## The Double Loop On 30 Meters

I am a DX’er and finally decided to get on 30 meters. There were a few restrictions however. First I had no more room on my tower for a beam. I needed an antenna which would be most effective for DX and within the limits of my supporting structures. To put it more bluntly, my tallest trees were 80′ (24m) high. I knew from Dean Straw, N6BV’s, work[i] that the DX arrival angles on this band were all below 20 degrees in elevation and, a substantial percentage of the time, were 5 degrees or lower. Now the problem became one of seeing what kind of antenna I could come up with, within my height limit, that would radiate most effectively in the required range.

30 meters is, what I would consider, a transitional band. By this I mean the band is just about at the point in the HF spectrum where a horizontally polarized antenna might be more effective at low elevation angles than a vertically polarized one. There is no question that on 40 – 160 meters a low-to-the-ground vertically polarized antenna will outperform any horizontally polarized one that is not mounted on a really tall tower – way above 100′ (30m). There is also no argument that the ground reflection gain and the wider azimuthal coverage of a horizontally polarized antenna makes it the one of choice on the bands above 20 meters, where 70′ (21m) puts it a full wavelength up.

What I will try do here is to show you how I arrived at my choice of the ideal wire antenna given my height constraints. Since this antenna ultimately turned out to be a derivative of the rectangle I will begin by introducing you to the theory behind the rectangle and its offspring. We will then get into the tradeoffs between polarization modes and the effects of ground proximity on the take off angle (TOA) of these antennas. The end-point, which I have arbitrarily chosen for low angle effectiveness, is the performance of the antennas at a TOA of 5 degrees.

What I will also show you is that the free-space gain of these antennas really doesn’t correlate well with their gains above ground and that smaller antennas with lower theoretical gain will give you higher real gain at the desired low angles.

#### The antennas:

The antennas discussed will be rectangular loops – single and double – and the two variants of the double-loop, the SDR or symmetrical double rectangle and the ADR or asymmetrical double rectangle. The SDR has had many names: at VHF and HF it has been described as the “skeleton-slot”, on 30 meters as the “H – Double Bay” and on 80 meters as the “double magnetic slot” or DMS. The ADR, on 10 meters and higher and when horizontally polarized, is better known as the Hentenna. It is assumed that a choke-type balun will be used on coaxial feeders and that a simple impedance transformation network will be necessary.

Since the antennas discussed here will all be variations on the rectangular loop we should, at first, examine how a rectangle works.

#### The Rectangle

It has been known for a long time that the quad or equilateral loop is not the one having the most gain. If you lengthen the section between the radiating elements and shorten the radiators, the gain goes up – to a point. L.B. Cebik, W4RNL, in discussing the self-contained vertical antennas or SCV’s on his web site and in his National Contest Journal series[iv], started me thinking as to why a rectangular loop, fed at the center of one of its short sides has its gain peak at a specific length. What I mean by length is the distance between its radiators or its long side. This length is just one among an infinite number of choices among the long and short sides where a loop can be made resonant. Note also that you can position a rectangle so that its short radiating wires are horizontal or vertical, yielding horizontal and vertical polarization respectively. The simple loop, on the left in **Figure 1**, is a rectangle.

The variations in rectangle gain and loss as a function of inter-radiator length can be seen in **Figure 2**. Here we are modeling, with NEC-2, antennas constructed of #10 wire and resonated at 10.1 MHz. This will be the resonant frequency of all of the antennas we will be discussing. You can see that this group of rectangles shows a gain peak, 4.64 dBi in free space, at a length of 41′ (12m). You may notice that I also threw in a “quad” for comparison. This antenna is the one, on the x-axis under the heading “25.64’” (8m) which is the length per side of the quad.

In trying to determine why a rectangle performs the way it does, it is best to visualize it as a two-dipole broadside in-phase array fed with equal currents. The two dipoles are bent at the top and bottom with the ends facing each other and where the tips of the wires, or high-voltage points, touch. The loop size is always over 1 l, except in the extreme case, which we will be discussing next. Therefore, the more you separate the radiators, the shorter the radiating section must be in order to keep the loop circumference relatively constant and the antenna resonant. Note that, up until the gain peaks, the gain of a rectangle is equal to that of an array of two full-sized 47′ (14m) dipoles separated by the distance between the rectangle’s radiating elements.

My studies of the rectangle show that the reason for the peaking of its gain, at a specific length and radiator size, is that there is a dynamic equilibrium between the antenna’s lossless or theoretical gain, which increases relatively linearly with the separation of its radiators, and its losses which increase exponentially. **Figure 2** shows the real gain at any antenna length is simply the difference between the theoretical gain and the losses.

When you look at lossless rectangles, the end-point is an “extreme” rectangle, which is 0.5 l long and has infinitesimally small radiators – in effect a transmission line shorted at both ends. This “extreme” rectangle has a gain, at the limit of modeling programs, which is over 6.1 dBi. Of course, its feedpoint impedance approaches zero ohms and its currents approach infinity as its length approaches the 0.5 l limit.

This lossless example gives you a clue as to what happens in real life with lossy wires. For each type of wire, depending on its resitivity and diameter, the losses begin to mount with rectangle length until they overcome the gain increase and the actual gain then decreases. This gain pattern, seen as the free-space gain in Figure 2, is typical of all closed loop antennas, be they single or multiple rectangles. The term I use to characterize this phenomenon of the rectangle and all of its derivative antennas is that they are “loss limited” at a specific length beyond which the losses predominate and the gain falls.

We have already seen that the longer you make the rectangle the shorter the radiators must be to maintain resonance. The shorter the radiators the lower the feedpoint impedance and the higher the currents and the power losses. For instance, a peak-gain rectangle on 80 meters, constructed with #10 wire, is 115′ (35m) long (0.41 l) and has radiators which are slightly less than 30′ (9m). Its gain, in free space, is 4.30 dBi and the feedpoint resistance at the center of either end-wire is 18 ohms.

Now, on the higher bands, your loop size is smaller and the resistive losses lower. This means than you can now stretch the long dimension of the rectangle even more, in terms of wavelength. On 10 meters, I have shown that a maximum gain rectangle (.47 l long), made from 1″ diameter aluminum tubing, has over 1.3 dB more free space gain (5.6 dBi) than the 80 meter antenna. The price you pay for the gain is an unmatchable 1-ohm feedpoint impedance.

On 30 meters the peak-gain rectangle is 41′ (12m) long (.43 l) and has a feedpoint impedance of only 14 ohms. So, from this band and higher a rectangle is no longer “loss limited”, it is “impedance limited”. All of the antennas we will be playing with will have more “matchable” feedpoints.

#### In one corner, the vertical antenna standard:

We are going to stack the deck in favor of vertically polarized antennas. The reference antenna, seen as the horizontal symmetrical double rectangle on the right in Figure 1, will be a long SDR consisting of two equal-sized rectangles. The horizontal length or long side of each rectangle is 35′ (10m) so the overall length of the antenna is 70′ (21m). The vertical short dimension or radiator size is 11.93′ (3.6m). The antenna is positioned so that the top wire is 34′ (10m)above ground and the lower wire is about 22′ (7m) up. We will assume a ground quality which is “average” and we will not get into the usual tradeoffs that you are all familiar with comparing desert terrain and sea water. Its TOA is 18 degrees.

Just how much I am stacking the deck can be seen in Figure 3 which is an overlay of the elevation patterns of this SDR and a full-sized vertical dipole (47′ or 14m tall) which has been positioned 1′ (.3m) over ground. Why these specific heights for the vertical and the SDR? Because, with vertical polarization, a TOA of 18 degrees gives you the cleanest elevation pattern without an annoying secondary lobe. The parameters for the dipole (“Dipole V”) and our reference antenna (“SDR V”) are found in** Table 1**, as well as those of all of the antennas we will be discussing. The gain figures for the vertically polarized 70′ (21m) SDR will be our standard of comparison.

###### Comparison of all the antenns tested: NEC-2 10.1MHz, #10 wire og = Over Ground, fs=Free Space, Length in Feet, Gain in dBi, R and X in Ohms, G 5 Degrees is the Gain at 5° elevation.

Antenna | Height Upper | Height Lower | Length | Radiator | Rin | Xin | Gain fs | Gain og | TOA | G5 Degrees |
---|---|---|---|---|---|---|---|---|---|---|

Dipole V | 48.25 | 1 | NA | 47.25 | 90.8 | -1.4 | 2.11 | 0.10 | 18 | -4.81 |

SDR V | 34 | 22 | 2 x 35 | 11.93 | 62.9 | -12.9 | 5.81 | 4.66 | 18 | -0.24 |

SDR H | 80 | 10 | 61.8 | 0.2 | 8.48 | 22 | -0.16 | |||

Dipole H | 80 | 47.25 | 79.3 | 2 | 2.11 | 7.15 | 17 | 0.47 | ||

70 | NA | 72.9 | 8.3 | 7.45 | 19 | -0.21 | ||||

60 | 63.9 | 3.5 | 7.90 | 22 | -0.90 | |||||

Quad H | 80 | 54.36 | 25.64 | 25.64 | 122 | 7 | 3.24 | 8.36 | 19 | 0.68 |

70 | 44.36 | 116 | -3 | 8.28 | 22 | -0.49 | ||||

60 | 34.36 | 126 | -13 | 7.57 | 27 | -2.24 | ||||

Rectangle | 80 | 42 | 38 | 12.64 | 26.4 | -0.3 | 4.49 | 8.95 | 20 | 1.09 |

ADR 39/1 | 80 | 41 | 39 | 15.07 | 37.5 | 0.1 | 4.66 | 9.08 | 20 | 1.21 |

70 | 31 | 38 | -0.8 | 8.57 | 23 | -0.30 | ||||

60 | 21 | 39.2 | -0.1 | 7.69 | 26 | -2.25 |

Table 1 – Comparison of all the antennas discussed in the text. 1 Foot = 0.3048 meters.

The gain of this antenna far exceeds that of simple 1/2 wave vertical dipole but the price you pay is directionality. The azimuthal patterns of the reference antenna and the dipole are overlaid for comparison in Figure 4. The gain, of the SDR over that of the dipole, comes from azimuthal lobe compression and you lose the ability to work around the compass. On the other hand, you may find the directionality an advantage so I really cannot call it a positive or a negative factor in choice. Just be aware that the higher the gain of such an antenna the narrower the azimuthal lobe.

#### In the other corner – the horizontals:

For all of the horizontal antennas I will use a top wire height of 80′ (24m) which, on 10.1 MHz, comes to .83 l. Lets see, for the sake of reference, how a dipole fares at this height. Its elevation pattern, seen in **Figure 5**, shows that a good part of the radiation goes straight up – not a good omen for DX’ing. **Table 1** compares the gains of three dipoles, “Dipole H”, at heights of 80, 70 and 60′. Lets see if we can do better with a horizontally polarized quad.

The elevation pattern of a square quad loop, 25.64’ (8m) per side, is given in **Figure 6** and the gain parameters in **Table 1**. Compared to the dipole there is definitely a slight improvement in low angle gain and a decrease in the obnoxious vertical secondary lobes. We are heading in the right direction by using a loop. Quads modeled at 80, 70 and 60′ top-wire height are found under Quad H in Table 1. But notice this: the gain at 5 degrees of the quad falls off more rapidly with decreasing height than does that of the dipole. This deterioration of low-angle gain is a characteristic of all horizontally polarized loops as the lower wires near the ground. A quad suffers more from ground proximity than does the dipole.

Now let’s see what happens when you “stretch” the square and turn the antenna into a rectangle. This antenna is shown in **Figure 1** and its elevation pattern in **Figure 7**. This is the rectangle in **Table 1**. If you look closely at the elevation pattern you see that a price you pay, for having the lower wire closer to the ground than that of the quad, is that the elevation peak is now at 20 degrees instead of at 18 degrees. However the gain at 5 degrees is now +1.09 dBi.

The relationship between rectangle length and the gains in free space, peak gains at 20 degrees and at 5 degrees is seen in **Figure 8**. The gain peaks at 20 and at 5 degrees do not correlate at all with the gains in free space. The antenna that performs best is relatively short at 38′ (11m). What appears to be happening with the longer rectangles is that their performance at lower elevation angles is adversely affected by the ground proximity of their lower wires.

At this point look at Figure 9, which is the azimuthal pattern of the optimized rectangle, and see why I prefer horizontally polarized antennas – if I can get away with them. The pattern width is 90 degrees at the -3dB points. Two horizontals at right angles can cover 360 degrees.

Okay, let’s double up on the rectangles and flip our vertically polarized reference symmetrical double rectangle 90 degrees so it is now vertically oriented and horizontally polarized (we could now call it a symmetrical Hentenna). This antenna is labeled as “SDR H” in **Table 1**. With the top wire at 80′ (24m) it leaves 10′ of ground clearance under the lower wire. The feedpoint of this antenna is in the middle of the lower horizontal wire. The good news is that the elevation pattern is “clean” with no secondary lobes at all – the bad news is that its peak gain comes at 23 degrees elevation and the gain at 5 degrees is -0.18 dBi which is essentially no improvement over our reference antenna.

I am not bothering to graph the results of the SDR’s. Now matter how short we make a symmetrical double loop antenna, the overall antenna height and the ground proximity of the lower wire are such that we cannot get the main lobe below 22 degrees and the gain at 5 degrees peaks at only 0.38 dBi.

Now our task is to find an antenna which combines the gain of a double-loop and still has a lower- wire height high enough to reinforce the far-field at 5 degrees.

#### And the winner is:

The antenna we are looking for is the ADR, or asymmetrical double rectangle, which is composed of two rectangles of unequal size. The larger loop that we will start with, or the primary loop, is the size of the simple rectangle discussed earlier. The secondary loop can be any size, from infinitesimal to equal in size to the primary. Of course, in the latter case, the antenna then becomes a SDR. An ADR/Hentenna is also pictured as the middle antenna in **Figure 1**.

This antenna is really interesting and I would like to point out some of its unusual characteristics. To this end I would like to briefly discuss its gain, feedpoint impedances and tuning. A more detailed analysis of this antenna is in the works.

#### Gain:

The gain of the ADR is dependent on the gain of the primary loop with an additional component due to the secondary loop. This component is due to two factors: loss reduction and additive gain.

The secondary loop is an impedance step-up transformer and works this way: When you add a shorter loop to a resonant rectangle the mutual reactances of the three radiators are such that all of the feedpoints become very capacitively reactive. If you leave the inter-radiator lengths constant you must then make the radiators considerably longer to resonate the antenna. This results in significantly higher feedpoint impedances, lower currents and lower losses. The gain realized from adding on a very short secondary loop is all from loss reduction. Additionally, a secondary loop that is more than minute in size will add to the gain of the antenna. This effect is directly related to the size of the secondary loop and is maximal when it becomes the same size as the primary – when the antenna becomes a SDR.

#### Feedpoint Impedances:

The far-end wire of the asymmetric double loop antenna has a relatively stable feedpoint impedance over a large spectrum of overall lengths – the lengths of the primary plus the secondary loops. It falls in the 20-40 ohm range.

Because of the mutual impedances related to the proximity of the center and near-end wires the feedpoint impedances at these wires are not at all constant and vary greatly in resistance and reactance as you change the size of the secondary loop.

#### Tuning:

A characteristic of all ADR’s where the center wire is not near the geometric center – where the primary and secondary loops are quite different in size – is that they can be easily tuned by moving the center wire. You can resonate the antenna at a lower frequency – or tune out capacitive reactance – simply by moving the center wire toward the near-end. Moving it toward the geometric center moves your resonant frequency up or tunes out inductive reactance. The fact that it is more difficult to move the center wire with the feedpoint attached and the constancy of the far-end wire impedance are the reasons why these antennas are modeled with a far-wire feed.

In modeling ADR/Hentennas, I started with a 34′ (10m) primary loop and lengthened it and the secondary loops until I found the right combination for maximum gain at 5 degrees. These antennas were modeled with the far-wire down so that they would be easier to feed. The results are illustrated in Figure 10 and in **Table 1**. Overall length is the length of both loops. Spacing is the position of the center wire from the near end or the size of the secondary loop.

The conclusion is that, for a top-wire height of 80′ the ideal antenna from the point of view of gain at 5 degrees is a ADR/Hentenna of overall length 39′ with a primary loop/secondary loop size of 38/1′ and a radiator width of 15.07’ (4.6m). The feedpoint impedance at the bottom radiator is an easily matched 37.5 ohms and the gain at 5 degrees is +1.21 dBi. In Figure 11 I overlaid the elevation pattern of this antenna over that of the reference vertically polarized SDR.

This antenna is simply the optimum rectangle with a 1-foot loop added to it. The difference in free space gains between them, noted in **Table 1**, is approximately half from loss reduction and half from the additive gain of the smaller loop. As expected, from our brief discussion of ADR theory, the radiators are significantly longer and the feedpoint impedance higher than the rectangle’s.

You can use the dimensions given here without pruning any wires. Just refer back to the section on “Tuning” to find out how to resonate the antenna by moving the center-wire a few inches.

###### Table 2 – ADR/Hentennas Top Height varied 80-60 feet above ground

Antenna | Height Upper | Gpeek | TOA | G 5 Degrees |
---|---|---|---|---|

39/1 | 80 | 9.08 | 20 | 1.21 |

70 | 8.57 | 23 | -0.3 | |

60 | 7.69 | 26 | -2.25 |

The last thing I want to discuss is what happens when you lower the top-wire height from 80 to 60′. The results are in Table 2. Below 70′ there is a clear advantage to the vertically polarized antenna at low elevation angles – the same phenomenon you find on 40 – 160 meters.

As to how the antenna performs – it performs well toward the Northeast and Southwest quadrants where the main lobes are pointed. I work QRP on this band and am really enjoying it. The ADR performs a lot better, transmitting and receiving, than the 40-meter Yagi at 90′ (27m) I have been using with an antenna tuner.

#### Summary:

On 30 meters, if you have supporting structures tall enough, – 70’ or higher – you can put up an ADR/Hentenna or asymmetrical double rectangle which will maximize DX gain and take up little room. The top wire will be the same height as the dipole you already may be using but it will certainly take up much less horizontal space.

If your trees or towers are too low then you can erect a vertically polarized SDR or symmetrical double rectangle which will be almost as good at low elevation angles and far better for DX than any horizontally polarized antenna that you can erect.

#### References:

- The Antenna Handbook, Chapter 23, 18th Edition, ARRL, 1997. An updated version of the IONCAP data is included with N6BV’s latest YT terrain modeling program.
- Peter Dodd, G3LDO, The HF Skeleton Slot Antenna, The ARRL Antenna Compendium, Vol. 6, p. 70, ARRL, 1999. This is a multi-band 10-30 meter version of the SDR. Lew Gordon, K4VX, The Double Magnetic Slot Antenna For 80 Meters, ARRL Antenna Compendium, Vol. 4, p.18, ARRL, 1995. N4PC’s, H-Double Bay Antenna, CQ, September, 1995
- Shirow Kinoshite, JF6DEA, The Hentenna – The Japanese “Miracle” Wire Antenna, ARRL Antenna Compendium, Vol. 5, p 66. JH1FCZ was the designer in the ‘70’s.
- L.B. Cebik, W4RNL – SCV’s: A Family Album; Part 1: The Group Picture, National Contest Journal, Sept.- Oct., 1998, pp. 12-16. The contents of the NCJ series and additional information is available at his web site at: http//cebik.com/radio.html under Self-Contained Vertically Polarized Wire Antennas: A Family Album, Parts 1-5.
- Dan Handelsman, N2DT, The Self-Contained Vertical Antennas: Part 1: The Not So Simple Rectangle. Communications Quarterly, accepted for the upcoming Spring Issue, 2000. Subsequently this publication has been bought by the ARRL and has been merged with QEX. The article has been resubmitted.

Originally posted on the AntennaX Online Magazine by Dan Handelsman, N2DT

*Last Updated : 16th May 2024*