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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.

In future updates to this page, I hope to add the following topics:

Effect of installation height above ground on feedpoint impedance and resonance frequency.

Effect on radiation pattern & gain of tuning capacitor located at the top vs. at the bottom of a vertical loop ( = effect of ground proximity).

Multi-turn loops.

Latest page update: June-August 2020 (expanded "Effects of corrosion" section, expanded "air variable capcitor in oil" paragraph)



Previous page updates: 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)

©1999-2020 F. Dörenberg, unless stated otherwise. All rights reserved worldwide. No part of this publication may be used without permission from the author.

INTRODUCTION

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".

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!

Fig. 2: approximate radiation pattern of a vertically oriented Small Transmitting Loop

(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. Loop performance close to that of a full-size dipole.

Figure 7: Printed circuit board loop for the 2m band

(source: ref. 4B)

SAFETY

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.

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.

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. 8H)

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.

: 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 capacitance.

: 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 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.

: 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.

: 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 kB 10-500 πФ" in other words: "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.

Figure 15: My vacuum capacitor

CAPACITOR RATINGS

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: V S = (30xD + 1.35) kV, where D is spacing in cm. For 1 mm (D = 0.1 cm), this yields V S = 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

where

C = ideal, lossless capacitance

R series = equivalent series resistance (ESR, loss)

L series = equivalent series inductance (ESL)

R parallel = insulation resistance

R DA = resistive component of the dielectric absorption

C DA = 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 I RMS 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 R parallel 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 L series 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:

where

C = capacitance in Farad

ε 0 = absolute permittivity of free space ("pure vacuum"); ε 0 = 8.85x10-12 F/m

ε r = 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

r 1 = inner radius of the outer electrode in meters

r 2 = 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 C 0 = capacitance of the tuning capacitor at a particular temperature T 0 . 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 T 0 to T 1 . 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:

where

L = inductance in Henry

μ 0 = absolute permeability of free space ("pure vacuum"); μ 0 = 4π x 10-6 H/m

μ r = 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 ε r = 1 for vacuum. Dry air has an ε r ≈ 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 μ r ≈ 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:

Note: this is only a overview of the most common methods. The list is not exhaustive.

INDUCTIVE COUPLING

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 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.

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.

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. 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.

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.

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.

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.

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 mm 2 , but these days I use soft copper tubing of about 6 mm diameter in my large loop (see Fig. 79 below), and thin brass tubing (see Fig. 9 of my small STL project). This is mechanically quite stable.

, but these days I use soft copper tubing of about 6 mm diameter in my large loop (see Fig. 79 below), 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 over a frequency range of up to 2 decades (factor 4), see Fig. 79 & 80 further below.

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 V max /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! It cannot be used to generate or receive an EM field! It appears as an "open" to the coax that is connected to the transceiver.

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.

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 anything 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, the shielded coupling loops had better coupling: S11 was more negative by about 6 dB ( = return-loss decreased by 6 dB). See the figure below.

= +20 x log(abs(Γ)), where Γ is a complex number (a vector entity). It has a magnitude that is commonly denoted , and a phase angle . is 0 for a full reflection and negative for anything else. "Return-loss" is simply that same dB value of , but with the opposite sign (at least for passive devices such as antenna systems). "Return loss" does not mean loss reflection ( = "return"), but rather means loss reflection. Jochen observed that 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, the shielded coupling loops had better coupling: was more negative by about 6 dB ( = return-loss decreased by 6 dB). See the figure below. With my feed-loop experiments, I have noticed that I generally cannot obtain SWR < 1.5-1.7 unless the feed-loop is almost against the main loop (< 1 cm ≈ 1/2 inch).

Figure 26: Return-loss S11 as a function of distance between coupling loop and main loop

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

CAPACITIVE COUPLING

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 A L 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.

Some notes:

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.

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.

skewed, causing a front-to-back ratio that 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

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.

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 46: 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 47: 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 48: 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")

: 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 49: 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 f res ). 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). I realize that this says nothing about RF losses. However, 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, not hardened (heat treated) tubing, which is typically sold as straight tubing, not coiled.

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

(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 86: My STL close to the terrace floor and 4 mtrs above it

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 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 surfa