal for 80 mtrs: only about 0.06 λ. Note that the connections between the loop and the capacitor increases the circumference, but hardly the loop's surface area. The cross-shaped support is made of standard PVC tubing. The "mast" fits in my heavy cast-iron umbrella stand.
Figure 47: The construction concept of my first STL antenna - 1.5 m (5 ft) high & wide
An octagonal loop requires nine sections of straight copper tubing. They are connected with copper elbow-pieces - no bending required. Note: industry standard is to refer to the outer diameter when talking about tubing, and the inner diameter when referring to a pipe. Just so you know, hihi.
Figure 48: The "plumbing" parts of my STL antenna (tubing, elbow pieces, T-piece) and a cutting tool
Here are the copper components of this loop (all European standard 16 mm outer diameter (OD), ≈ 5/8 ich):
- 7 sections of copper tubing, each 62.5 cm (24.6") in length
- 2 sections of tubing, each 29 cm (11.4") in length
- 8 elbow pieces, 45º, female-to-female, for 16 mm OD tubing
- 2 elbow pieces, 90º, female-to-male, for 16 mm OD tubing
- 2 reduction pieces, from 16 mm to 10 mm OD (to connect tube to braid to capacitor)
- 1 copper T-piece,2 x 16 mm ID, 1x 10 mm ID (for Gamma Rod coupling as described above)
Figure 49A: Terminating of the ends of the loop, for connection to the capacitor
("spark" gap between the elbow pieces above must have at least the same voltage rating as the capacitor: here: 10 kV)
Components for connecting the tuning capacitor to the loop:
- 2 stainless steel hose clamps (UK: jubilee clips), large enough for the end-caps of my vacuum capacitor (6 cm OD, 2.4")
- 2 x 25 cm (10") thick & wide copper braid (also available from automotive supply store, as ground strap for car batteries). Alternatives: silver-plated 2-layer braid from large-diameter coax, or heavy multi-strand copper wire (e.g., AWG #4)
Figure 49B: Heavy multi-strand wire and hose clamps for connecting the loop to the capacitor
Components for the mounting plate of the capacitor:
- 10x12 cm (4x5")polyethylene cutting board, 8 mm (5/16") thick - from the kitchen.
- 2 bolts, M6, stainless (long enough to pass through the board + 2mm thickness of the 63 mm OD PVC + lock nut).
- 2 washer,6 mm ID.
- 2 self-locking nuts, M6, stainless.
- 4 large tie-wraps (cable ties). For some reason, black ones (tie-wraps that is), generally hold up better in sunlight than white ones...
Figure 50: The components of the mounting plate for the vacuum capacitor
The vacuum capacitor "bottle" is not a cylinder. I used a grinding bit to carve out recesses in the cutting board, for the shape of the "bottle". I also cut 2 x 2 slits in the board, to pass the tie-wraps through the board. Well, I actually drilled a series small holes for each slit. Each pair is spaced less than the width of the capacitor (10 cm), to be able to get the tie-wraps to pull the bottle tighter onto the board.
Figure 51: The components of the mounting plate for the vacuum capacitor
Components for the mast and the cross-braces:
- 2 mtr (6.6 ft) PVC tubing, 63 mm OD (2.5") - mast
- 1.75 mtr (5.7 ft) PVC tubing, 32 mm diameter OD (1.25") - main cross-brace
- 2 sections of 40 cm (16") PVC tubing, 32 mm diameter OD (1.25") - top & bottom supports
- 6 snap-in clamps for 14 mm OD tubing (yes, tighter than the 16 mm OD of the copper)
- 6 M6x45 bolts for the clamps (long enough to pass through the 32 mm OD PVC tubing and into the nut of the clamp)
Figure 52: One of the six tube clamps
Initially, I tried to braze the copper elbow pieces to the straight copper tubing with a household propane/butane blowtorch and plumber's silver solder. Such a blowtorch just doesn't generate enough concentrated heat. So I took my pieces to a friendly neighborhood plumber, who used his oxy-acetylene blowtorch. Much better! I did do some pre-planning, and put the roof rack on the car, to bring the assembled loop back home!
Figure 53: Propane blowtorch
Obviously, an acetylene + oxygen blowtorch will do a much better job than a propane blowtorch: you can weld with it, instead of just solder. However, they are very expensive and you typically cannot rent them. But you pay a local welding shop to do it, or ask a friendly plumber (which I ended up doing).
Figure 54 The back side of the capacitor mounting
(the hole in the mast is for inserting a socket wrench for tightening the nut on the bottom bolt of the capacitor mounting board)
Fig. 55: Close-up of the capacitor connection wire, brazed to a copper reduction piece on the loop-ends
Figure 56: Close-up of the hose-clamp with the heavy wire brazed onto it
Figure 57: Commercially produced mounting clamps for a vacuum capacitor
Figure 58: The vacuum capacitor mounted at the top of the mast
Figure 59: My first STL, erected on my terrace. Beautiful at any time of day or night, hihi
Figure 60: Another picture of this STL.
(it's the umbrella stand that is tilted, not my STL. I finally took the grinder and fixed that late 2015)
Fig. 61: My miniVNA - a tiny antenna analyzer for 0.1-180 MHz, with USB connection to a PC
As I had several FT-140-43 ferrite cores in stock, that is what I used. These cores have an outer diameter (OD) of 1.40" and an inner diameter of 0.9" (≈ 23 mm). This is large enough to slide over a tube with 16 mm (5/8") OD, and still have room for about 16 windings of insulated heavy installation wire of 1.5 mm2 (AWG 14-16). The G4FGQ calculator (ref. 2D) predicts that my loop would require 24 secondary windings at 3.5 MHz, and 8 at 14.230 MHz - for a ferrite core of "suitable grade". K3JLS (ref. 6E) uses 3 turns of 14 AWG enameled wire on an FT-240-43 core for his 40-20m loop. AA5TB (ref. 8A) used 2 turns on his 30 m loop.
Figure 62: Coupling transformer: FT-140-43 ferrite core with 8 & 14 secondary turns
(bottom of the antenna loop is placed 80 cm (2.5 ft) above ground)
The above plots suggest that workable SWR ( < 1.5) can be obtained over a 2+:1 frequency range. However, I'd like to have 4:1, to cover 80 - 20 mtrs...
The curve below shows that for maximum capacitance (500 pF), the resonance frequency is 3064 kHz; with minimum capacitance (15 pF) it is around 15.8 MHz. This range covers 80-20 mtrs and is larger than what the various calculators estimated - suits me fine! Note that the connections between the loop and the tuning capacitor do add to the size of the loop.
Fig. 63: Coupling transformer: FT-140-43 ferrite core - same curve for 8 & 14 secondary turns
As the resonant loop is an LC-circuit, the resonance frequency varies with the square-root of the tuning capacitor's value. My capacitor has a 15-510 pF = 1:34 capacitance range. As shown above, I measured a corresponding resonance frequency range of about 3-15.8 MHz = 1:5.2, whereas the expected resonance frequency range would be 1:√34 = 1:5.8; the difference is explained by the accuracy of the capacitance measurement and the loop's parasitic capacitance. Loop calculators (such as ref. 2A-2E) estimate that this parasitic capacitance is often of the same order of magnitude as the minimum value of a tuning capacitor. Note: read ref. 2F for caveats about mag loop calculators.
The plot below shows that towards minimum capacitance, the capacitance does not vary linearly with the capacitor's shaft position: the frequency-vs-capacitance curve is no longer quadratic. This is caused by edge effects in the vacuum capacitor, when its concentric plates have little or no overlap.
Fig. 64: Non-linear change in resonance frequency vs. varco shaft position
(coupling with FT-140-43 ferrite core)
The "Q" (Quality) factor depends inversely on the bandwidth. It is a measure for how lossy the resonant circuit is: peak energy stored in the circuit, divided by the average energy that is dissipated per cycle, in the circuit at resonance. This can be expressed as:
where BW is the normalized bandwidth for a given SWR (referenced to SWR=1 at fres). E.g., the bandwidth between the "half power" frequencies ( = the -3 dB frequencies) is the bandwidth between the SWR = 2.62 frequencies. The plot below shows both bandwidth and Q for the ferrite transformer coupling with 14 secondary windings. The bandwidth varies from 6.8 kHz around 3 MHz, to 50 kHz around 15 MHz. The associated Q varies from 450 to 300, with a maximum of 600 around 5 MHz.
Fig. 65: Bandwidth & Q - transformer coupling with FT-140-43 core and 14 secondary turns
I built this STL primarily for DX on 80 mtrs. To test antennas by myself, I typically use remote receivers on the internet: Web-SDRs. The screenshots of the waterfall display of a Web-SDR in The Netherlands (my QTH is in the south of France) clearly showed my signal:
Fig. 66: My carrier, visible (with some fading) in the waterfall display of a Web-SDR 80 at a distance of 1000 km (600 miles)
(19-Oct-2010 ,19:00 local time,80 watt)
Fig. 67: Same conditions as above, but now sending a series of "E" characters in Hellschreiber mode
The Web-SDRs have audio. So, when operating in a digital mode, you can print your own signals:
Fig. 68: My Hellschreiber signal, received on 80 mtrs by a Web-SDR receiver at a distance of 1000 km (600 miles)
(31-Oct-2010 ,17:00 local time, 80 watts; my signal received at the SDR-RX is in the magenta boxes)
In the above tests, the plane of the loop (not the opening of the loop!) was pointing at the remote receiver. When I turned the antenna 90 degrees, the S-meter of that receiver went down by roughly 2 points (12 dB). In November of 2010, I did some comparative receive tests with the loop and my short "Cobra" dipole (2x7 m). A coax relay allowed quick A-B switching. The loop was noticeably quieter than that dipole, and a couple of S-point stronger. I also ran some tests on 40 mtrs with my dear friend Rolf, DF7XH, at a distance of 750 km (465 miles). With all my other antennas (short dipoles and short verticals), we only have marginal communication at best. This time it was FB and 59+ in both directions.
I also did a quick experiment by installing the loop horizontally. It appeared rather "deaf" on 80 mtrs, since it is installed at only 2 mtrs ( = 0.025 λ) above ground, and the ground is "poor" (concrete). As I am not interested in local QSOs, I did not pursue this.
Figure 69: My STL, installed horizontally
The mast of my STL is installed on top of another PVC mast with a PVC T-piece. I cut a slit into the T-piece, so it can be clipped onto the STL mast and still hold tightly, without needing to glue anything.
Figure 70: The modified PVC T-piece
MY SECOND SMALL TRANSMITTING LOOP
Some "lessons learnt" from my first loop:
- Reduce the losses in the loop by reducing the number of joints: bend long copper tubing into a circular or octagonal.
- Use a different method to connect the ends of the loop to the vacuum capacitor:
- After about a year and half after construction, the total DC-resistance of the copper part of the loop has not changed: still at 3.2 milliohm (measured with an HP4328A professional milliohm meter). Obviously, DC measurements say nothing about RF losses. However, even at DC, the resistance between the copper wire and the stainless steel hose clamps had increased to a little over 4 milliohms - per clamp! This kills the efficiency of the antenna. All loop calculators (ref. 2) will quickly show this, and I had already noticed a decline in performance over time. Note: read ref. 2F for caveats about mag loop calculators.
- As I am primarily interested in using this antenna for DX on 80 m, or 80-40:
- Increase the loop circumference from 5 to about 7 m (16 to 23 ft). I.e., from 0.06 λ to almost 0.09 λ on 80 mtrs. This is still well below the optimum 0.15 λ, but on 80 mtrs that optimum implies a diameter of 4 m (13 ft)! The increased size will double the area of the loop, and should more than double the efficiency of the antenna on 80 m!
- Try a Gamma Rod coupling, or change over to ferrite rings made of material type 31. This should be better than type 43 material for frequencies below 10 MHz.
- Simplify the attachment of the vacuum capacitor to the mast.
Obviously, I had to make an new loop and mast - which is what I did late 2012. This time, I used a 20 ft (6.1 meter) roll of soft copper tubing with an OD of 5/8 inch.
Don't make the mistake to assemble a loop of this size inside the house: it probably will not fit through a regular door. Don't paint yourself into a corner, hihi.
Figure 71: Diagram of my second STL
My second loop is (nearly) circular. I had my copper tubing bent by local company that makes railings for staircases and balconies. However, one can home-build a tube bender - but it will only work work soft tubing (which is "annealed" = heat treated), not hard drawn tubing.
Figure 72: A tube bender built by Roger Dunn (VK4ZL)
(description: ref. 10; photos and image used with permission)
Figure 73: A sturdy tube bender made by Twan van Gestel (PA0KV)
(photos used with permission; his large loop with motorized vacuum capacitor is described on his website [pdf])
Figure 74: An adjustable tube bender that I made for my third (smaller) STL
(note: my third STL is made of 12 mm (0.5") soft copper tubing)
I made clamps for the vacuum capacitor out of soft copper strip, about 2-3 cm wide (≈1") and 2-3 mm thick (≈0.1"). I have toyed with the idea of silver plating the copper loop and clamps to further reduce RF loss resistance (ref. 9A), but that may not be worth the effort (see half way down the page of ref. 9B). The clamps are dimensioned such that the inner circumference is just about 1-2 mm too small for the end-caps of the capacitor. This way, when I tighten the bolt of the clamp, it is nice and tight. I used stainless steel bolts and a heavy stainless washer on both side of the clamp. I squared the washers to make them fit better, and also to make them touch the full width of the circular part of the clamp. I (carefully) pinched the ends of the copper loop with a pair of vise-grip™ (locking) pliers.
Figure 75: Copper connecting clamp for my vacuum capacitor
The "bottle" of the vacuum capacitor is now attached directly to the mast, with two large tie-wraps. With my first STL, the tie-wraps were passed through slits in the mounting board. Here, they are passed through slits in the PVC mast. The tie-wraps do not full immobilize the capacitor. However, once the ends of the copper loop are attached to the clamps, the installation is quite stable.
Figure 76: My vacuum capacitor, attached to the mast and connected to the loop
I finished building the loop in January of 2013, and took some measurements with my miniVNA analyzer. I used an FT-240-31 ferrite ring for coupling. The first measurement, with a single secondary winding (just a wire stuck once through the ferrite ring), showed an impedance of about 10-12 ohms. So, I needed a 4:1 transformation ratio to get close to 50 ohms. I.e., a 2:1 current transformer. So I doubled the number of secondary turns to 2. I also added a 1:1 current choke right at the coupling transformer. The plots confirm the suitability of type 31 ferrite material for the lower frequencies.
Fig. 77: Coupling transformer: FT240-31 ferrite core with 2 secondary turns, 1:1 current choke at feedpoint
Fig. 78: Coupling transformer: FT240-31 ferrite core with 2 secondary turns, 1:1 current choke at feedpoint
Fig. 79: Coupling transformer: FT240-31 ferrite core with 2 secondary turns,1:1 current choke at feedpoint
I measured the following SWR values for various placements of the ferrite transformer around the main loop:
Fig. 80: SWR for several positions of the ferrite transformer around the circumference of my STL
(transformer: 2 secondary turns on FT-240-31 core, 3600 kHz,)
I also tried a standard 1:5 size coupling loop, made of standard 1/4 inch (6.3 mm) soft copper tubing. I mounted the coupling loop onto the 63 mm PVC mast with PVC clamps, so its position is easy to adjust up & down, and rotate around the mast. Initially, I had mounted the coupling loop with the BNC connector at the bottom, i.e., near the main loop. As I had the BNC connector on the outside of the coupling loop, the gap between the coupling loop and the main loop is rather large. SWR was good, but I wanted to get the most out of it. Instead of making a coupling loop with the BNC connector on the inside, I just turned the coupling loop upside down. Now the coupling loop could be placed very close to the main loop. Also see the coupling discussion around Fig. 25-27 above.
Figure 81: The two configurations of my coupling loop
(the BNC connector is mounted on a small aluminium L-bracket)
Note that in both photos above, the plane of the coupling loop is not aligned with the plane of the main loop: the coupling loop is rotated about the mast until lowest SWR is obtained. So, it sticks out both sides of the plane of the main loop. However, for minimum SWR, the angle between the two loops is larger in the photo on the right. This is to be expected, as the coupling is tighter. Had the coupling loop been slightly smaller, the required angle would also have been smaller.
I prefer this type of coupling loop to the ferrite ring transformer coupling methds. Reasons: easily adjusted, no power limits, larger frequency range.
With both configurations, SWR is quite good over a frequency range of at least 1 : 3 (in my case, 80-30m). The second configuration is basically perfect over that range. The small bandwidth confirms the very high "Q".
Fig. 82: SWR vs. frequency for the two coupling loop configurations - tuning capacitor at the top of the main loop
(position of the coupling loop was optimized for 80m; "BNC at bottom" vs. "BNC at top" only impacts distance between the coupling loop and main loop)
Figure 83: SWR vs. frequency in the 80m band
The table below shows the efficiency and "Q" of my loop, calculated with an on-line calculator (ref. 2G) for the measured SWR bandwidth shown in Fig. 81:
Figure 84A: Calculations based on measurements in Fig. 81
(calculator: ref. 2G)
With this particualr calculator, the resulting "Q" is 845 and efficiency is around 3.4%. Note that this calculator assumes that the antenna is placed in free space. I.e., far away from ground and objects. The calculator's default settings for the parameters "Rr/Rrfs" and "directivity" were used, rather than adjusting them for ground effects.
Based on the loop inductance (6.18 μH) and "Q" (845) as calculated above, and assuming 100 W transmit power, the peak voltage across the capacitor at the 3.583 MHz resonance frequency can be estimated with the following formula (ref. 2H):
For the same measured half-power bandwidth, the formulas in ref. 3E yield a "Q" of 833 and an efficiency of 7%, also for free space:
Figure 84B: Calculations based on measurements in Fig. 81
(source formulas: ref. 3E; MS Excel spreadsheet calculator: ref. 3F)
I implemented the formulas of ref. 3E in an MS Excel spreadsheet (ref. 3F). To put the effciency into perspective: compared to 100% efficiency, the 3.4% implies 15 dB down, or 2.5 S-points. Likewise, 7% implies 12 dB down, or 2 S-points.
PLACEMENT OF THE ANTENNA
There are operators who claim that an STL antenna works just as well (or poorly, as the case may be) indoors as outdoors. I believe this to be nonsense, or pure coincidence at a particular indoor and outdoor placement (and I don't believe in coincidence). For simplicity, let's define "antenna performance" as the resulting signal strength (field strength) at the receiving station, and vice versa for reception. All objects near the antenna influence the antenna's radiation pattern, as some radiation will reflect from them, or refract around them. Furthermore, conductive objects (metals, plants, trees, people and other animals, soil) couple with the antenna, and put a load on it. Note that antenna radiation pattern diagrams are typically for onobstructed free space, and change drastically when ground is introduced, or other objects.
Antenna performance not only changes significantly when going from indoors to outdoors. When moving the antenna around outdoors, the antenna performance also depends on the location with respect to other objects. Example: the standard placement of my STLs is at the center of my terrace (see point "X" in the photo below). At this position, my STL is half way between two parallel reinforced concrete walls: the outside wall of my apartment, and the wall between my terrace and my neighbor's terrace. These walls are spaced by 6 m (20 ft). The floor of the terrace is also reinforced concrete.
Figure 85: The STL placement situation on my terrace
At one end of the terrace, there is a reinforced concrete overhang and a grounded, heavy steel I-beam pergola to the wall with the neighbor's terrace. On top of the overhang, there is a free view in all directions, and the antenna is about 25 m (80 ft) above street level. When I put my antenna here (with my heavy iron umbrella stand, and the bottom of the loop at 75 cm above surface), pointing in the same direction, two things happened. First of all, SWR changes from 1.1 to 1.3. Not as good (power is reduced by a percent or 2), but I did not bother to adjust my coupling loop. Despite this deterioration, my signals at a DX receiving station on 80 mtrs (ca. 1000 km, 620 mi) increased by 1/2 to 1 S-point, i.e., 3 to 6 dB. This is equivalent to as much as doubling the power!
Late 2019, I did a similar experiment. This time, I stuck the same loop onto my 6 meter telescopic handcrank mast. I raised the bottom of the loop to about 4 m (≈13 ft) above the terrace floor. The resonance frequency dropped about 2 kHz. Both the tuning capacitor and the coupling loop is motorized, so I could easily optimize the SWR without lowering the antenna. At the same remote receiver, the received signal was now 1-2 S-points stronger than with the loop at 75 cm (≈2.5 ft) above the terrace floor. That is the equivalent of increase in power by a factor of 2-4! Needless to say: I am quite pleased with this performance! The difference/improvement is explained by several factors.
- Increasing the installation height (here: from < 0.01 to 0.05λ on 80 mtrs) decreases ground (absorption) losses (ref. 2K).
- Note: my terrace floor consists of large cement tiles, raised 10 cm (4 inch) above the concrete base with pedestals. Most of the year, there is water standing below the entire terrace (fortunately, mosquitos do not seem to breed there!).
- The radiation pattern, feed-point impedance, and losses are affected by nearby objects:
- Nearby conductive objects such as antenna feed line, metal fences (e.g., my grounded terrace railing and grounded pergola), metal rain gutters (mine is ca. 60 m long zinc), domestic power lines (e.g., the wiring of my terrace lighting system), water pipes, trees and plants.
- Reflections (and "screening") by the surrounding walls, floor, and steel structures.
- Dielectric objects such as local ground and nearby terrain, the housing structure, trees & plants, people and animals.
Figure 86A: My STL close to the terrace floor and 4 mtrs above it
Late February 2021, I decided to take some more measurements. The polar plots in the next Figure show how the SWR and resonance frequency vary when my antenna is installed in a heavy steel umbrella stand (bottom of the loop 60 cm (2 ft) above the terrace floor) and is rotated 360° with 10° steps. At 60°, the plane of the loop is pointing straight at the steel pergola, and parallel to the white concrete wall in the photos above (the parallel outside wall of my apartment, is not visible in these photos). Clearly, this is a situation with complex coupling between the loop antenna and the environment - in particular the steel reinforcement bars in the walls and in the floor below the tiles, as well as the steel pergola, that is also connected to ground of the electrical system. Clearly, this complex coupling varies when the antenna is rotated and/or the installation height is changed.
Rotation was started with the plane of the loop in the North-South direction (0°), a resonance frequency of 3579.24 kHz, and the coupling loop adjusted for best SWR (1.03):
Figure 86B: variation in SWR and freqres when my antenna is rotated - at my location, at a fixed height
(bottom of loop is 60 cm (2 ft) above ground, as in the left-hand image in Fig. 86A)
The resonance frequency varied by 1.75 kHz max (almost 5%), and the SWR increased from 1.03 to 1.12 max. I.e., no adjustment of the coupling loop necessary. Note: the frequency and SWR changes are quite sensitive to how the coax cable and motor drive control cable are directed away from the antenna. Asymmetry in the East-West direction is due to the asymmetry of the loop and of the walls and large metal structures around my terrace. See Fig. 86A above. I'm not sure about the outlier around 270° in the SWR plot. I also have no explanation for the 20° difference in the direction with max deviation in the SWR and Δfreqres plots...
To measure the direction, I simply stuck my smartphone onto the top of my motor-drive hood with a piece of double-sided industrial sticky tape, and used the phone's compass app:
Figure 86C: measuring the direction of the plane of the loop with the compass function of my smartphone
The SWR and freqres variation is much larger when the antenna installation height is increased, instead of rotating the antenna at a fixed height. The next plots clearly illustrate this. In each plot, a reference measurement is taken with my loop antenna in the umbrella stand and the bottom of the loop 60 cm (2 ft) above the ground. I then put my telescopic mast at the same spot as the umbrella stand (this is easy with the mast tripod that I built recently), and raised the bottom of the loop with 50 cm increments from ca. 2 m to 4 m. My Mk 2 loop antenna has circumference of 6.1 m. This is about 0.07 λ, 0.14 λ, 0.2 λ, and 0.28 λ in the 80m, 40, 30, and 20 m band, respectively. So, only in the 80 m band it is a true Small Transmitting Loop with < 0.1 λ and, hence, near-constant current amplitude around the circumference. All measurements were done with my miniVNA antenna analyzer.
Figure 86D: variation in SWR and freqres when my antenna is raised - at my location
(only the antenna installation height is changed)
The SWR increase in the 80 and 40 m bands was easily corrected by moving my coupling loop up or down - which is why I had made a new motor drive with remote control to do this!
In general, and not entirely unexpected, the plots show that the variation is most pronounced when moving away from close to the ground and away from the pergola (at 2.5 m above ground). Note that at 4 m (≈13 ft), the bottom of the loop is at a height of about 0.05 λ, 0.1 λ, 0.13 λ, and 0.2 λ in the 80m, 40, 30, and 20 m band, respectively. When raising the antenna, the resonance frequency appears to first decrease, and above a height of about 0.1 λ, it begins to increase again. The smallest change in resonance frequency was observed in the 80 m band: 8 kHz or 0.23%. The largest change in resonance frequency was observed in the 20 m band: 55 kHz or 0.4%. In the 40 and 30 m bands, the change was 11 kHz, or about 0.14%.
One factor that contributes to variation of the resonance frequency vs. height, is the configuration of the loop: my rather large variable vacuum capacitor is located at the bottom of the loop. The cylindrical copper plates of the capacitor are fully unmeshed at the highest operating frequency ( = smallest capacitance), and fully meshed at the lowest frequency. The loop's resonance frequency is determined by it self-inductance and capacitance: both inherent, and parasitic due to coupling to the environment. When the loop height is increased, there is less parasitic capacitance caused by coupling to ground. This is more noticeable when the capacitance value of the tuning capacitor is relatively small, i.e., at higher operating frequencies, where the total loop inductance is more dominant in determining the resonance frequency. As ususal, it's all relative!
In March of 2021, I ran some 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 Web-SDR locations relative to my QTH in the south of France
(most Web-SDR's world-wide are here: www.websdr.org)
My transmitter output power was around 100 watt. The plane of the loop was aligned with the ≈20°/200° direction. 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.
Figure 86F: conditions during my tests and antenna positions
The table below shows the data that I recorded. The very high local QRM level clearly went down for the highest installation. Signal strength at the remote receivers was about 1-2 S-points higher for the highest installation. This is equivalent to of a factor 4-16 increase in power!
Figure 86G: signal levels at four Web-SDR's for three different antenna positions & heights
Not bad at all!
EFFECTS OF CORROSION
I sometimes get emails from fellow amateur radio operators, who claim that the surface oxidation of the copper loop causes a significant increase in loss resistance. This would supposedly cause a significant decrease in performance. These operators claim that the loop should be polished until all oxidation is removed, and the copper is nice and shining. The same opinion can be found in forums. However, none of these people are able to provide any references from refereed, scientific literature, or from credible experiments, that support their opinion. Some of them actually report significant loss of performance. However, when I ask them, they cannot at all exclude that they have a problem with corroded contact surfaces between the loop and the tuning capacitor. Corroded connections do cause IR loss! And this is quite noticeable with "high Q" HF magnetic loop antennas and the associated high resonant ciculating current levels, as well as rectification effects (incl. harmonics). If your STL is "high Q" ( = narrow bandwidth at resonance, with SWR close to 1), then your antenna simply does not have any significant loss resistance - no matter how oxidized the loop is.
If you search around, you will quickly find out that there is little or nothing published on this topic. Which is why this misconception perpetuates... The following is my current understanding:
- Copper oxides are semiconductors, and for HF antennas can be considered as insulators. Therefore, the longitudinal electric field is not high enough to overcome the potential barrier and there will be no conduction current along the antenna surface. Likewise the tangential electric field is not high enough to cause conduction current. There will be essentially little or no conduction current in the oxide. However, there will be displacement current (which is the kind of current that makes an antenna radiate, which is good).
- I'm sure you are familiar with "skin effect". At RF, most of the current in the conductor flows in the outermost layer of a conductor. As frequency increases, the skin effect crowds the current into an increasingly thinner thinner part of the outermost layer of the conductor. This causes conductor loss to increase at higher frequencies. If we add an insulating layer to the outside of an antenna radiator conductor, nothing much changes, other than dielectric constant and VL - but not losses. Antennas made of insulated wires work without any problems. The current does not flow in the insulator, it is crowded into the conductive part of the wire/pipe/tube directly underneath the insulation.
- When the outside of a copper conductor oxidizes, the diameter of the conductor is reduced by the tiny thickness of the oxide layer. On realistic tube/pipe diameters such as used for magnetic loop antennas, this reduction is negligible. Copper oxide is fairly good insulator (contrary to popular belief, silver oxide is not a good conductor), as are most oxides. Of course, if copper oxide were a good conductor, you would not notice any difference in performance either.
- Copper oxide would cause a problem if it were a half way decent conductor (which it isn't). In that case, RF losses would indeed go up significantly, as the skin effect would force the current into the less-conductive outer layer.
- The possible significant losses with, e.g., copper oxide have to do with its relative dielectric constant ( = relative electrical permittivity) and its relative magnetic permeability. This is a highly complicated matter, even for "pure-and-clean" conductors, see ref. 9C. These properties do indeed decrease the skin depth, thereby increasing losses. This is also why you want to avoid bare ( = without copper or silver plating) iron and steel conductors for RF applications: iron oxide has a very high magnetic permeability. The effect of the permittivity and permeability depends on frequency.
- Corrosion at connections will cause significant loss resistance! In my loop, I very carefully remove all corrosion before I tighten the connection beteen the ends of the loop and the capacitor brackets. If I loosen the connection a year or two later, they are still perfectly clean, with no visible corrosion. The loop itself, however, is fully covered with black copper oxide (CuO, "cupric oxide", tenorite). Note that this oxide is a p-type semiconductor. Fully oxidized connections may cause strange rectification effects on small signals.
For HF frequencies, there is no credible theory or evidence that surface oxidation on the loop causes significant loss resistance! Oxidized copper does have higher loss than bare copper, but this effect does not become noticeable until you get to the upper portion of VHF and above.
However, oxidized copper contact surfaces (e.g., between loop and tuning capacitor) do cause significant losses!
MOTOR DRIVE FOR THE VACUUM CAPACITOR
My loops are installed on the terrace of my penthouse apartment, so they are quite accessible. Even so, it is entirely impractical having to go outside several times to manually adjust the capacitor position when changing operating frequency, or when the resonance frequency drifts away for whatever reason. Standing next to the loop also de-tunes it a bit. The loop has a very narrow bandwidth, esp. on 80 m. A remote-controlled motor-drive for the capacitor is a must! The basic motor options are a stepper motor (D: Schrittmotor, F: moteur à pas), and a DC motor. Especially with a DC motor, down-gearing will be required.
When I built my first STL, I could not figure out an easy way to motorize the vacuum capacitor with a DC-motor, while providing end-stop protection at both ends of the motion range of the shaft (36 revs). So, why not make a little science project out of it?
Primary parameters for the motor-drive are:
- required minimum torque at the capacitor shaft,
- required minimum angular resolution, and
- drive speed.
Note that "precision" and "accuracy" are not on this list. I am not particularly interested in the ability of the drive-system to move exactly to some (pre-)selected position, or exactly follow some predefined acceleration and speed profile. Depending on the outside temperature, the alignment of the moon, planets and the stars, etc., the exact capacitor shaft position for a given resonance frequency will vary. So, one will have to search around a bit anyway, for fine-tuning. It is important, however, to change the position just a tad.
The first design parameter for the motor-drive is the torque required to overcome the stiction (static friction), and turn the shaft of the variable capacitor. This drives the size of the motor and reduction gear (if required). Variable vacuum capacitors have a torque value that depends on the position of the capacitor (mid-range vs. close to the end-stops), and the direction (towards or away from an end-stop). I do not have the data sheet of my Russian capacitor. To get an order-of-magnitude idea, I checked the values for a comparable capacitor (25-500 pF, 10 kV test, 9 inch length) manufactured by Jennings: 6 inch-pound (in.lb) or 6 x 0.113 ≈ 0.68 Nm = 68 Ncm.
I then decided to measure it myself ("trust, but verify!"). This is actually quite easy to do! I clamped a standard 30 cm (1 ft) ruler onto the shaft of the capacitor with a small C-clamp. Pushing slowly down onto a kitchen scale until the shaft barely turns, and read the "weight". Voilà. See photo below. The force was applied to the shaft with half of the ruler, i.e., an arm of 15 cm.
Figure 87: Determining the torque values of my capacitor
Here are the measurement results:
- Depending on the turn-direction, I measured about 80 to 100 grams at positions up to mid-range (starting at minimum capacitance). So, the applied torque was (0.1 kg x 9.8) x 0.15 m ≈ 0.15 N.m = 15 N.cm (≈ 21 oz.in).
- Somewhere mid-range, it became harder to turn the shaft, and I needed to apply about 140 gram, i.e., 20.6 N.cm (≈ 29 oz.in).
- I needed about 300 gr to get completely to the opposite end (maximum capacitance), i.e., 44.1 N.cm (≈ 63 oz.in).
- I cranked it up to 1000 gr without breaking anything, i.e., 150 N.cm (≈ 208 oz.in). If the motor-drive (motor + gearing) delivers less than this, I do not have to worry about not having end-stop protection. I decided to not measure the torque required to go beyond the end-stop of the capacitor, hihi.
The second important design parameter is the angular resolution of the motor-drive. The loop antenna has a large Q, or - equivalently - a very narrow bandwidth. The motor-drive must be able to make angular displacements that are small enough, such that the associated capacitance change does not change the resonance frequency more than a fraction of the bandwidth. Otherwise it will be next to impossible to tune the resonance frequency close enough to the desired operating frequency.
Let's simply assume that the capacitance changes linearly with rotation of the capacitor's shaft (which is actually only true for about 2/3 of the motion range). Then we get 500 pF / (36 rev x 360º per rev) ≈ 0.04 pF / degree. For my first STL, one of the loop calculators (ref. 2B) suggest the following:
In the middle of the 80 m band:
- Calculated bandwidth is about 3.5 kHz. I actually measured 4.6 kHz for my loop. The difference is probably because I did not enter a value for additional loss resistance in the calculator...
- A capacitance change of 1 pF results in a calculated change in resonance frequency of 4.2 kHz. I.e., 0.24 pF per kHz.
At the high end of the 20 m band:
- Calculated bandwidth is about 52 kHz. I actually measured 61 kHz.
- A capacitance change of 1 pF results in a calculated change in resonance frequency of 275 kHz. I.e., only 0.004 pF per kHz.
Clearly, variation around the minimum capacitance (highest frequency) is the critical case!
Let's assume that practical tuning requires changing the resonance frequency with a resolution that is better than 20% of the bandwidth. The above data implies a required resolution of better than 20% x 52 kHz = 10.4 kHz. That is: 10.4 / 275 kHz/pF = 0.038 pF! Based on the 0.04 pF / degree change in capacitance as estimated (assumed) above, I need an angular positioning resolution of better than 0.038 pF / 0.04 pF/deg = 0.95 degree.
Note that an air variable capacitor goes through its capacitance range in a single revolution of the capacitor shaft. For multi-band tuning (large capacitor value), this implies a positioning resolution that is at least an order of magnitude better than what is needed for a multi-turn (10-40 turns) vacuum variable capacitor!
A secondary design parameter is the minimum drive speed. We don't want to wait an hour for the capacitor position to move from min to max value, or vice versa. My capacitor requires 36 turns for this min-max range, which should cover the 80-20 m bands. If I could live with 1 minute, that would be 36 rpm at the capacitor shaft = 0.6 rev/sec.
Now we can choose a motor and associated drive electronics. Gearing must be added, as necessary for torque, speed, and/or position resolution. There are two basic options:
- DC-motor with gearing + position feedback (unless you just want to move the motor while observing the SWR or antenna impedance and don't care about the motor position). If the DC motor is not a brushless type, then (as a minimum) a noise suppression capacitor must be installed across the motor wires. Otherwise the brushes will generate electrical noise when tuning the antenna in receiver mode.
Open-loop control of a DC motor is simple. Apply DC power with the correct polarity, and turn of that power when at the target position. Speed can be controlled (again: open-loop control without position feedback, no speed regulator) with a cheap and simple Pulse Width Modulator (PWM) circuit, such as I used for my third STL. Small DC-motors with large down-gearing are relatively inexpensive.
Stepper motors do not have built-in position feedback, but their movement is deterministic, as long as the motor does not stall or lose sync. Their control/driver electronics are more complicated than what is needed for DC-motors. Positioning accuracy and torque requirements are easily met with a stepper-motor: they have a specified torque and step size. Stepper control electronics often have half-stepping capability (though this typically reduces available torque by about 30%). Common step sizes are 1.2, 1.8, 3.6, 7.5, and 15 degrees. I.e., 300, 200, 100, 48, and 24 steps per revolution, respectively. Smaller step sizes do exist, e.g., 0.9 and even 0.36 deg, but at a cost...
When one of my colleagues donated a stepper-motor (thank you Helmut!), I decided to throw all caution to the wind, and go with that. It is an old Slo-Syn SS25-1001. This is a 5-wire brushless permanent magnet inductor motor that can be operated as a constant-speed AC synchronous motor, and as a 1.8º uni-polar DC stepper motor. As I needed better than 0.95 deg positioning resolution, at least 2:1 gearing is required.
Figure 88: An old Slo-Syn SS25-1001 motor
"SS25" stands for "Standard Slo-Syn" with 25 oz.in (17.7 N.cm) torque at 72 rpm (120 Vac, 60 Hz). However, as a stepper motor, it has different torque ratings:
Figure 89: Specification of the Slo-Syn SS25 stepper motor
There are several kinds of stepper-motor torque to consider:
- holding torque (a.k.a. break-away torque): the amount of torque required to break the shaft away from its holding position, with motor at standstill and coil(s) energized with rated current & voltage.
- pull-in torque: max torque at a given speed, for stopping/reversing without losing sync.
- pull-out torque: max torque at a given speed, without losing sync or stalling.
- residual torque (a.k.a. detent torque): torque produced by the motor's permanent magnets, when no coils are energized.
The holding torque and residual torque are not interesting for my application, as the motor will not be holding a load. Of interest are the pull-in and pull-out torque, typically provided as a torque vs. speed curve. The curves are highly dependent on the type of motor-driver that is used.
Figure 90: Typical shape of the torque curves
I do not have the torque curves for this motor, but typically it appears to be about a factor three smaller than the holding torque. That would imply a torque of about 10 oz.in (7 N.cm). Less than half of what I need! But why not determine the actually required torque, the same way I measured the required torque. With the motor energized, just make the "arm" push down on the scale until the motor turns.
Figure 91: Determining the break-away torque value of my SS25 motor
With my simplistic kitchen scale method, I measured a break-away torque of approximately 140 grams x 15 cm = 2100 g.cm = 20.6 N.cm = 29.2 oz.in. Almost exactly as specified! The same value is obtained by fixing the motor in place, and commanding it to turn, one step (or 1/2-step) at a time until it "pops". This very easy to do with the controller software I wrote (see further below).
Keep in mind that I need at least 44 N.cm (≈65 oz.in). So I have to add down-gearing of at least 3:1.
The SS25 is a 5-wire device. It has a common wire (white) and four coil wires (green, green/white, red, red/white, for coil 1-4). This corresponds to the connections "+", and A-B-C-D on the Phidgets motor controller card that I use.
Figure 92: Wiring of the SS25
We have a motor, so now we need to control it. I wanted to control the motor from my PC, rather than having a separate control box. This means that the controller hardware must have an interface to the PC. Standard options are an RS232 interface via a COM port, or - more modern - a USB interface. My PC only has one COM port, and that one is already used for the PTT-interface from the PC to my transceiver. Yes, I could add a USB-serial interface. But if I go USB, I might as well skip the RS232.
The main choice to make now, is "make" vs. "buy". Yes, there are many stepper-motor controller hardware designs floating around in cyberspace. Few have a USB interface. I determined that piecing a design together, building and debugging it, was too much of a hassle. Instead, I searched for a relatively inexpensive off-the-shelf USB solution. I decided to go with a Phidgets 1062 controller card. It handles up to 4 unipolar stepper motors simultaneously (e.g., an antenna rotor as well). It is almost "plug-and-play", via USB. This controller card is really tiny: 5 x 6.3 cm (2 x 2½ ")! And: it is rated for 1 amp per winding, without a heatsink! It does come with some rudimentary software, to check out the card and the motor.
Figure 93: The small USB controller board for four uni-polar stepper-motors
The unipolar Phidgets card (model 1062) does not support speeds above 383 half-steps per sec! That is almost 1 rps with a 1.8 deg stepper motor (200 full steps/rev).
This Phidgets card uses half-stepping: the drive alternates between "two phases energized" and "single phase energized". This provides smoother motion and doubles the angular resolution from 1.8º to 0.9º. However, when half-stepping, the motor also typically produces about 30% less torque (at the 1/2 step positions between full step positions). Maybe I will only get about 7 oz.in (5 N.cm) out of my SS25 motor! This means I will probably need a 4:1 gear ratio between the motor and the shaft of the variable capacitor...
Phidgets also sells a controller card (model 1063) for a single bipolar motor. As the name suggest, control of bipolar stepper motors involves changing the polarity of the applied voltage across the motor windings. This makes bipolar controller hardware inherently more complicated (typically H-bridges instead of simple transistor switches). Yes, unipolar motors are very old-fashioned and generally produce less torque then bipolar/hybrid steppers. The latter can also be micro-stepped, whereas half-stepping appears to be the limit for unipolar motors. The bipolar controller card supports much higher speeds, and also has 4 discrete/digital inputs.
The instruction set of the Phidgets 1063 card is a super-set of the 1062's instruction set. I.e., the 1063 has all functionality of the 1052 - and some additional functions. E.g., limiting the motor current (= torque). This means that the control software that I developed for the 1062 will also work with the 1063. Leslie, EI5GJB, has confirmed this (November 2011) and is quite pleased!
Some other controller hardware options are:
- The "Stepper-Bee" card.
- The "Motor Hawk" card. Twan van Gestel (PA0KV) has made a big loop (160-40) with a Gamma match, and used one of these cards for a stepper motor in his 2015 design. He made nice controller software in Visual Basic. See here.
Both come with more useful demo software than the Phidgets.
External links last checked: January 2016
The next step is choosing a mechanical coupling of the motor to the shaft of the variable capacitor, including the necessary down-gearing.
Figure 94: Shaft dimensions of my capacitor and motor
IMPORTANT: you need non-conductive material or rod to couple the motor to the capacitor. The capacitor shaft is not insulated from the capacitor itself. Hence, it is at the same potential as the capacitor (up to several kV at resonance). You don not want the capacitor voltage on the motor (or its wiring)! Standard options are using a non-conductive (plastic, ceramic) driveshaft or a belt drive. The shaft and housing of the motor, and any metal gear wheels attached to it, must remain at a safe distance (at least 1 cm (1/2") from the shaft and connections of the capacitor.
I would have preferred a straight, rigid shaft-to-shaft coupling. But as as determined above, my motor doesn't generate enough torque for 1:1 coupling: I need down-gearing of at least 3:1. The easiest way to do this, is with pulleys (cog wheels) and a timing belt.
A timing belt (a.k.a. toothed, notch, cog, synchronous belt; D: Zahnriemen, F: courroie dentée) has teeth that fit into a matching toothed pulley. When correctly tensioned, there is have no slippage: motor and load remain "synchronized". Timing belts need the least tension of all belts, and are among the most efficient (though no issue at very low speeds of a few RPM). Standard belts are fiberglass reinforced neoprene or polyester-urethane (PU). There are several standard belt profiles, but this is not critical in our low speed, low torque application. The basic choice was between a simple T (trapezoidal) profile with 2.5 mm pitch and 6 mm width, vs. 5 mm pitch and 10 mm width.
Figure 95: Standard metric belt profiles (left to right: T, AT, HDT)
(similar British/Imperial profiles are L, H, XL, MXL)
There is a finite choice of standard pulleys. The standard number of "teeth" is typically 10-20, 22, 25, 28, 36, 40, 48, 60, 72, or 84. The diameter of the pulley is determined by this number, and the pitch of the belt (i.e., the distance between the centers of adjacent teeth). It is recommended that at least one of the two pulleys has flanges, to avoid the belt from running off the pulleys when the input and output shaft of the gear are not properly aligned. Standard materials are aluminium and plastic (typ. acetal resin). Pulleys for a T5 belt are significantly larger than for a T2.5 belt. Pulleys have standard bore sizes.
Figure 96: Plastic flanged pulley
- I did not want the pulley on the capacitor shaft to be larger than the end-connector of the capacitor (60 mm diameter).
- I want to be able to create a 3:1, 4:1 or 5:1 gear ratio.
- The diameter of the hub of the pulleys has to be large enough to increase the bore (with a drill press!) to the respective shaft size, and still have at least 2 mm hub thickness left.
- The height of the hub has to be enough to allow drilling a radial hole, thread it, and use a set-screw (grub screw) to fix the pulley onto (or through) the shaft.
I settled on a T2.5 x 6mm belt, a 60 teeth pulley (48 mm diam.) for the capacitor shaft, and a 15 teeth pulley for the motor. I.e., a 4:1 ratio (I also got a 10 teeth pulley, just in case I needed 5:1 gearing, but did not need it).
Now we need to figure out the length of the belt with the formula below (it is a very close approximation, as it neglects the fact that the belt does not touch the pulley over only half its circumference, unless the pulleys have the same size):
Figure 97: Pulley configuration parameters
For the diameter of the selected pulleys, and a minimum of 2 cm spacing between the pulleys, I ended up with a standard belt with a 200 mm (8") overall length (80 teeth). I.e., a standard T2.5 x 6 x 200 belt.
Fig. 98: paper disk "pulleys" on the motor and capacitor shaft to check dimensions and clearances
I installed the motor onto the antenna mast with two "worm drive" hose clamps (a.k.a. radiator clamps; UK: "jubilee® clips").
Figure 99: The pulleys and belt installed on the motor and capacitor
(note the 5-turn ferrite toroid "choke" on the motor wiring)
NOTE: I had to revise my choice of belt material! The original belt was reinforced with embedded steel tension cords. As you can see in the photos below, this caused arcing between the belt and the pulley of the motor. Luckily, no damage was done to the controller card, PC, or my transceiver. Clearly, one must use polyurethane or neoprene belts that are reinforced with fiberglass, polyester, or polyurethane cords!
Figure 100: Arcing damage to the steel-reinforced belt
Figure 101: Arcing damage to the pulley of the stepper-motor
The Phidgets cards needs to be connected to the PC via a standard USB printer cable (supplied with the card). My motor happens to be a 5-wire motor (some unipolar stepper motors have more wires), so I need to run a cable with at least 5 conductors from the card to the motor. Some options are:
- Standard Cat 5 (category 5) cable; this is for 10/100 Mbs Ethernet communication - no need to go for Cat5e or Cat6 cable (100/1000). This is an 8-conductor cable, usually 4 twisted-pairs. There are UTP (unshielded twisted pairs) and STP (shielded) cables. STP is recommended for the application at hand.
- 5 conductor thermostat cable,
- 5 or 7 conductor antenna rotor cable,
- 6 or 8-wire phone cable.
The advantage of an 8-conductor cable is that this leaves 3 conductors to accommodate a sensor at the motor drive, e.g., a potentiometer or end-stop switch. Of course, it can also accommodate an 8-wire stepper motor. As I had several long Cat5 cables laying around, I settled for one of 15 mtrs (50 ft). With two mating RJ45 chassis connectors (8P8C modular jacks), I'm in business.
The controller card takes its power from the USB port, but only for the control electronics - not to power the motor! The latter power must be supplied separately to the card: either via a standard barrel connector, or hardwired to a terminal block. My motor uses 12 volt DC. I use the barrel connector and a 12 V / 750 mA "wall wart" power supply, or a sealed 12 V / 4 Ah motor cycle battery.
IMPORTANT: As noted in the warning section above, the antenna generates strong a RF field when at resonance - enough to light up a fluorescent light tube, with just a couple of watts transmit power. You do not want to get this RF into the controller card and damage it, or into the PC connected to it.
As for most of my HF-chokes, I use FT140-43 ferrite rings. One is placed at the controller card, between the RJ45 connector and the card. I use a short section of Cat 5 cable between the connector and the card. This cable is wound 5 times through the ferrite ring. This has been adequate so far (I use 100 W max).
Fig. 102: Toroidal current choke on the CAT5 cable between controller card and stepper-motor
Figure 103: A second ferrite ring current choke is placed at the motor
According to various loop antenna calculators, the highest capacitor voltage for my size antenna, occurs for a resonance frequency around 7 MHz. Running 100 W into the antenna - with the controller card operational - did not cause any damage or abnormal behavior.
I may move the motor away from the capacitor, to the "neutral" point opposite the capacitor. This requires a long, torsionally-stiff drive shaft. I found very stiff green plastic rods of 1.8 m (6 ft) length and 16mm diameter in the gardening section of the local do-it-yourself store (thanks for the idea Mark, KF7KIN). Be careful: some of these green garden rods are just plastic-coated metal tubes or rods. It is not easy to tell! I ended up with a 1.8 m section of regular 16 mm PVC electrical conduit. It is flexible, but torsionally stiff.
The bore of my large gearwheel is 12 mm, as is the diameter of the capacitor-shaft. Adapting the 16 mm rod to the 12 mm bore (inner diameter) is easy, with a 16-to-10 mm copper adapter piece. It has 1 wall-thickness of 1mm, so 10+1+1= 12 mm outer diameter. I pressed it in with the bench vise. Adapting the 16 mm rod to the 12 mm outer-diameter of the capacitor shaft is equally simple, with a 16-to-12 mm adapter piece. The store didn't have that one in stock, so I used a 3 adapters: 16-to-10, 10-10 (female-female), and 10-to-12 mm. I will install a ball bearing with 16mm bore on the rod, close to the motor.
Figure 104: Gear wheel and copper adapter piece
Figure 105: Plastic drive-shaft with gear wheel installed
STEPPER-MOTOR Controller software
Obviously, the Phidgets motor controller card needs to be controlled from my PC. This requires the user (me) to somehow create software. The Phidgets website provides a library of dll and API files, and some simplistic code samples and low level suggestions on how to control the card via Visual Basic, C/C++, LabView, MatLab, Java, etc.
I decided to go with LabView, because I have access to it, and it is graphically oriented (both design and the controller). It has taken me over a week of spare time to learn "LabView 8 Pro" well enough to make a quite decent controller with a nice Graphical User Interface (GUI). My GUI has three tabs: "Control", "Cal", and "Config".
Next time around, I may have a go at Visual Basic, though it is limited to "Windows". The development tools are basically free, whereas LabView is prohibitively expensive for private use. And unlike LabView, no enormous Real Time Operating System needs to be installed.
Figure 106: The "Control" tab of the GUI of my varco motor-drive control software
The "Control" tab provides the GUI for the following functionality:
- Indication of whether the software has established contact with the Phidgets card.
- A toggle switch for commanding the Phidgets card to energize the motor. Default is de-energized. A LED indicates energization status feedback from the card. Note that the card does not know whether a motor is actually attached or electrical power is available, so this (and of other parameters such as speed and position) is only a feedback of the commanded state.
- Three ways to enter the desired motor position. A 3-position slide switch (lower right-hand corner) is used to select one of them (a small LED lights up next to the selected source):
- Type-in the desired antenna frequency (followed by "enter" on your keyboard), with incremental up/down buttons (+/- 1 KHz).
- Radio-buttons for eight preset (and configurable) frequencies.
- A magenta slider (with incremental up/down buttons, +/- ½-step) to command motor position, rather than frequency. There is a push button next to this slider. When pushed, the slider position is synchronized to the actual motor position. This is useful when using a pre-set frequency, and needing to tune around this position.
- Two blue sliders that indicate the selected motor position and the actual motor position. The associated numerical positions are expressed in both motor ½-steps, and revolutions of the tuning capacitor. The upper limit of all three control & indicator sliders is initialized based on the gear ratio and the number of 1/2 steps per motor rev. Note that the actual motor position is not measured - the controller card just keeps track of how many steps it commanded with respect to the initialization position.
- A "stop" button, that halts execution of the control software and commands the controller card to de-energize the motor.
If a desired frequency is selected (numerical entry or preset), then the software interpolates the antenna's calibration data to calculate the corresponding motor position. This interpolation scheme, and assigning the labels of the radio buttons based values read from a file, was the trickiest part of the software design! Note that the calibration data is only valid at a certain temperature and position or the antenna. E.g., if the data was obtained with a cold antenna, and the sun (or QRO operation) heats it up, then the actual resonance frequency will drift.
When turning a vacuum capacitor, there is no need to apply holding torque when not moving (unlike other applications. Hence, there is no need to keep motor energized while at rest. However, no harm is done when the motor is kept energized, and turning the energization on & off for each movement makes the controller software more complex. Also, when the motor is re-energized, it may jump a step. So: my controller software keeps the motor energized (with manual override).
Upon start-up, the controller reads-in three tiny text files:
- Initialization settings for the Phidgets card and the controller: acceleration limit, velocity limit (½-steps/sec), the number of ½-steps per revolution of the motor, gear ratio between the motor and the tuning capacitor, offset (½-steps), number of capacitor revs for end-to-end travel.
- Preset frequencies of the operator's choice.
- Calibration data (resonance frequency of the antenna, measured for each full revolution of the capacitor shaft). Obviously, the calibration data from my antenna will not be correct for someone else's antenna (or my own antenna at a different location).
Figure 107: The "Config" tab of the GUI of my varco motor-drive control software
The "Config" tab provides the GUI for the following functionality:
- Indication of the serial number read from the Phidgets card.
- Setting of which motor to command (the Phidgets 1062 card handles four motors; default is 0). Note: this not the number of motors that are attached to the card.
- Location of the initialization data for the card and the controller. The file location has a default, but a browser button can be used to locate the file.
- A numerical entry (with incremental up/down buttons) for modifying the offset. I added this feature, to be able to adjust the applied offset (from the init file) when (re)starting the software, without having to modify the initialization data file. This allows to adjust for imprecise positioning at the reference position.
- Indication of the eight preset frequencies red from the presets data file. The file location has a default, but a browser button can be used to locate the file.
Figure 108: The "Cal" tab of the GUI of my varco motor-drive control software
The "Cal" tab provides the GUI for the following functionality:
- A plot of the calibration data. The file location has a default, but a browser button can be used to locate the file.
- Two push-buttons, for resetting the card's internal "current position" either to zero or to max position (the motor's ½-steps per rev, times the number of revs of the capacitor). This feature is used when the motor is positioned at the known reference position ("end stop"). The LED next to the button indicates whether it is OK to push the button (OK = when the motor is not moving).
- A block for future functionality.
IMPORTANT: I have made the entire design and software package of my controller application available below. It comes without guarantees. Please note that I do not have the time to provide support for its installation or operation. Sorry!
- The graphical design (detailed block diagram) of V21 of my controller is here (the image has enough resolution for fully zooming-in on the details).
- The actual LabView "virtual instrument" design file (.vi) of my controller is here.
- LabView "Pro" supports creating a LabView-independent .exe file. The zipped executable package of my controller is here.
- This .exe application can run without the LabView development environment (i.e., you don't need the costly LabView suite), but is does require the LabView Run-Time Engine (RTE) Version 8.0. This is available for free - for all standard operating systems - from the National Instruments website. It appears that using RTE version higher than 8.0 causes problems with my software.
- Of course you must install the drivers that came with the Phidgets card (or download from phidgets.com). I used this executable drivers package.
- The zipped package of the three data files that I use (initialization, presets, calibration data) is here. Changes to these files must be made with an ASCII-editor such as Notepad or Wordpad - do not use a word-processor such as Microsoft Word!
- As noted further above, my control software can also be used with the Phidgets 1063 controller for a single bipolar stepper motor. The 1063 is based on 1/16 steps, whereas the 1062 is based on 1/2 steps. When using my software with a 1063 card, the MagLoop-card-init.lvm file must be edited accordingly (again, only with a simple ASCII text editor, not MS Word or similar).
- This means that I do not know if my software can work at all with Phidgets cards other than 1062 and 1063! You can try it at your own risk. Sorry: I can not provide support for your experiments.
- In 2016, Patrick Nobecourt (F5TJZ) adapted my design in LabView2015, to make it work with a Phidgets 1067 card for his NEMA17 motor. He included current monitoring/protection and increased the velocity limit. Patrick actually uses two cards and two motors in the remote matching unit for his vertical antenna: one for a vacuum variable capacitor, the other for a variable inductor. His .vi design file is here, the two executable are here, and the associated initialization data files are here.
Before I get into all the details of the DC motor-drive that I developed for my vacuum capacitor, here is a simple-yet-effective way to motorize such a capacitor - if the shaft of the capacitor moves in & out of the capacitor as the shaft is turned. Unfortunately, this is not the case with my capacitor.
If the shaft does move out when the shaft is unscrewed, then an inexpensive small DC-motor with down-gearing can be used. If mounted on a thin, flexible L-bracket, the motor (and the bracket) will be pushed away from the capacitor when the shaft unscrews. This can be used to actuate a micro-switch when the shaft is approaching its maximum position. With some simple circuitry, the motor will then only be allowed to reverse direction. The geared-down motor can produce a certain maximum torque. It should be small enough, such that it cannot damage the capacitor when the shaft is completely screwed in. The motor will simply stall at that point. This is easily detected with a simple motor-current monitor, consisting of an LED across a current-sensing resistor in series with the supply voltage. Ref. 11A.
Figure 109: Motor-drive with end-stop protection by Rich Fusinski (K8NDS)
(source: ref. 11A)
This concept can actually be expanded to a provide end-stop protection for a capacitor shaft that does not move in & out. The rotational movement of the motor-capacitor shaft has to be converted to linear motion. This can be done with a threaded rod (lead screw, feed screw) and a screw nut that is installed on the rod. It has to be prevented from turning with the shaft, and only be allowed to slide along the rod. The nut can then actuate a micro switch (or two such switches, to obtain end-stop protection at both ends of the motion range). An implementation of this by Dominique, F1FRV, is illustrated below (ref. 11F). The design includes a remote control unit and a 10-turn potentiometer (down-geared) for position feedback.
Figure 110A: Top view & side view of the 2004 motor-drive by Dominique Delerablee (F1FRV)
(source: ref. 11F)
I liked Dominique's implementation: it is compact, and the shafts are inherently properly aligned. However, the important parts of his design are not readily available. So I decided to roll my own - not very compact, but basically all parts available via eBay. See the next section.
In 2020, Dominique updated his design, with the structure and some other parts made with a 3D printer:
Figure 110B: Top view & side view of the 2020 motor-drive by Dominique Delerablee (F1FRV)
(source: ref. 11G)
MY DC-MOTOR Drive
At the heart of my drive system is a small 12 volt DC motor:
- The shaft of my vacuum capacitor makes 36 turns, end-to-end. I would like the motor to turn the required 36 revs in about 1 minute. I.e., a speed of about 36 rpm.
- I selected a motor with a gearbox that has 2 output shafts. This way, I can add a multi-turn potentiometer for position feedback in the shack. If you do not want this feedback, you can use a motor with a single output shaft. However, I recommend that you do add the feedback, or at least get a 2-shaft motor, so you can easily add the feedback when you finally find out that you really need or want it.
- I purchased the motor via eBay ("worldwide" search on "DC 12V 35RPM Double Shaft Worm Geared Motor GW31ZY"). It delivers a nominal torque of 147 N.cm (15 kg.cm). This is plenty! The output shafts have a diameter of 8 mm.
- I made the motor mount out of pieces of 8 mm thick poly kitchen cutting board, and threaded holes for the bottom mounting screws. When I completed the construction, I found that a matching metal mounting bracket was also available via eBay ("worldwide" search for "worm gear motor mounting bracket")...
Figure 111: The 35 rpm / 12 VDC motor and a matching mounting bracket
The motor must turn the shaft of the capacitor, so we need a drive shaft system. Its purpose is threefold:
- Connect one motor shaft to the capacitor shaft.
- Convert the shaft rotation to linear motion, with actuation of an end-stop switch at both ends of the linear travel.
- Connect the other motor shaft to a multi-turn potentiometer for position feedback.
I selected a lead screw (feed screw, threaded rod, D: "Spindel, Leitspindel", F: "vis-mère") with a length of 200 mm (20 cm, 8 inch) and a pitch of 2 mm. I.e., the thread makes 200/2 = 100 turns. A nut can spin on the lead screw. For 36 revs, this nut will travel 36 revs x 2 mm/rev = 72 mm = 7.2 cm. The nut must be prevented from turning. It shall only translate along the lead screw. To do this, I used an 8 mm guide shaft. It is installed parallel to the lead screw. A slider block can move freely on the guide shaft. The lead screw nut is fixed in a groove of a piece of poly cutting board that is mounted onto the slider block.
I mounted the lead screw just above the guide shaft. The two pillow block bearings of the lead screw are raised with standard M6x30 mm standoffs (I also needed washers between the standoffs and the bearings, to raise the bearings another 3 mm). Sets of a lead screw with one or two guide shafts and mounting material are easily available via eBay (do "worldwide" search for "Lead Rod Linear Shaft Rail Support Slide Block Couplings").
Fig. 112: The assembly for converting shaft rotation to linear motion - for actuating the end-stop switches
One end of the lead screw is connected to one of the motor shafts. This is done with a flexible shaft coupler (8 mm to 8 mm). The other end of the lead screw must be connected to the capacitor shaft. This must be done via an insulating shaft, to avoid the capacitor voltage from ever reaching the drive system and remote control. I used a 10 cm (4 inch) section of acetal copolymer (polyoxymethylene-C, POM-C). This is acetal resin, a thermoplastic that was discovered in the 1920s by the German scientist Hermann Staudinger. POM trade names incl. delrin® ( = acetal homopolymer = POM-H). This insulating material has high strength and stiffness, good dimensional stability, is abrasion resistant, easy to machine (lathe, mill, drill, laser cut,…), and is generally unaffected by solvents, fuels, other chemicals. Its mechanical properties are somewhere between metal and plastic. Two flexible shaft couplers are required: 8-to-8 mm between the lead screw and the insulating shaft, and an 8-to-12 mm coupler between the insulating shaft and the capacitor shaft (12 mm diameter).
The motor is probably strong enough to destroy the capacitor when continuing to drive when the end of the capacitor's shaft is reached. In the opposite direction, the capacitor shaft becomes unscrewed and can fall out of the capacitor. So, we need end-stop protection at both ends of the 36 rev travel! This is why we convert shaft rotation to linear motion, and use micro-switches to detect reaching the end of the travel. 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.
The capacitor shaft makes 36 revs, and a standard multi-turn potmeter makes 10 turns. So we need 4:1 down-gearing. I decided to do this with two gears (note: "gear wheel" is a misnomer) and a small timing belt (toothed belt, synchronous belt). The pulley on the second motor shaft has a width of 10 mm and 15 teeth. This is a flanged pulley, so the belt will stay on. The pulley on the potmeter shaft has a width of 10 mm and 60 teeth. The belt is an 8T2.5x150, i.e., 8 mm wide, with a "tooth" pitch of 2.5 mm, and length of 150 mm ( = 60 teeth).
The capacitor and the entire drive system are mounted on a 10x60x1.1 cm plate of acetal copolymer (polyoxymethylene-C, POM-C), bought via eBay. All holes are countersunk on the back side of the plate, and used with countersunk ("undercut") M4, M5, and M6 screws. See the photos below.
IMPORTANT: even though flexible shaft coupler are used, alignment of the capacitor shaft, the leads screw rod, and motor shaft must be done very accurately! This means that the various holes in the POM plate must be located accurately: much better than 0.5 mm = 0.02 inch = 20 thou. So, you must use a caliper when marking the drill holes, and use a drill stand to drill straight and at the marked location!
IMPORTANT: as stated, the capacitor shaft shall not be driven all the way to its physical limits. To avoid destroying the capacitor, the end-stops are carefully adjusted such that only 35 of the 36 capacitor shaft revs are used, with 1/2 rev margin at each end. I mounted the micro-switches on a small piece of poly kitchen cutting board. It has a slot in it, so its position can be adjusted parallel to the lead screw and guide shaft over a distance of about 1 cm (see Fig. 112 and 116 below). Make sure that the micro-switches are wired correctly: before fixing the flexible shaft coupler to the capacitor shaft, drive the motor so as to center the lead screw nut about half way between the mirco-switches. Then drive in one direction and manually actuate the associated micro-switch. Then repeat in the other direction. As stated before, the lead screw nut will move over 70 mm for 35 revs. So the micro-switches must have a nominal spacing of 70 mm, plus the length of the slider block on the guide shaft. Adjust the position of the second micro-switch, such that it switches after moving exactly 35 revs away from the opposite switch. Then drive until the micro-switch corresponding to the capacitor's hard mechanical limit is actuated (CW rotation for my capacitor). Then manually rotate the capacitor shaft to that stop, and back off 1/2 rev. At this point, the capacitor "bottle" is fixed in place. I used two long cable ties that go through the mounting plate. Note that the plate has a hole for the nub of the capacitor bottle. See the far left side in Figure 113. Now the shaft coupler on the capacitor shaft is fixed. Likewise, the 10-turn potentiometer has physical limits. The 4:1 down gearing of the second motor shaft results in 35 / 4 = 8.75 revs of the potmeter shaft. This leaves a margin of (10 - 8.75) / 2 ≈ 0.6 revs on each side of the travel of the potmeter shaft. Once the micro-switches are adjusted, the system is driven until one of the micro-switches is engaged. Make sure (!!!) you know the turn direction of the second motor shaft during this system movement. If you get the direction wrong, you will immediately destroy the potmeter! Turn the potmeter shaft all the way to limit that corresponds to the actuated micro-switch. Then back off 1/2 rev and do not rotate that shaft any more, until the timing belt is installed.
Figure 113: Top view of the DC motor drive assembly with vacuum capacitor
Figure 114: Bottom view of the DC motor drive assembly
Figure 115: Right hand view of the DC motor drive assembly
Figure 116: Left hand view of the DC motor drive assembly
Figure 117: Close-up view of the drive shaft, end-stop slide, motor, and position feedback potmeter
Figure 118: Close-up view of one end-stop with micro-switch, actuated by the sliding block
Fig. 119: RJ45 connector and second output shaft of the motor's gear box with 4:1 belt drive to the 10-turn potmeter
The complete drive (capacitor + plate + motor drive) weighs a hefty 4.2 kg (9.3 lbs), about twice the weight of the capacitor by itself. The drive assembly is mounted onto the PVC mast (63 mm diam.) with two M6 bolts. Initially, I installed the loop with the capacitor drive at the top. Clearly, this configuration keeps the high-voltage part away from people and animals. However, it also makes the antenna very top-heavy. My antenna is not installed permanently on my terrace. On a windy day, I attach guy wires to the upper half of the PVC mast, in three or four directions. When I stick the loop on top of my telescopic mast (see Fig. 83B above), I install the capacitor at the bottom. This is more stable. This has another effect: my loop has a circumference of about 6 m (20 ft). This is about 0.07 λ in the 80m band, and the current around the loop is basically uniform. In the 40m - 20m bands, this is about 0.15 - 0.3 λ and the current is higher at the neutral-voltage point across from the capacitor. As "current radiates", having the highest current point a bit closer to free-space (obstacle-free), might just help a bit with the far-field strenght in the bands where the circumference is > 0.1 λ. NOTE: I have neither modelled this, nor verified this statement experimentally!
Figure 120: Motor drive installed on the PVC-tube antenna mast
WEATHER PROTECTION FOR THE MOTOR DRIVE
The motor drive definitely needs to be protected against rain and other forms of precipitation, as well as dust and dirt.
Originally (February 2018) I made a hood by combining two inexpensive plastic storage boxes that measure 35x20x15 cm (LxWxH, ≈13.8x8x6 inch). I cut one end of both boxes and of both lids. I combined the two boxes with industrial 1-sided sticky "duckt" tape (sometimes referred to as "duck" tape, which is a brand name; I actually used Gorilla® tape), both on the outside and on the inside of the seam, and combined the two lids with industrial 2-sided sticky tape. NOTE 1: these clear plastic storage boxes are made for indoor use, so they have no UV protection. Outdoors, they will become brittle and opaque fairly quickly, depending on how sunny your QTH is! NOTE 2: regular sticky tape, such as electrical insulation tape is useless for this application.
Figure 121: Protective hood made of two clear plastic boxes and their lids
The merged lids are installed between the plate of the motor drive and the PVC mast. I drilled two 20 mm holes in the hood at the appropriate place for the ends of the 12 mm diameter copper tubing of the main loop. With a thin blade saw, I then very carefully cut a slit between each hole and the open side of the hood. This makes it easy to install and remove the hood. An other hole was made for the cable between the motor drive and the remote control box. I closed the ventilation holes at the top, but left the ones at the bottom open.
Figure 122: Weather protection Mk 1 - installed
The above protective hood was basically a short-term solution, and not suitable for continuous outdoor exposure. Also, it was not nearly as weather-tight as I would like. Also, sooner or later (typically "sooner"), the sticky tape comes undone. As I don't leave my loop antenna out in the weather permanently, this was not that big of a problem. Of course, I do want to be able to use the antenna when it is raining. So I have to do much better!
Early 2021, I designed a completely new protective hood. This time 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 glueing outdoors or in a very well ventilated area! I used SCIGRIP® 16 glue. Note that some MMAs are colored when cured - not what I wanted! SCIGRIP 16 is (still) available at do-it-yourself stores an on-line shops in the US (,but 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 surface-mail within the US). As my current QTH is in Europe, I had to do some creative importation from the UK, and I only managed to get a 1 pint can (16 oz., ≈ 475 ml !) + applicator bottle, instead of a 1.5 oz or 5 oz. tube + plastic "micro tip" applicators. One or two 1.5 oz. tubes would have been enough...
As you can see in Fig. 113-120 above, the DC motor sticks out one one side of the white POM base plate of the motor drive. However, to mount the hood, I need a base plate that is wider then the entire motor drive, including the DC motor. I did not want to transfer the motor drive to a new, wider plate. So, unfortunately, I had to add a second back plate behind the existing white plate. A lesson learned...
The next Figure shows the the design. All polycarb pieces have a thickness of 4 mm, with exception of the two "wing" guide strips on the back (5 mm, though 4 mm would also have done the job). The hood design is basically a long box, with an open back and bottom. The back side is not completely open: it has narrow "wings" that slide behind the new back plate that is attached between the original white POM plate and the PVC mast. On the inside of the two side walls of the box, close to the guide "wings", there are two more guide strips. They are installed such that there is a small gap that is slightly wider than the thickness of the new back plate. Polycarb has only half the weight of same-dimensions glass - nevertheless, my hood + back plate adds a hefty 2.5 kg (≈ 5.5 lbs) to the antenna. This brings the total weight of the antenna to 12.3 kg (≈ 27 lbs)!
Figure 123: my design for the sliding hood
The next figure shows the polycarb plates that were accurately cut per the design above.
Figure 124: the custom-cut pieces of polycarbonate sheet - white protective film on both sides
The vacuum capacitor will be inside the box. The two ends of the copper tubing of the main loop are attached to the ends of the capacitor. So they will have to stick out sideways, through the left and right side of the hood. Where they will pass through the hood, I slowly drilled a hole that is slightly larger than the diameter of the tubing. before drilling, I covered the location of the hole on both sides of the plate with painter's masking tape. Clamp the polycarb plate onto wood backing, to help prevent splintering the exit hole when drilling through the plate. Slowly pre-drill with a small drill and then slowly increase the drill diameter. Next, I had to make the cut-outs for sliding over the copper tube ends. I stuck a wide strip of masking tape between each hole and the bottom end of that side plate. Then I marked two parallel lines, spaced by the hole diameter, from the hole to the bottom end of the plate. I used a sharp hacksaw with a very thin blade ("kerf") and fine teeth. Note that I always use a Japanese-style hand saw for this kind of work! Contrary to western saws, they cut on the pull, not on the push. This makes it much easier to cut straight and precise! Saw slowly, without applying a lot of force.
One more small operation to do before glueing all the pieces together. The two "wing" guide strips on the back of the box will have to slide down behind the back plate. To maximize weatherproofness, I want the top plate of the box to also cover the tops of these guide strips. However, this will cause some interference between the top of the box and the PVC mast, in the area where the back plate touches the mast. I filed away a small round indentation into the back side of the top plate. See the left-hand photo in Fig. 126. The depth of this indentation is equal to the thickness of the guide strips (5 mm in my design). The radius is that of the PVC mast (which has a 63 mm OD).
Now we can finally glue all the pieces together. As I indicated above, I used SCIGRIP 16 MMA. And I first watched a couple of YouTube instructional clips (search for "bond polycarbonate", "weld polycarbonate", and/or "weld acrylics"). Out of pieces of scrap wood, I also improvised a couple of simple jigs, to maintain 90° angle between pieces that I am glueing, and to help maintain pressure. Solvent glues have "working time", "fixture time", and "80% of final strength" curing time. See the label on the glue can or tube, and product datasheets. For SCIGRIP 16, this is 5-6 minutes, 10 minutes, and 24 hours, respectively. However, this depends a lot on ambient temperature etc. I found the working time (between application of the glue, joining the pieces, and making final position & angle adjustments) to be closer to 2 minutes then 5-6... I tried to apply the glue with the applicator bottle and the specified 16 gauge injection needle. I found the flow too small. Pouring straight from the bottle without the screw cap caused the flow to be too hard to control. I settled for using the bottle with the screw cap, but without the needle. See Fig. 125 below for the final result. I am pleased - not too bad for a first polycarb project! But not perfect: if you look closely at the photos below, you will see some sags where, or where I squeezed it out from between two joined pieces. You cannot wipe off excess glue without leaving a mark!
Figure 125: The various pieces of the hood - all glued up
Figure 126: top and bottom view of the installed hood
Do not throw away the two narrow strips that were cut out for the copper tubing! One is a lot longer than the other. I did not want to leave the cuts in the side of the box open. So, I re-used the cut out strips. The polycarb supplier that I used, has 35 mm minimum width for ordered cuts. For the internal guide strips, I actually only needed about half that width. So I cut those guide strips in half lengthwise befor gluing them in. My cuts are not nearly as precise and smooth as the machine-cuts, but the resulting narrow strips all still have one smooth long side. They are 5 mm wider than the narrow strips that I had cut out the sides of the box. I glued a piece of narrow strip to both sides of each cut out strip. See Fig. 127 for the long cut out. This way, I obtained two inserts that fit snugly in the cut outs. They stay in place all by themselves.
Figure 127: The long insert at the bottom of the right-hand side of the hood
Figure 128: views of the hood - installed onto the mast-mounted back plate
Polycarb plates are stiff, but they are still a bit flexible. And my box is long compared to its width, and the back is open. So the bottom of the box does not snugly fit the width of the back plate. No problem. I drilled through the bottom end of the guide strip "wings" and the backplate, while holding them in the desired position. Two screws + wing nuts now hold it all in place perfectly. See the left two photos in the Figure above, and the left photo in the Figure below.
Figure 129: fixation of the hood bottom and entry of the remote control cable & the power cable to the coupling loop drive
Two more holes to drill and we are done! Two cables have to enter the box: the 1/4" diameter (6+ mm) ethernet remote control cable and the 6 mm diameter power cable to the coupling loop DC motor drive. I drilled two holes (with pre-drilling) in the back plate, near the top. The holes are angled upward to the inside of the box, so water cannot drip into the box via the holes. With my hand saw, I cut out the material between the holes and the top of the back plate. So I can feed the cables to the inside of the box, without having to remove the connectors on the cables. See the right-hand photo in the Figure above. The cables also have a drip loop: they are angled downward on the outside of the backplate and then upward.
Figure 130: my 80-20 loop antenna with its new hood
REMOTE CONTROL BOX
Obviuolsy, I need a remote control box. t should have the following controls, indicators, and interfaces:
- Power on/off switch.
- Selection of motor rotation direction: clockwise (CW), off, counterclockwise (CCW). This will correspond to "increase frequency" and "reduce frequency" (or vise versa).
- Indication of the drive shaft position (some representation of 0-36 revs).
- Indication of "end-stop reached", separately for the CW and the CCW direction.
- Motor stall current warning (not mandatory, but nice to have and easy to implement).
- Standard 12-13.8 VDC input (13.8 is the normal supply voltage for transceivers and for charging 12 volt batteries).
- Multi-wire cable to the motor drive: 2 wires to the motor, 2 wires for the "NO" contact of the CW and CCW end-stop switches, 3 wires for the position feedback potentiometer. So, at least 7 wires. I decided to use a standard Ethernet cable (8 wires).
I originally intended to install one or more ferrite rings on these cable, as common mode chokes. However, with 100 watt transmit power, I did not notice any interference in any equipment in the house. So I did not install such rings. Not good! As you can see in Fig. 132 and 135 below, the 12 VDC powerplug on my remote control box is a little too long. The common/ground barrel is exposed. It became "RF hot", which is a rather unpleasant experience! I have added a ferrite choke on the power cord between the control box and the power supply (near the power supply). I placed another one on the control cable to the motor drive (at the control box end). This took care of my problem. I did not give the placement of the the ferrites much thought. Note, however, that a ferrite choke is most effective at the point along the cable where the common mode current wave is at its maximum, per the standing wave pattern. Depending on the length of the cable, there may be severeal such points - and they move with the operating frequency (frequency band).
Fig. 131 below shows the simple schematic for a remote control box. It includes high/low speed selection, by switching in a series-resistance of a couple of ohms. The shaft position feedback indication is done with the 10-turn potmeter. I use a separately regulated; supply voltage of 9 VDC for the potmeter, to make the feedback voltage independent of voltage drops in the motor drive circuitry (e.g., across the current-sensing resistor of the motor stall detection). The voltage of the potmeter wiper is measured with a simple and cheap 4-digit digital voltmeter (via eBay; search for "0.36" 4-Digit Digital Voltmeter Range 0-33V").
Figure 131: Remote control schematic - with simple high/low speed selection
Figure 132: The prototype remote control box, and the "ugly style" wiring
(the project box measures 7x10.5x2 cm; high-low speed switch and the associated resistor is not shown in the left-hand photo)
Reducing speed with a series resistor ( = voltage drop) also reduces motor torque. For fine-tuning the antenna, this is very undesirable! So, I decided to modify my remote control, and re-use the simple Pulse Width Modulator (PWM) controller of my small STL project. My PWM is a 6-24 VDC, 3A type (inexpensive purchase via eBay; search for "DC motor speed control PWM"). It measures only 3x5 cm (≈1.2x2 inch):
Figure 133: The small PWM speed controller card
The PWM circuit must be placed before the "direction" toggle switch. This means that the brightness of the green motor direction LEDs and the red end-stop LEDs now depends on the duty cycle of the PWM ( = speed setting)... To me, that is a small price to pay for being able to smoothly (and continuously) vary the motor speed between zero and max - with full torque! It just works beautifully!
Figure 134: Remote control schematic - with PWM variable speed adjustment
Figure 135: The prototype remote control box - now with variable speed adjustment
(red contrast filter added to the 4-digit DVM display)
MOTOR DRIVE FOR THE COUPLING LOOP
One of the standard coupling methods is a Coupling Loop, see the "Inductive coupling" section above. This is basically an air-core transformer. Normally, the configuration is as follows:
- The size of the coupling loop is fixed. Standard recipe is 1/5 the size of the main loop.
- The position of the coupling loop is fixed, after adjusting it once for lowest SWR on the frequency (or the middle of the frequency range) of interest.
- Sometimes the shape of the coupling loop is (also) adjusted to obtain best SWR.
- It should be relatively easy to obtain SWR < 1.1 (except maybe when the antenna is placed indoors).
In my experience, once the coupling loop has been properly adjusted, SWR remains < 1.2 over a frequency range of about 1:2.5. Beyond that, the SWR gradually (and rapidly) becomes worse than 1.5. Also, if you change the installation height of the antenna, the SWR will change noticeably. In 2018, I acquired a 6 m (20+ ft) telescopic mast (German army surplus). Depending on the weather conditions (we have a lot of heavy wind at my current QTH), I use my STL anywhere between 50 cm and 4m above ground level ( = my terrace floor). Raising and lowering the mast several times to re-adjust the coupling loop is no fun. So, I decided make the coupling between the coupling loop and the main loop variable, with remote-control motorization.
In principle, there are several basic ways to do this:
- Change the shape of the coupling loop. This is not very practical with a rigid coupling loop, and I did not try this.
- Rotate the coupling loop about its vertical axis, such that it no longer lies in the same plane as the main loop. See Figure 136 and the next section.
- If the orientation of the main loop and the coupling loop is close to perpendicular (90°), then the coupling factor is basically zero. There is no need whatsoever, to be able to go this far. I decided to design my motorization for a maximum swing of about 40-50° ( = 20-25° to either side of co-planar or parallel).
- Keep the coupling loop co-planar with the main loop, but translate ( = slide) it up or down, such that its distance to the main loop changes. See Figure 137 and the following section.
Fig. 136: Rotating the coupling loop about its vertical axis to change the coupling with the main loop
Fig. 137: Translating the coupling loop to change the coupling with the main loop
COUPLING LOOP MOTORIZATION - PART 1: ROTATION
There are several ways to motorize rotation of the coupling loop out of, and back into, the plane of the main loop:
- Stick the mounting-end of the coupling loop onto the shaft of a very-low-rpm DC motor. To get low enough RPM (e.g., 0.2-0.3), you will have to use motor with a attached down-gearing. And even then, you probably want to add (or need) variable PWM motor rpm control, to further reduce the rpm of the coupling loop. And you will have to add two end-stop switches:
- Unless your STL is dimensioned for VHF, or is really self-supporting ( = made of large diameter rigid tubing), your STL will be attached to a support mast. This makes it impossible to place the coupling loop exactly in the plane of the main loop. This also makes it impossible to rotate the coupling loop 360° without hitting the mast.
- Also, there is a coax cable attached to the coupling loop. It will wrap around itself, or the coupling loop drive, if rotation is unlimited. Not good when you don't have visual contact with coupling loop!
- Rotate the coupling loop not about its own axis, but about another axis. This other axis is parallel to the vertical axis of the main loop, and preferably close to the latter. Again, rotation has to be limited - with end-stop switches, or mechanically.
- The standard way to convert 360° motor shaft rotation to a limited rotation angle ( >0° but <180°) of the load, is to use a double-eccentric ( = "off center") drive. This is also known as "crank-and-rocker" and "4-bar linkage". No end-stop switches are required!
- This is the same method that is used in continously oscillating fans for room ventilation.
Motion of a double-eccentric / crank-and-rocker / 4-bar-linkage arrangement
In the video clip above, it looks like the linkage only has 3 bars. However, it is generically called a 4-bar linkage. The fourth bar is the "vertical" offset between the axis of rotation of the motor and of the load. I.e., if the motor is moved up or down along the gray vertical line in the image.
A crank-and-rocker mechanism has several parameters that must be chosen to obtain the desired angular swing range:
- The length of the crank on the motor shaft ( = distance between shaft axis and swivel point at the end of the motor crank).
- The length of the crank on the load ( = distance between axis of rotation of the load, and swivel point at the end of this crank).
- The length of the push-pull bar between the two cranks ( = distance between the two swivel points).
- The distance between the two axes of rotation.
I like a good challenge, so I decided to implement the eccentric-drive method - yes, you may call me crazy. When I started this little project, my coupling loop was mounted onto the PVC mast with two standard PVC tube clamps. By loosening the clamps a little bit, they can rotate around the mast without too much resistance or wiggle. I use the same approach during manual adjustment. I decided to motorize the clamp that is farthest from the main loop. Somehow, this clamp must be rotated around the mast with a small electric motor. I do not need position feedback for this motor, and I did not want to add end-stops.
For installation on the antenna mast, these parameter must be chosen such that the crancks, and the bar between them, do not touch the mast. Otherwise, the drive mechanism will self-destruct! This can all be calculated with trigonometry. Good luck! Or, you can model it with a CAD tool - which I don't have. I simply took a large sheet of paper, drew the cross section of the PVC mast tube on it (scale 1:1), added the rotation radius of the coupling loop, and assumed a simple mount for the small 12 Vdc / 3 rpm motor that I happended to have. I placed the motor 135° away ( = behind the mast) with respect to the plane of the main loop. Then I started to play with crank lengths and the push-pull bar length:
Figure 138: Design drawing of my double-eccentric drive
The drawing above shows the dimensions that I finally selected. The motor mount, the two "arms", and the push-pull bar are all made of 11 mm thick polyethylene ( = kitchen cutting board). This material is light, strong, and easy to machine (drill, saw, grind,...). I fixed the motor mount to the PVC tube mast with a standard "munson" type tube/pipe clamp and a heavy angle bracket. The swivels are made of 6 mm bolts, with washers and lock nuts ( = nut with a nylon insert).
Figure 139: Side view of the double-eccentric drive for the coupling loop
Figure 140: Top view of the double-eccentric drive for the coupling loop
Note that the crank bars on the motor shaft and on the coupling loop have some extra length and holes. This was done, just in case I needed to make some adjustments to the swing range. Actually, my original design was very close to "perfect".
Figure 141: the double-eccentric drive for the coupling loop - installed
Full motion cycle of the motorized coupling loop (max speed)
©2019 Frank Dörenberg (N4SPP)
Note: clearly, it is very difficult (if not impossible/impratical) to make this motor drive weatherproof!
I am using the same remote control method as for motorizing the tuning capacitor, see Fig. 124. I use a standard 8-conductor ethernet cable between motor drive(s) on the antenna and the remote control box in the shack. With only the capacitor drive motor + position feedback + end-stop switches feedback, only 7 of 8 conductors of the cable are used. I use the 8th conductor to actuate a small relay at the antenna. It switches power between the capacitor drive motor and the coupling loop drive motor. Other options are to run a separate cable with a separate control box. Or: run a separate cable and switch the control box between the two cables at the shack end. I clearly prefer my solution with the relay. I did not have a small 12 volt DPDT relay in my junk box, so I used two very small 5 volt SPDT relays (type DR-5V) that I happened to have, and connected their solenoids in series:
Fig. 142: Simplified remote control schematic - with toggle switch for motor-selection and one DPDT relay
Figure 143: The remote control box - with toggle switch for motor-selection and two SPDT relays
Figure 144: The remote control box - now with a toggle switch for motor selection
Fig. 145: The SPDT relays (glued together with blue Loctite) near the Ethernet cable connector at the antenna
(compare to Fig. 118)
Note: I could have added more relays, all controlled by the same signal, to also switch end-stop switch wiring and position feed back wiring (if I had added any of these to my coupling loop drive).
COUPLING LOOP MOTORIZATION - PART 2: LINEAR TRANSLATION
I completed a linear translation drive in January of 2021, two years after my eccentric rotation drive. Mechanically, this is much easier. It is also much easier to weatherize. I use exactly the same motor control box and motor switching at the antenna, as shown above for the rotation drive.
Instead of constructing a translation drive myself, I went the easy route: I bought an off-the-shelf 12 VDC motor drive via eBay (search for "electric linear actuator"; prices vary considerably). Such actuators are typically used for opening/closing skylight windows and for rotating satellite dish antennas. They are available with a large variety of stroke ( = extension distance) and force. I got one with a stroke of 100 mm ( = 10 cm = 4 inches), a nominal speed of 5 mm/sec, and an enormous force of 1000 N (≈100 kg, ≈220 lbs). This stroke is more than I need for normal operation, but I wanted to have plenty of margin for experimentation. Such actuators have built-in end-stop switches (the SPST contacts are not accessible), or a simple slip-clutch mechanism. They work well in combination with a PWM variable speed controller. Of course, the length of the actuator housing is a bit larger than the stroke. More expensive linear actuators may include a built-in potentiometer for position feedback.
Fig. 146A: Linear actuator - M7 thread added for attaching my coupling loop, silicone caulking added for weatherproofing
Fig. 146B: Cutaway view of a typical linear actuator
(note one of the two end-stop switches below the visible part of the lead screw)
I re-used the soft copper tubing (standard 1/4 inch = 6.35 mm diameter) of my previous coupling loop, and built a weatherproof box to mount it onto the tip of the actuator, with an M7 bolt. I did not have a suitable mounting box at hand, but I did have a 2 meter section of standard 4 cm wide hard PVC angle profile. I cut pieces out of it, and glued them up with regular PVC glue. The box looks like a tiny birdhouse. Via the entry hole, I can access the coax cable with a soldering iron, and access the M7 mounting bolt (with hex socket) - without having to break open the box. The entry hole is closed off with a piece of clear plastic. The two ends of the copper tubing enter via standard cable glands (F: presse-étoupe, D: Kabelverschraubung). I used PG07 glands. They are watertight (IP68 standard), and are made for cables with a 3-6.5 mm diameter - perfect for my copper tubing! The tube circumference is 122 cm (48 inch), which is 1/5 of the 610 cm of the main loop.
Fig. 147: My new coupling loop with mounting box
The coupling loop drive is firmly mounted onto the PVC mast of my STL with two hose clamps (UK: "jubilee clips"):
Fig. 148: My coupling with linear motor drive
Mounting height was adjusted such that with the actuator fully extended, the coupling loop almost touches the main loop. Note the small black shrink tubing insulation at the top of the coupling loop. The point of the main loop that is diametrically opposite of the variable capacitor (i.e., half way around the main loop), is electrically neutral. But I decided to add some insulation anyway.
When fully retracted, the bottom of the "birdhouse" completely hides the black top of the actuator. See the right hand photo in Fig. 148 above. In this parking position, no rain water can enter the actuator via the top.
Fully extended, the actuator rod has noticeable radial play and backlash (rotational play). However, I tilted the coupling loop slightly against the PVC mast of the STL, and the back of the "birdhouse" rides against the PVC mast. This appears to sufficiently stabilize the installation.
NEXT PROJECT: AUTOMATIC TUNING
To be added...
Two methods: select operating frequency and vary the capacitor value so as to minimize SWR or to maximize power or current. Typically do not result in exactly the same capacitor setting.
Work on this has been done by the (primarily) Japanese "MLA 48" group, in particular Hajime Nakajima (JR1OAO). His automatic antenna coupler measures the RF voltage and current at a point along the coax to the antenna. The position of the coupling loop position is adjusted based on the ratio of these two parameters (effectively an impedance value), to minimize the SWR. The measured phase angle between the current and voltage is used to adjust the motorized tuning capacitor until the resonance frequency matches the operating frequency. Note: the phase angle to be adjusted/calibrated is measured at the antenna feedpoint (or a point along the transmission-line that is at an electrical distance of a whole multiple of 1/2 λ away from the feedpoint).
Just like the motorization of the tuning capacitor can be automated, so can the coupling loop drive. Excessive luxury. Switchable.
- Ref. 1: "Magnetic Loop Antenna" with video clips about radiation direction and voltage/current distribution of STLs, Ben Edginton (G0CWT), May 2012. [pdf]
- Ref. 2: Loop calculators and formulas:
- Ref. 2A: KI6GD calculator
- Ref. 2B: AA5TB calculator, version 1.22F, accessed 15 March 2021 (Microsoft Excel file - if you don't have MS Excel on your PC, you can download a freeware viewer from Microsoft here)
- Ref. 2C: "66pacific" on-line loop calculator (based on ARRL Antenna Handbook)
- Ref. 2D: RJELOOP1 calculator for performance of single-turn magloop antennas of various regular shapes and MAGLOOP4 calculator for performance versus height and type of ground, by Reg Edwards (G4FGQ, SK)
- Ref. 2E: "DG0KW Magnetic - Loop Antenna - Calculator", Klaus Warsow (DG0KW); note: 3 GUI languages selectable via the "options" tab.
- "Quick reference Guide" [pdf]
- Ref. 2F: "Small transmitting loop calculators – a comparison", Owen Duffy (VK1OD, VK2OMD), November 16, 2015 [pdf]
- Ref. 2G: "Calculate small transmitting loop gain from bandwidth measurement", V. 1.03, on-line calculator for efficiency and and gain of a small single turn transmitting loop in free space from VSWR bandwidth, matched frequency, loop radius and conductor radius or resonating capacitance, Owen Duffy (VK1OD, VK2OMD), 2014/2015.
- Ref. 2H: "Estimating the voltage impressed on the tuning capacitor of a small transmitting loop", Owen Duffy (VK1OD, VK2OMD), 6 June 2017. Accessed 29 August 2019. [pdf]
- Ref. 2J: "Accuracy of estimation of radiation resistance of smal transmitting loops", Owen Duffy (VK1OD, VK2OMD), Version 14 august 2015. Accessed 5 January 2020. [pdf]
- Ref. 2K: "Small transmitting loop – ground loss relationship to radiation resistance", Owen Duffy (VK1OD, VK2OMD), Version 8 august 2015. Accessed 5 January 2020. [pdf]
- Ref. 3: Some discussions about the efficiency of STL antennas:
- Ref. 3A: "Magnetic loop or small folded dipole?", M.J Underhill, M.J. Blewett, Proc. IEE Conf "HF Radio Systems and Techniques", 1997, pp. 216-224.
- Ref. 3B: "Small Loop Antenna Efficiency", Mike Underhill (G3LHZ), May 2006.
- Ref. 3C: "All sorts of small antennas – they are better than you think – heuristics shows why!", Mike Underhill (G3LHZ), February 2008.
- Ref. 3D: "Small, high-efficiency loop antennas", Ted Hart (W5QJR), in "QST", June 1986, pp. 33-36.
- Ref. 3E: "How Efficient is Your QRP Small Loop Antenna?", Amir Findling (K9CHP), Kazimir Siwiak (KE4PT), in "The QRP Quarterly", Summer 2012, pp. 22-23; accessed 6 June 2019. [pdf]
- Ref. 3F: Small-Loop-Antenna-Efficiency-calculator, Microsoft Excel spreadsheet (based on ref. 3E), Frank Dörenberg (N4SPP), 6 June 2019.
- Ref. 4: Flat-strip and PCB STL antennas
- Ref. 4A: "The Midnight Loop - An Experimental Small Transmitting Loop ~ Theory & Practice ~", G. Heron, N2APB and J. Everhart, N2CX, Massachusetts QRP Convention 2010, 52 slides.
- Ref. 4B: "Portabel-Magnetschleifantenne für das 2-m-Band", Tomas Schiller (DC7GB), in "Funkamateur", Nr. 8/17, pp. 746-748. [pdf] See note at bottom of this page.
- A kit is available from the "Funkamateur" shop here. [pdf], retrieved 16 March 2021.
- Ref. 5: Helically-wound STL antennas
- Ref. 5A: "Helically Loaded Magnetic Loop Antenna", web page by Rich Fusinski (K8NDS, SK). Accessed 29 June 2019.
- Ref. 5B: "Helically Loaded Fractional Wave Loop Antenna" Yahoo-group. Accessed 1 August 2021.
- Ref. 5C: "Slinky Loop aerial", Tom Haylock (M0ZSA), in "RadCom", November 2010, p. 49.
- Ref. 5D: "A Helical Loop Antenna for the 20-meters Band", Vladimir Kuzmin (UA9JKW), in "Antentop", Nr. 5, 1-2004, pp. 60-62.
- Ref. 5F: "The SLINKY-HULA", by John Heys (G3BDQ), in "Practical Wireless", November 2003, pp. 44-45.
- Ref. 6: Coupling and Matching Networks
- Ref. 6A: "Magnetic Loop Koppelschleifen" [in German; "Coupling-loops for magnetic loops"], Jochen Huebl (DG1SFJ). Source:dg1sfj.de.
- Ref. 6B: "Down-to-Earth Army Antenna", K. H. Patterson, in "Electronics", 21 August 1967, pp. 111-114. Source: worldradiohistory.com, accessed 19 September 2020.
- Ref. 6C: "The DL2JTE Loop: A Novel Antenna - Translation, possible theory of operation and comments by Paul Lukas - N6DMV/HA5CCV", antenneX, Issue No. 168, April 2011 (translated from "Die HA-Loop-Antenne - auf Vor- und Endselektion kommt es an", Lásló Rusvai (DL2JTE/HA7HN), in "CQ-DL", 10-2011, pp. 717-719).
- Ref. 6D: "Neue Speisetechnik für Magnetic Loops" [new feeding method for magnetic Loops], Lásló Rusvai (DL2JTE/HA7HN), in "CQ-DL", 6-2007, pp. 421.
- Ref. 6E: "Building the Magnetic Loop Antenna" [ferrite ring transformer], (KJ3JLS). Accessed 1 August 2021 [pdf]
- Ref. 6F: "The Rockloop - A Compact Antenna for the 15, 20 and 30 meter Bands" [incl. ferrite transformer], C.F. Rockey (W9SCH), SPRAT, Nr. 60, autumn 1989, p. 15.
- Ref. 6G: "How to design gamma-matching networks", Harold Tolles (W7ITB), in "Ham Radio Magazine", May 1973, pp. 46-55.
- Ref. 6H: "An examination of the Gamma Match", D.J. Healy W3PG/W3HEC, in "QST", April 1969, pp. 11-15, 57. [pdf]
- Ref. 6J: "What's with the Gamma Match Equations?" (Gamma Match Equations and Associated Confusion), Bill Wortman (N6MW).
- Ref. 6K: "The G3LHZ Twisted Gamma Match", p. 3 in "Surrey Radio Contact Club Newsletter", no. 797, February 2009.
- Ref. 6M: "My Experiments - Antennas", Jo Lourenço (CT1ECW). [pdf]
- Ref. 6N: "DX-Antennen mit spiegelnden Flächen - Teil 12 & 12b", Hans Würtz, in "CQ-DL", 2/1983, pp. 64-67 and 4/1983, pp. 170, 171.
- Ref. 6P: "The Army Loop in Ham Communication", Lewis G. McCoy (W1ICP), in "QST", March 1968, pp. 17, 18, 150, 152.
- Ref. 6Q: "Sources of Magnetic Fields" & "Inductance and Energy in Magnetic Fields", Sen-ben Liao, Peter Dourmashkin, John W. Belcher. Source: chapter 9 and 11 of course notes used in Physics 8.02 "Electricity and Magnetism" at MIT.
- Ref. 6R: "Nogmaals koppellus voor raamantennes" [in Dutch, "Coupling loop for loop antennas - revsited"], Koos Fockens (PA0KDF), in "Electron", October 2000, p. 405.
- Ref. 7: "FAIR-RITE Material Data Sheets for Materials Nr. 31 -98", Fair-Rite Products Corp; Core Loss vs. AC Flux Density - Type 61 Material; Initial Permeability and Loss Factor vs Frequency of Type 43 material".
- Ref. 8: Some general STL "Magnetic Loop" articles and links (incl. NEC modeling)
- Ref. 8A: "Small Transmitting Loop Antennas", Steve Yates (AA5TB), August 2013.
- Ref. 8B: "Welcome to W2BRI's Magnetic Loop", Brian Levy (W2BRI).
- Ref. 8C: "G3LDO's experiences with a small transmitting loop antenna", in "RadCom", September 2010, pp. 34, 35.
- Ref. 8D: "Loop Antennas", Chapter 5 in "ARRL Antenna Handbook", 21st edition.
- Ref. 8E: "An Overview of the Underestimated Magnetic Loop HF Antenna", Leigh Turner (VK5KLT), V1.2, October 2015 (used with permission).
- Ref. 8F: "My Magnetic Loop Antenna", A. Krist (KR1ST), in "AntenneX", Issue No. 111, July 2006. [pdf]
- Ref. 8G: "Small Gap-Resonated HF Loop Antennas", Kai Siwiak (KE4PT), Richard Quick (W4RX), in "QST", September 2018, pp. 30-33. [pdf] See note at bottom of this page.
- Ref. 9: corrosion, silver plating
- Ref. 9A: "Silver plating RF components", Dirk Winand (ON4AWU).
- Ref. 9B: "Components and materials", David Knight (G3YNH).
- Ref. 9C: "Measuring the permittivity and permeability of lossy materials: solids, liquids, metals, building materials, and negative-index materials", J.R. Baker-Jarvis, M.D. Janezic, B.F. Riddle, R.T. Johnk, P. Kabos, C.L. Holloway, R.G, Geyer, C.A. Grosvenor, NIST Technical Note 1536, US Dept. of Commerce, National Institute of Standards and Technology (NIST), 2005, 160 pp. Source: nist.org, retrieved 22 June 2020.
- Ref. 10: "Tube roller" by Roger Dunn (VK4ZL), September 2011, 2 pp., used with permission.
- Ref. 11: Motor drives for tuning capacitors
- Ref. 11A: "Helical loop - direct drive with limit travel and motor stall Warning LED on control unit" (about half way down the page), Rich Fusinski (K8NDS), 2013. [pdf of schematic]
- Ref. 11B: "Easy Step'n - An Introduction to Stepper Motors for the Experimenter", David Benson, Square 1 Electronics (publ.), 2001, 199 pp.
- Ref. 11E: "To automatically tune a Magnetic Loop Antenna" [stepper motor control with display], Loftur E. Jónasson (TF3LJ / VE2LJX).
- Ref. 11F: "Multiturn Coils and Capacitors Drive", Rev. 2, Dominique Delerablee (F1FRV). [pdf]
- Ref. 11G: "F1FRV Flea Market" [French & English on the same page], Dominique Delerablee (F1FRV), accessed 2 November 2020. [pdf]
- Ref. 12: Capacitors
- Ref. 12A: "Variabele condensator in olie" [in Dutch, "Variable capacitor in oil"], Otto Kühn (PA9OK, SK), in "Electron" (VERON), December 2010, pp. 527-529. See note at bottom of this page.
- Ref. 12B: "Vacuum Capacitors", G.H. Floyd, in "Proceedings of the IRE", Vol. 32, Nr. 8, August 1944, pp. 463-470. Source: worldradiohistory.com, accessed 1 August 2021.
- Ref. 12C: "A highly stable reference standard capacitor", John Hersch, in "General Radio Experimenter", Vol. 37, No. 8, August 1963, pp. 1-8. [pdf]
- Ref. 12D: Equation 13.5 in "Capacitive sensors", Section 13.2 in "Handbook of modern sensors: physics, designs, and applications", Jacob Fraden, Springer-Verlag New York, 2010, 663 pp.
- Ref. 12E: "Electrical properties of atmospheric moist air: a systematic, experimental study", Hugh Carlon, U.S. Army Research Directorate, Chemical Research, Development & Engineering Center, Report nr. CRDEC-TR-88059, September 1988, 31 pp. [pdf]
- Ref. 12F: "The Dielectric Constant of Air at Radio Frequencies", A. B. Bryan, I. C. Sanders, in "Physical Review", Vol. 32, Iss. 2, August 1928, pp. 302-310. Source: en.booksc.org, access 1 August 2021. [pdf]
- Ref. 12G: "Vacuum Capacitor Characteristics", Jennings Technology Tech Note. [pdf]
- Ref. 12H: p. 73 in "Capacitive sensors: design and applications", L. K. Baxter, IEEE Press, 1997, 320 pp.
- Ref. 12K: "Diagnostic of vacuum on the basis of the dielectric strength", W. Chmielak, Z. Pochank, in "Przeglad Elektrotechniczny", Vol. 88, Nr. 12b/2012, pp. 311-314. [pdf]
- Ref. 12L: "Vacuum Variable Capacitors - An Introduction to their Design, Rating and Installation", Lars Giers, in "Cathode Press" (The Machlett Labs, Inc.), Vol. 23, Nr. 4, 22 February1994, pp. 22-29. [pdf]
- Ref. 12M: "Measuring the loss in variable air capacitors", Alan Payne (G3RBJ), Issue 2, September 2013, 14 pp. [pdf]
- Ref. 13: Variable inductors
- Ref. 13A: "A New Tune for the Loop", John Seager (G0UCO), in "QEX", September/October 2010, pp. 35-37. Accessed 9 April 2019. [pdf] See note at bottom of this page.
- Ref. 14: Radiation safety
- Ref. 14A: "HF Small Transmitting Loop - Safety Compliance Distances (FCC, ICNIRP, and Canadian Guidelines)", Peter DeNeef (AE7PD), rev. 17 February 2019. Accessed 20 June 2019. [pdf]
- Ref. 14B: "Safety Distances for HF Small Transmitting Loops", by Peter DeNeef (AE7PD), in "RadCom" (RSGB), June 2017 (accessed 20 June 2019), pp. 46-47. [pdf] See note at bottom of this page.
- Ref. 15: Shielded coupling loops
- Ref. 15A: "The Screen Loop Aerial - A Theoretical and Experimental Investigation", R.E. Burgess, in "The Wireless Engineer", Vol.16, No. 193, October 1939, pp. 492-499. Retrieved 20 August 2019. [pdf]
- Ref. 15B: "Special aspects of balanced shielded loops", L.L. Libby, in "Proc. of the I.R.E.", Vol. 34, Issue 9, Sept. 1946, pp. 641-646. Retrieved 20 August 2019. [pdf]
- Ref. 15C: "Characteristics of the Mobius Strip Loop", Carl E. Baum, "Sensor and Simulation Notes VII", 1964, 15 pp. Retrieved 20 August 2019. [pdf]
- Ref. 15D: "Analysis of the Moebius Loop Magnetic Field Sensor", Paul H. Duncan, in "IEEE Trans. on Electromagnetic Compatibility", Vol. EMC-16, no. 2, May 1974, pp. 83-89. Retrieved 20 August 2019. [pdf]
- Ref. 15E: "Probing the magnetic field probe", Roy Ediss, in "EMC & Compliance Journal", Issue 47, July 2003, 6 pp. Retrieved 20 August 2019. [pdf]
- Ref. 15F: "Using close field probing to reduce EMC design risks - Part 1", Keith Armstrong, in "EMC Journal", Issue 112, June 2014. Retrieved 20 August 2019. [pdf]
- Ref. 15G: "A Practical Approach to building and Evaluating a Broadband Active Loop Antenna, looking at the Mobius, Conventional Shielded and Wire Loops", Everett Sharp (N4CY, frmr. N8CNP), in "Medium Wave News", Vol. 62, Nr. 2, May/June 2016, pp. 11-20. Retrieved 20 August 2019. [pdf]
- Loop antenna simulations
- Ref. 16A: "A Universal HF Magnetic Loop Antenna NEC Model", Carol F. Milazzo (KP4MD), 16-Sept-2011. [pdf NEC1 NEC2 NEC3]
- Ref. 16B: "NEC simulation model for Config #1", "NEC simulation model for Config #2", Frank Dörenberg (N4SPP/F4WCN), 4 March 2021.
Note: due to copyright reasons, this file is in a password-protected directory. Contact me if you need access for research or personal study purposes.
External links last checked: October 2015 unless stated otherwise