Getting On The Air

Designing a Balcony HF Magnetic Loop Antenna - Part 1

#magloop #antenna #hf #balcony #urban #nec2 #diy #qrp #homebrew #modelling #theory

Reading time: 35 minutes

This post has been a long time coming, and is my understanding of the commonly termed magnetic loop antenna. I invite people to please let me know if there are issues with my understanding, the TLDR; version:

Balcony Operating Constraints

Operating a HF station in an urban Indian environment is tricky (at best)! Previously, when I was operating from my QTH, I used to throw a wire outside the window using a telescopic fishing pole. However, this is highly sensitive to nearby concrete rebar, wind and metal railings, each of which tends to detune the system in an unpredictable manner. This structural proximity causes the SWR to change inconsistently across bands, limiting operations to late-night hours when the ground below is vacant and requiring a tedious, 30-minute setup and tear-down sequence. Operating from a 5th-floor balcony (without access to the terrace) in a dense residential neighbourhood like Bangalore immediately rules out traditional full-sized wire dipoles or quarter-wave verticals, which require expansive outdoor real estate. Consequently, a self-contained, quiet balcony antenna, with an acceptable performance1, becomes an absolute necessity.

  1. Rebar- Shielding and Detuning: In India, multi-storey apartment buildings are constructed of heavily reinforced concrete. From an electromagnetic standpoint, this dense grid of steel reinforcing rebar acts as a lossy, reflective Faraday shield. Placing an antenna inside or directly against the balcony floor and ceiling significantly dampens signals and heavily attenuates both receive and transmit performance. Even if the steel is not a “dense” grid, it still detunes the antenna and adds loss!
  2. Urban QRM Floor: Densely populated urban environments suffer from an exceptionally high floor of man-made electromagnetic interference (QRM). This localised electrical noise is continuously emitted by switched-mode power supplies (SMPS), cheap LED lighting, and consumer household electronics, resulting in a persistent S-meter noise floor of S7 to S9 on traditional wire antennas (at some point I’d like to give you folks measurements for it).
  3. Compliance & Portability Mandate: To remain compliant with strict rules of the apartment association2, any antenna installation must be completely within the balcony with nothing protruding beyond the balcony railing. Nothing can be permanently fixed to the railing or the balcony, so the antenna must be quick to set up and take down, and even while deployed it must pose no risk to residents below.
  4. Radios and Power: The loop needs to work with my QMX, zBitx and sBitx, so it must handle 5–10 W comfortably and up to about 25 W with the sBitx. Which bands to target is something I’ll work out from the numbers later in this post as we go along. Since we are working QRP mostly, my design should work with it, but the challenge with loops is that the tuning capacitor has to withstand about 2–3 kV at 10 W, and over 4 kV at 25 W, on 40 m (we shall see the calculation in the later sections).

Please note that I have used LLMs to create the scripts to generate the images in this post. They serve as good ways for me to understand the theory of antennas, and creating cleaner images than drawing them by hand is a good choice for this kind of post.

Theory

Near-Field Physics: Electric vs. Magnetic Coupling

Figure 1: 3D vector representation of propagating electromagnetic wave showing orthogonal E and H fields.

Figure 1: 3D vector representation of propagating electromagnetic wave showing orthogonal E and H fields.

According to classical electrodynamics, time-varying electric (\(E\)) and magnetic (\(H\)) fields are inherently coupled. In a transmitting antenna both fields are established simultaneously as co-existing components of an electromagnetic wave.

Typically, antennas are classified based on the dominant type of reactive energy stored in their immediate vicinity:

What is the near-field region? The space around an antenna is usually divided into three regions, two of which make up the near-field. \(D\) is the largest dimension of the antenna, \(λ\) is the wavelength and \(r\) is the distance from the antenna, in the equations below:

  1. Reactive near-field region: The region immediately surrounding the antenna where the reactive (non-radiating) fields dominate. The boundary is defined as:
\begin{equation} \label{eq:reactive\_near-field\_boundary} r < 0.62 \sqrt{\frac{D^3}{\lambda}} \end{equation}

For an electrically small antenna (\(D \ll \lambda\)), such as the small loop antenna we wish to design, this boundary is commonly taken as the radian distance:

\begin{equation} \label{eq:reactive\_nearfield\_small} r < \frac{\lambda}{2\pi} \approx 0.159\lambda \end{equation}
  1. Radiating near-field (Fresnel) region: The region where radiation fields begin to dominate, but the angular field distribution is still dependent on the distance from the antenna. The boundaries are:
\begin{equation} \label{eq:radiating\_nearfield\_boundary} 0.62 \sqrt{\frac{D^3}{\lambda}} \le r < \frac{2D^2}{\lambda} \end{equation}

Note: This region may not exist if the antenna is electrically small relative to the wavelength (as is the case with our design).

  1. Far-field (Fraunhofer) region: The region where the angular field distribution is completely independent of the distance. The radiation pattern is fully formed, and the waves behave as local plane waves. The boundary is defined by:
\begin{equation} \label{eq:farfield\_boundary} r \ge \frac{2D^2}{\lambda} \end{equation}

Subject to the additional constraints of \(r \gg D\) and \(r \gg \lambda\).

Figure 2: The three field regions surrounding an antenna based on radial distance.

Figure 2: The three field regions surrounding an antenna based on radial distance.

So what does this mean for a balcony loop? Looking at the table below3, there is no band where I can get the antenna “away” from its surroundings. Even on 10 m the reactive near-field reaches out about 1.7 m, and on 40 m it is close to 7 m. Either way, the railings, the rebar in the slab and every charger and LED driver in my flat (and probably my neighbour’s) are well within it. This cuts both ways. On the plus side, it is exactly why a magnetic loop makes sense here: it is far less bothered by the local electric-field noise that a wire antenna happily soaks up, and the lower the band, the more of that noise sits in the near-field. On the minus side, the loop’s strong magnetic near-field will couple into all that nearby steel, including the rebar inside the concrete, and lose power there, so where I place it on the balcony matters a lot. In short, from a near-field perspective the loop helps on every band; which bands it actually works well on comes down to its size and efficiency, which I’ll work out in the calculations section below.

Table 1: Indian amateur bands from 160 m to 6 m, with the reactive near-field (\(\lambda/2\pi\)) calculated at the lower band edge (worst case).
BandLower edge (MHz)Upper edge (MHz)\(\lambda\) at lower edge (m)Reactive near-field \(\lambda/2\pi\) (m)
160 m1.8001.825166.626.5
80 m3.5003.90085.713.6
60 m5.35155.366556.08.9
40 m7.0007.20042.86.8
30 m10.10010.15029.74.7
20 m14.00014.35021.43.4
17 m18.06818.16816.62.6
15 m21.00021.45014.32.3
12 m24.89024.99012.01.9
10 m28.00029.70010.71.7
6 m50.00054.0006.01.0

In a typical urban apartment, depending on the source of the man-made noise (QRM), either the \(E\)-field or the \(H\)-field can dominate. A wire antenna is an electric antenna, so it couples strongly to local E-field noise. Its feedline, which runs through the same near-field, adds common-mode noise on top of that4.

Conversely, an electrically small, balanced loop antenna operates as a magnetic dipole. In its near-field region (less than \( \lambda/2\pi\)), the loop responds mainly to the magnetic (H) field component of the local field. The reasons are simple: it picks up less local \(E\)-field noise; being balanced, it picks up far less common-mode noise via the coax; its narrow bandwidth admits less noise; and we can rotate a null towards a noise source. In this case, it’s the signal-to-noise ratio that matters, not the S-meter reading. Operators commonly report a noticeably lower noise floor, sometimes 10 dB or more5. Since the loop is less efficient, signals drop too, so this is something to consider when using a loop antenna.

Figure 3: Near-field coupling to local electric-field noise: a dipole’s E-field spreads out between its arms and couples strongly to nearby noise, while a small loop is H-field dominant, with its E-field mostly confined to the tuning capacitor.

Figure 3: Near-field coupling to local electric-field noise: a dipole’s E-field spreads out between its arms and couples strongly to nearby noise, while a small loop is H-field dominant, with its E-field mostly confined to the tuning capacitor.

Furthermore, as a high-Q resonator, the magnetic loop acts as a sharp, highly selective bandpass preselector directly ahead of the receiver’s front-end. With an extremely narrow instantaneous SWR bandwidth (only a few kHz on 40 m), it heavily attenuates strong out-of-band broadcast signals, preventing receiver desensitisation and front-end overload. However, it does mean it needs retuning every few kHz because of the narrow bandwidth.

It is vital to clarify a common electromagnetic myth: that a ‘magnetic’ loop radiates or receives only the magnetic field. Once a radio wave propagates into the far-field (beyond a wavelength or so), the ratio of the \(E\)-field to the \(H\)-field is permanently fixed at \(120\pi\) or 377 Ohms (the intrinsic impedance of free space). Therefore, in the far-field, both dipoles and loops generate and respond to both components identically. However, because the loop’s near-field \(E\)-field is mostly concentrated around its tuning capacitor, it puts much less electric field into the surrounding ground and concrete, so it loses less there than a low wire antenna would, and works reasonably well even when mounted low or in compromised spaces. Its magnetic near-field still couples into nearby steel, though, so it is not loss-free. In practical terms, that concentrated E-field means over 2.5 kV across the tuning capacitor even at 10 W on 40m (see the calculations below), which is enough to give a nasty RF burn.

The Uniform Current Assumption

Textbooks treat a loop as electrically “small” when its circumference (\(C\)) is below about \(\lambda/10\), because the current around it is then practically uniform6. In practice, hams use loops up to about \(\lambda/4\) on their highest band (some go up to about \(\lambda/3\)), and much below \(\lambda/10\) the efficiency drops off sharply. The practical sweet spot is therefore roughly \(\lambda/8\) to \(\lambda/4\)7. The fundamental operating principle of the loop relies on the Uniform Current Assumption.

When the current is (nearly) uniform:

If the loop’s circumference grows beyond about \(\lambda/4\):

Thus, keeping the loop between about \(\lambda/8\) and \(\lambda/4\) on the bands we care about, and no more than about \(\lambda/4\) on the highest one, preserves its predictable pattern, its nulls and its quiet near-field behaviour.

Figure 4: Free-space radiation pattern of a vertical small loop. Face-on, it radiates equally in every direction within the plane of the loop; seen from above, it is a figure-8 with deep nulls straight through the face. Near the ground and a building, the real pattern will be distorted.

Figure 4: Free-space radiation pattern of a vertical small loop. Face-on, it radiates equally in every direction within the plane of the loop; seen from above, it is a figure-8 with deep nulls straight through the face. Near the ground and a building, the real pattern will be distorted.

To see what this means in practice, the table below shows how “big” a 1 m × 1 m square loop (\(C = 4\) m) is on each band. It sits in the \(\lambda/8\) to \(\lambda/4\) sweet spot from 30 m to 17 m, is slightly over \(\lambda/4\) on 15 m, is just below \(\lambda/10\) on 40 m, and stops being a small loop altogether by 10 m. Efficiency will decide how far down we can realistically go, which we’ll calculate later.

It would be wonderful to check real-world propagation with the loop mounted vertically and horizontally!

Table 2: Electrical size (\(C/\lambda\)) of a 1 m × 1 m square loop (\(C = 4\) m) on each band, at the lower and upper band edges.
Band\(C/\lambda\) (lower edge)\(C/\lambda\) (upper edge)Verdict
160 m0.0240.024Far too small, very inefficient
80 m0.0470.052Too small, very inefficient
60 m0.0710.072Small, inefficient
40 m0.0930.096Just below λ/10, works but lossy
30 m0.1350.135Sweet spot
20 m0.1870.191Sweet spot
17 m0.2410.242At λ/4, the upper limit
15 m0.2800.286Just over λ/4, still usable
12 m0.3320.333λ/3, pattern distorting
10 m0.3740.396Too large
6 m0.6670.720Not a small loop any more

The Resonant LC Circuit & Mutual Inductance Model

Electromagnetically, a transmitting magnetic loop is not merely a radiator; it is a resonant LC (tank) circuit8. The same large current flows through the loop and the capacitor, and every loss can be modelled as a small resistance in series with them. This gives the following equivalent circuit:

  1. The Inductor (\(L_2\)): The main outer loop conductor acts as a high-Q, single-turn inductor. Its inductance is determined by the physical perimeter/shape of the loop and the cross-sectional diameter of the conductor. A 1 m × 1 m square of 22 mm copper tube is about 3 µH.
  2. The Capacitor (\(C\))9: A tuning capacitor connected across a gap in the loop (usually at the top) closes it into a resonant circuit. It can be an air-variable, butterfly or vacuum capacitor, or a home-made sliding-tube “trombone”. It sets the resonant frequency, \(f = 1/(2\pi\sqrt{LC})\).
  3. The Coupling Loop (\(L_1\)): A smaller loop, often a shielded (Faraday) loop, though a plain wire loop also works, sized at about \(1/5\) of the main loop as a starting point and then adjusted for the best SWR. It is connected directly to the 50 Ohm coaxial transmission line 7. Sited opposite the tuning capacitor, it has no physical electrical connection to the main loop. Instead, it acts as the primary winding of an air-core transformer, inductively transferring RF energy to the main loop through Mutual Inductance (\(M\)). In doing so, it transforms the loop’s tiny resistance up to about 50 Ohms.

Figure 5: Equivalent circuit of the main loop: inductor and tuning capacitor with the conductor, capacitor, environmental and radiation resistances in series.

Figure 5: Equivalent circuit of the main loop: inductor and tuning capacitor with the conductor, capacitor, environmental and radiation resistances in series.

Because of the loop’s electrically small size, its radiated power is represented by an incredibly tiny Radiation Resistance (\(R_R\)). On the 40m band (7 MHz), a 1 m × 1 m square loop has a radiation resistance of only about \(0.009\ \Omega\). To maximise overall antenna efficiency, we must minimise all other series loss resistances in the loop damping equation:

\begin{equation} \label{eq:total\_damping\_loss} R\_{\text{Total}} = R\_L + R\_C + R\_E + R\_R \end{equation}

Where:

Putting it together: the transmitter drives the coupling loop, which is magnetically coupled to the main loop. At resonance, the reactances of \(L\) and \(C\) cancel, leaving only \(R_{\text{Total}}\), a fraction of an Ohm, and the coupling loop transforms this to about 50 Ohms. That is why changing the size, shape or position of the coupling loop is how you fine-tune the SWR.

Practical considerations

Choosing the Bands: 40 m to 15 m

Before choosing a shape or a construction method, I need to decide which bands the loop has to cover, because that sets everything else: the size of the tuning capacitor, the voltage it must survive and how fat the conductor needs to be. Three things decide the bands for me: what my licence allows, what a loop of this size can do well, and what I actually want to do on the air.

  1. What my licence allows: with a Restricted Grade licence, I can use 160, 80, 40, 20, 17, 15, 12 and 10 m at up to 50 W. 60 m and 30 m are not available to me (see the band table and its footnote earlier).
  2. What the loop can do well: from the electrical-size table, a 1 m × 1 m square sits in the \(\lambda/8\) to \(\lambda/4\) sweet spot from 30 m to 17 m. It is slightly over \(\lambda/4\) on 15 m, and just below \(\lambda/10\) on 40 m, where it still works but is lossy.
  3. What I want to do: mostly QRP, with the occasional DX contest.

Putting these together, each band earns its place for a different reason:

Together, 40, 20 and 15 m also cover the contest bands I am realistically likely to use.

And the bands I am leaving out:

One consequence of this choice is worth flagging now: 7.000 to 21.450 MHz is roughly a 3:1 frequency range. Since the capacitance needed goes with \(1/f^2\), the tuning capacitor has to cover roughly a 9:1 or 10:1 range, plus a little margin for stray capacitance. One good variable capacitor can do this, and the calculations section sizes it.

Finally, power: the QMX and zBitx give me 5–10 W, and the sBitx up to about 25 W, all comfortably under the 50 W limit of my licence. As the calculations will show, it is the capacitor voltage, not the licence, that makes 25 W the hard part.

Choosing the Shape

A magnetic loop does not have to be round. Electrically, only two things about the shape matter: the area it encloses, because the radiation resistance goes up with the square of the area, and the length of conductor, because that sets the conductor loss. So I compared five shapes in two ways: first with the same area (1 m²), then with the same length of tube (4 m, enough for a 1 m × 1 m square). All the numbers assume 22 mm copper tube and conductor loss only, as in the calculations section.

Figure 6: The five shapes, drawn to scale, with the same area (top) and the same length of tube (bottom).

Figure 6: The five shapes, drawn to scale, with the same area (top) and the same length of tube (bottom).

Same area: 1 m²

Table 3: Shapes enclosing the same 1 m² area, built from 22 mm copper tube (best case).
ShapeSizeFootprint (m)Tube needed (m)40 m20 m15 mReaches \(\lambda/4\) atJoints
Square1.00 m sides1.00 × 1.004.0020%73%92%18.7 MHz4 × 90°
Diamond1.00 m sides1.41 × 1.414.0020%73%92%18.7 MHz4 × 90°
Hexagon0.62 m sides1.24 × 1.073.7221%75%92%20.1 MHz6 × 60°
Octagon0.46 m sides1.10 × 1.103.6421%75%93%20.6 MHz8 × 45°
Circle1.13 m diameter1.13 × 1.133.5422%76%93%21.1 MHzContinuous bend

With the same area, every shape has the same radiation resistance, so the only difference is how much tube it takes to enclose that area. The circle needs the least, so it has the lowest conductor loss, but the advantage is tiny: at most 2 percentage points, well under 0.5 dB. What changes a lot is the footprint: the square is the only one that fits a 1 m × 1 m space, while the diamond, which is electrically identical to the square, needs a 1.41 m space because it stands on its corner.

Same length of tube: 4 m

Table 4: Shapes made from the same 4 m of 22 mm copper tube (best case).
ShapeSizeFootprint (m)Area (m²)\(R_R\) vs square40 m20 m15 mJoints
Square1.00 m sides1.00 × 1.001.00100%20%73%92%4 × 90°
Diamond1.00 m sides1.41 × 1.411.00100%20%73%92%4 × 90°
Hexagon0.67 m sides1.33 × 1.151.15133%25%79%94%6 × 60°
Octagon0.50 m sides1.21 × 1.211.21146%26%80%94%8 × 45°
Circle1.27 m diameter1.27 × 1.271.27162%28%82%95%Continuous bend

With the same length of tube, the shapes enclose different areas, and here the differences are bigger. A circle encloses 27% more area than a square from the same tube, which gives it 62% more radiation resistance. On 40 m, that is 28% versus 20% efficiency, about 1.5 dB. On 15 m, it hardly matters. The catch is that every shape except the square needs more than 1 m of space.

So which shape?

The two tables tell the same story from different sides: the more “round” the shape, the better it uses its tube, but the advantage is at most about 1.5 dB on 40 m and almost nothing on the higher bands. On my balcony, the space is the hard limit, not the tube, and in a 1 m × 1 m space the square encloses the most area. That is why the calculations use a square.

The square has one drawback: its 4 m perimeter passes \(\lambda/4\) at 18.7 MHz, so on 15 m it is slightly beyond the usual limit (about \(0.29\lambda\)). It is still usable, but the pattern will be a little less tidy there.

What each shape means to build

The shape and the construction method are not independent; some combinations are easy and some are a fight:

Choosing the Construction

The loop conductor is where most of the loss happens, so how I build it matters as much as its size. There are three practical options for a home-brewer: copper tube, copper foil on PVC pipe, and wire on a frame. The calculations section puts numbers on each, but the short version is this: the conductor barely matters on 15 m, and matters enormously on 40 m.

All three are limited by the same piece of physics. At RF, current flows only in a thin skin on the surface of the conductor, so what matters is the surface, not the bulk. A fatter conductor has more surface, and so less loss:

Table 5: Skin depth: the thickness of the conductor surface that actually carries the RF current.
BandFrequency (MHz)Copper (µm)Aluminium (µm)
40 m7.02532
20 m14.01823
15 m21.01419

As a rule of thumb, the conductor should be at least two to three skin depths thick. Any solid tube or wire easily meets this; foil may not, as we will see.

Copper tube

This is the classic magloop: rigid copper tube, soldered at every joint.

Aluminium tube is a lighter and cheaper alternative. Its higher resistance costs a little (roughly 30% more conductor loss than copper of the same size), and it cannot easily be soldered, so joints have to be firmly clamped and kept clean.

Copper foil on PVC pipe

Here, the PVC pipe is just a former, and a layer of copper foil on it (or inside it) does the conducting.

Wire on a frame

The simplest option: a wire run around the tips of a frame made of PVC, wood or fibreglass.

Common to all three

The joints between the loop and the tuning capacitor carry the full loop current, which the calculations show can exceed 20 A on 40 m at 25 W. Thin wires here can quietly add more loss than the whole loop, so whichever construction I choose, those connections need to be wide copper straps, soldered or firmly bolted.

Since 40 m is one of my target bands, wire is ruled out as the main conductor, which leaves copper tube or foil on PVC. The calculations section below compares all three in detail. I will have to figure out what works best from a construction possibility and modularity to keep changing things when I build this antenna!

Calculations

Time to put numbers on all of this. I have run the calculations for a 1 m × 1 m square loop, the shape that makes the most of my balcony space based on the choice of shape discussed earlier, built in the three ways discussed above: 22 mm copper tube, copper foil on 32 mm PVC pipe, and plain 2.5 mm² house wire on a frame. Each table below has the three builds side by side, so you can read across a row to compare them on a band.

Assumptions

The equations

Inductance of a square loop of side \(s\), made from a conductor of radius \(a\), and the capacitance needed to resonate it at frequency \(f\):

\begin{equation} \label{eq:inductance\_capacitance} L \approx \frac{2 \mu\_0 s}{\pi} \left[ \ln\left(\frac{s}{a}\right) - 0.774 \right], \qquad C = \frac{1}{(2\pi f)^2 L} \end{equation}

Radiation resistance (from earlier) and conductor loss, where \(d\) is the conductor diameter, \(\sigma\) the conductivity of copper, and \(k\) the extra-loss factor of the build:

\begin{equation} \label{eq:rr\_rl} R\_R \approx 31171 \\, \frac{A^2}{\lambda^4}, \qquad R\_L = k \\, \frac{\ell}{\pi d} \sqrt{\frac{\pi f \mu\_0}{\sigma}} \end{equation}

Efficiency, quality factor and the 2:1 SWR bandwidth:

\begin{equation} \label{eq:eff\_q\_bw} \eta = \frac{R\_R}{R\_{\text{Total}}}, \qquad Q = \frac{2\pi f L}{R\_{\text{Total}}}, \qquad BW\_{2:1} \approx 0.707 \\, \frac{f}{Q} \end{equation}

Loop current and peak voltage across the capacitor for a transmit power \(P_{TX}\):

\begin{equation} \label{eq:current\_voltage} I = \sqrt{\frac{P\_{TX}}{R\_{\text{Total}}}}, \qquad V\_{pk} = \sqrt{2} \\, I \\, (2\pi f L) \end{equation}

Tuning capacitor range

Table 6: Loop inductance and the tuning capacitance needed across each band (1 m × 1 m square).
Copper tube (22 mm)Foil on PVC (32 mm)Wire (2.5 mm²)
Loop inductance2.99 µH2.69 µH5.00 µH
40 m capacitance163–173 pF182–192 pF98–103 pF
20 m capacitance41–43 pF46–48 pF25–26 pF
17 m capacitance26 pF29 pF15–16 pF
15 m capacitance18–19 pF20–21 pF11 pF

The thinner the conductor, the higher the inductance, and so the less capacitance it needs. Whichever build I choose, the capacitor has to swing over roughly a 9:1 or 10:1 range to cover 40 m to 15 m: about 18–173 pF for copper tube, 20–192 pF for foil on PVC, and 11–103 pF for wire. The loop’s own stray capacitance will shave a few pF off the minimum, which helps at the 15 m end.

Efficiency

Table 7: Best-case efficiency at mid-band (conductor loss only). The last column is how much worse wire is than copper tube.
BandCopper tube (22 mm)Foil on PVC (32 mm)Wire (2.5 mm²)Wire vs tube
40 m20% (−7.1 dB)21% (−6.7 dB)2% (−17.1 dB)10.1 dB
20 m73% (−1.4 dB)75% (−1.2 dB)18% (−7.4 dB)6.1 dB
17 m87% (−0.6 dB)88% (−0.6 dB)34% (−4.6 dB)4.0 dB
15 m92% (−0.4 dB)93% (−0.3 dB)48% (−3.2 dB)2.8 dB

This is the most important table in the post. Copper tube and foil on PVC are practically identical, as the fatter PVC pipe makes up for the lossier foil. Wire is a different story: it is only about 3 dB worse than tube on 15 m, but about 10 dB worse on 40 m, where it radiates just 2% of the power. If 40 m matters, the conductor has to be fat. Even then, 40 m is the hard band at about 20% (−7 dB), while 20 m to 15 m is where the loop shines, within about 1.5 dB of a perfect, lossless antenna.

Bandwidth

Table 8: 2:1 SWR bandwidth at mid-band (best case).
BandCopper tube (22 mm)Foil on PVC (32 mm)Wire (2.5 mm²)
40 m1.9 kHz1.9 kHz11.4 kHz
20 m8.0 kHz8.6 kHz19.3 kHz
17 m18.1 kHz19.8 kHz27.2 kHz
15 m32.1 kHz35.4 kHz37.0 kHz

The flip side of a low-loss loop is a razor-thin bandwidth. With tube or foil, 40 m gives under 2 kHz between the 2:1 SWR points, so I will be retuning every couple of kHz, and a fine-tuning mechanism (a reduction drive or a motor) is a must. Wire looks “better” here only because its losses are so high; a wide bandwidth on a small loop is a sign of loss, not of a good design.

Loop current and capacitor voltage

Table 9: RMS loop current and peak capacitor voltage at 10 W.
BandCopper tube (22 mm)Foil on PVC (32 mm)Wire (2.5 mm²)
40 m14 A / 2.7 kV15 A / 2.5 kV4 A / 1.4 kV
20 m7 A / 2.6 kV7 A / 2.4 kV3 A / 2.1 kV
17 m5 A / 2.2 kV5 A / 2.0 kV3 A / 2.3 kV
15 m3 A / 1.9 kV3 A / 1.7 kV2 A / 2.3 kV

Table 10: RMS loop current and peak capacitor voltage at 25 W.
BandCopper tube (22 mm)Foil on PVC (32 mm)Wire (2.5 mm²)
40 m22 A / 4.2 kV23 A / 4.0 kV7 A / 2.2 kV
20 m11 A / 4.1 kV11 A / 3.7 kV5 A / 3.4 kV
17 m7 A / 3.5 kV7 A / 3.1 kV5 A / 3.7 kV
15 m5 A / 3.1 kV5 A / 2.8 kV4 A / 3.7 kV

Even at 10 W, there are over 2.5 kV across the tuning capacitor, and at 25 W over 4 kV. The small plastic “polyvaricon” capacitors used in many QRP loops are not rated anywhere near this. To run the sBitx at 25 W, I will need an air-spaced capacitor with wide plate spacing (or a vacuum variable) rated for at least 5 kV. The currents are large too: over 20 A on 40 m at 25 W with tube or foil, so every joint, and the straps to the capacitor, need to be solid, wide and soldered.

What the numbers tell us

Checking the numbers when I build it!

The bandwidth equation also works backwards. Once the loop is built, I can measure its 2:1 SWR bandwidth with a NanoVNA and calculate the real total resistance, including all the capacitor and balcony losses ignored above:

\begin{equation} \label{eq:rtotal\_from\_bw} R\_{\text{Total}} \approx \frac{2\pi L \cdot BW\_{2:1}}{0.707} \end{equation}

The real efficiency is then simply \(R_R / R_{\text{Total}}\). A measured bandwidth wider than the table above means extra losses somewhere, and that is what I will be checking in Part 2.

Before I Build

The numbers above set the requirements. Before touching any hardware, there are a few decisions to make, and the biggest of them is the tuning capacitor.

The tuning capacitor

From the calculations, the capacitor has to do three things at once: cover roughly a 9:1 or 10:1 range (about 18–195 pF for tube or foil), survive over 4 kV peak at 25 W (and about 2.7 kV even at 10 W on 40 m), and add as little loss as possible while carrying 20 A or more. These are the options I am weighing:

Table 11: Tuning capacitor options for a balcony loop, against the requirements from the calculations.
TypeVoltage handlingLossNotes
Polyvaricon (plastic film)Far too lowHighFine for receive-only loops; will arc or burn at these voltages
Receiver air variableAbout 1 kV or soLow, but wiper contactPlate gaps too small for 10 W on 40 m
Wide-spaced air variableSeveral kVLow, but wiper contactFrom old valve transmitters and tuners; check the plate spacing
Split-stator / butterflyTwice a single sectionVery low (no wiper)Two sections in series: half the voltage each, but also half the capacitance
Vacuum variableVery high (many kV)LowestWide range and compact, but expensive and multi-turn, so it needs a drive
Home-made trombone or platesDepends on the gapLow with a good dielectricCheap; use PTFE or polyethylene, not PVC, which is lossy at RF

A few things worth keeping in mind while choosing:

Other things to sort out first

If you spot anything I have got wrong in this post, or have built a loop in a similar space, please do write to me!


  1. All antenna deployments come with some form of compromise, the question would be what suits our needs best! ↩︎

  2. Home-Owners’ Association (HOA) rules as the rest of the world calls it. ↩︎

  3. Band edges as per WPC Office Memorandum No. L-14011/255/2004-AMT dated 13 August 2010 (frequency allocation on pages 4–5), available at https://arsi.info/wp-content/uploads/2020/11/Amateur_New_Guidelines-L-14011-255-2004-AMT-13082010.pdf; under the Telecommunications (Amateur Services) Rules, 2024 (G.S.R. 675(E), 29 October 2024), the exact bands, power and emissions are those specified on your ASOC. 80 m is allotted as two segments, 3.500–3.700 MHz and 3.890–3.900 MHz, and the table shows the overall span. 60 m (5.3515–5.3665 MHz) is not available to Restricted Grade licensees. 30 m is not available to Restricted Grade licensees; 6 m is VHF and is included only for completeness. (Last accessed: 10 October 2026) ↩︎

  4. Urban near-field electromagnetic noise polarisation and signal-to-noise ratio (SNR) measurements detailed in “SMALL LOOP ANTENNAS” by Leigh Turner (VK5KLT) (Last accessed on Tuesday, 18 Aug 2026). ↩︎

  5. Again, this is reported in multiple places, but something for us to measure when we build the antenna. ↩︎

  6. Symmetrical current phase distributions and loop parameter thresholds analysed in Balanis, C.A., 2005. Antenna Theory: Analysis and Design. 3rd ed. Hoboken, NJ: John Wiley & Sons. ↩︎

  7. Faraday shield loops, primary air-core windings, and mutual coupling coefficients detailed in Steve Yates, AA5TB, “Small Loop Antennas”. URL: https://www.aa5tb.com/loop.html (Last accessed: 27 August 2026). ↩︎ ↩︎

  8. Peter Märki and Markus Niese, “Small but Tubby: A Magnetic Loop Antenna Made from 100 mm Copper Tubing”, arXiv:2607.10828. URL: https://arxiv.org/abs/2607.10828 (Last accessed: 27 August 2026). ↩︎

  9. Please note the C used in this section refers to capacitance whereas the C in the previous section was circumference! ↩︎

  10. Circulating currents, capacitor voltages, and contact resistance hazards analysed in Matt Roberts, KK5JY, “Small Transmitting Loop Project”. URL: http://www.kk5jy.net/magloop/ (Last accessed: 27 August 2026). ↩︎

  11. Split-stator (butterfly) capacitors, and the trade-offs of a wiper contact at low power, discussed by Julian Moss, G4ILO, “The G4ILO Wonder Loop”. URL: https://www.g4ilo.com/wonder-loop.html (Last accessed: 27 August 2026). ↩︎

  12. A loop whose tuning capacitor is formed from the loop tubing itself, using a sliding section, described by Sivan Toledo, “An Unusual Transmitting Loop Antenna”. URL: https://sivantoledotech.wordpress.com/2010/09/03/hello-world/ (Last accessed: 27 August 2026). ↩︎

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