The Perfect Loop
Let us get right to the point and look at Figure 1. This shows the bandwidths (BW) for front to back ratio (f/b) for two antennas. The antennas are 2 element arrays composed of the thickest commonly used antenna wire on the HF bands – 2.5 mm or #10 AWG. The reference antenna is a 2 element quad. The other is the “solution” to the quad’s obvious problem; the ADR or asymmetrical double rectangle array. The band, 10 meters, is the widest upper HF band with a bandwidth (BW) of close to 6%. Let us now see how we “fixed” the quad.
It is not at all surprising that a quad array, composed of thin wires, doesn’t have the f/b BW to cover such an extremely wide band. The smallest Yagis, which can do so are composed of relatively thick aluminum tubing and require at least 4 elements on a minimum boom length of about .38 wl. In fact, we can theoretically solve the quad problem quite easily. This is by using 1″ or 25 mm aluminum tubing for the wires. If we do so we have a 2-element antenna with the gain of a wide-band 4 element Yagi, but with a boom length of only .16 wl. Of course, we now have to use even more aluminum tubing than with the Yagi.
The challenge, which I shall address in this article, is to show you how to get a “free lunch” and design a 2 element loop antenna which will cover all of 10 meters and which can be constructed with cheap and readily available “thin” wires—all the while equaling the performance of the larger 4 element Yagi. For the purposes of this article, the “useable” f/b BW is defined as one where the f/b exceeds 15 dB.
The reference antenna we will use, shown in Figure 2, is a 2 element quad array consisting of square loops. The antenna that we will end up with, which has by far the widest f/b BW, is one composed of two asymmetrical double rectangle (ADR) loops. The simple ADR loop is pictured in Figure 3. This loop, as an array element, is as close to ideal as one can get. It “cures” the ills of simple loops by widening the BW and by increasing the feedpoint resistance.
Background
In our previous explorations we were concerned with gain. One way to get more gain, as compared to that of a simple square looped array was to transform the square into a tall/narrow rectangle whose radiators are shorter and the interconnecting or transmission line wires are longer. This separates the vertical apertures of the radiators by a greater distance and results in a higher “stacking” gain.
Another way to higher gain was to add another loop to each element – that is make each element a double loop. In the earlier articles in this series we examined three kinds of double loops. Two were variants of the SDR or symmetrical double rectangle and consisted of equal-sized double squares and double rectangles. The third consisted of ADR elements – that is asymmetrical double rectangles or two rectangles of different size – where we start out with a nominally 1 wl perimeter loop and add on another shorter loop on to it as shown in Figure 3.
Design Goals
The challenge, which I shall address in this article, is to design a 2 element double-loop array which is not much larger than a simple quad array and which is able to sustain a useable f/b BW (f/b > 15 dB) over the entire extent of the 10 meter band. The other design criteria are: the gain can be no less than the quad array’s and the maximum wire diameter is 2.5 mm.
Simple loops as array elements
The law of the conservation of gain
While individual, tall-narrow, rectangular loops have a significant gain advantage over the square, we found that a part of this gain was lost when we arrayed them. The range in overall gain of simple rectangular loops is from 2.14 dBi – for the folded dipole (FD) – to over 5 dBi for a .45 wl tall rectangle with .05 wl wide radiators. This is almost a 3 dB increase in gain.
Yet, when we look at 2 element arrays composed of these same rectangles, the overall gain goes from about 6.89 dB for an antenna composed of 0.1 wl tall x .4 wl wide rectangles (each individual rectangle has a gain of about 2.4 dBi) to about 8.4 dBi for one composed of the .45 wl tall rectangles. We are talking about a net increase of only about 1.5 dB over the range. I deliberately omitted the 2 element FD array for comparison since it is qualitatively different; it acts as a 2 element Yagi and not as a loop array. Its gain, f/b and BW are inferior to any loop array.
The reason behind this “conservation of gain” phenomenon is that, as the rectangular elements became taller, their coupling increases and their separation, at peak f/b, has to increase in turn. Unfortunately, array gain is inversely proportional to element separation. So we end up with arrays with moderate gain increases, long boom lengths and narrowing of their BWs as their loops are made taller and narrower.
Double loops as array elements
In the last article in the series, “Loops In Arrays”, we found that the double loop SDRs proved useful from the point of view of providing even more gain. They also suffered from a limitation of BW as we made their component rectangles taller and narrower. What we did note however that a 2 element array composed of double-square SDRs as elements had a substantially greater f/b BW than simple quad arrays.
As a point of reference, with respect to 10 meters and the thickest practical wire – 2.5mm diameter or about #10 AWG – the reference 2 element quad array has a f/b (20+ dB) BW of only slightly under 2% or about 550 KHz. This covers less than 1/3 of the 10 meter band which has a frequency BW of 1.7 MHz or 5.8%. The double-square SDR yielded a f/b (20+ dB) BW of about 850 KHz or 1/2 of the 10 meter band. The f/b > 15 dB BWs are about 70 % greater and do not come close to covering the full BW of 10 meters.
The 2 Element Quad Array
Lets go into how quads or square loop arrays work. Table 1 illustrates how a quad array, composed of very thin E-05 wl wires, tunes. The wires are “perfect” or non-resistive. Don’t believe for one second that an array using 0.01 mm copper wires will have these gain figures. Loop losses will render the gains significantly lower. This is the reason for the poor gain of 80 meter quads where the wire size is in this range – about 3E-05 wl. One such antenna is discussed in the earlier article on the “Well-behaved Antenna”.
Thin-wire simple 2 element quad arrays: Dimensions are in wl (meters), Rin in ohms, gain in dBi and f/b in dB. The SWR BW is for an SWR <=2.
You may notice that the peak f/b ratio is reached at a specific element spacing or separation. This condition is attained when there is equality (or close to it) between the currents in the reflector and driven element. David Jefferies, G6GPR and I have shown, in our article on the “Well-behaved Antenna”, that the coupling between loop elements is directly proportional to the size of their vertical (in horizontally polarized antennas) wires. This relationship is almost linear across a dimensional range from low-wide loops to tall-narrow loops. Therefore, for each type of loop, the element spacing necessary to attain equal current magnitudes is proportional to the relative length of the transmission line or phasing wires. You can also notice what I had alluded to earlier from the point of view of element spacing: the greater the spacing the lower the gain and the higher the Rin and the useable BW. You may also notice that the SWR BW is never an issue.
Equal sized quads – designed with identical wl dimensions for 1 and 10 meters: Dimensions are in wl/meters for the 1 meter model and in meters for the 10 meter antenna
Table 2 shows the data for antennas designed with .00025 wl diameter wires. It also shows how these antennas scale over a 10:1 frequency range. Note that the f/b > 20 dB BW has increased from 1.27 to 1.98% as compared with the first antennas we have discussed. Table 2 contains the dimensions, in meters and wl, for the quad which we have used as our standard of reference in Figures 1 and 5. The antennas are tuned for a center frequency of 28.65 MHz since, as with all loop arrays, the f/b falls off less steeply above the design frequency.
2 el quad – thick wires: Dimensions in wl/meters
We are seeing fabulous BW when we look at the antenna in Table 3. Unfortunately, it is useful only at VHF and higher since, when scaled for 10 meters, the wire diameter is totally unattainable.
What can we conclude about quads? First, the coupling is related to the size of the vertical wires and the greater the loop height the greater the necessary element spacing at peak f/b. Second, the f/b BW is related in some way to the size of the horizontal, radiating, wires. Third, the SWR BW is related to the wire diameter which is reflected in the Q factor.
Now the question is: what can we do to the quad dimensions to enable us to get a wider f/b BW?
2 Element Rectangles
We have just noted that the BW increases with radiator size. We also know from the previously published studies with rectangles that the taller and narrower the elements the narrower the BW. It seems logical therefore to try arrays using low-wide rectangles as the elements.
This discussion will be short. There is no dimensional combination using these rectangles which gives a greater f/b BW than that of a quad. We have seen that there is some sort of a law of “conservation of gain” operating with loops in that the array gains never keep up with the loop gains. This operates in the other direction also.
There is not much of a decrease in gain – over that of a quad array – as we make the loops wider and lower. This is accounted for by the narrower element spacing as the antennas are made lower.
What I did find was an antenna with 0.1 wl tall vertical wires and a width of about .4 wl which had a feedpoint Rin of close to 50 ohms on a boom of .06 wl. It was narrow banded but still outperformed a 2 el Yagi in all parameters. But this is not enough.
2 Element ADRs
Figure 4 shows what a low-wide 2 element ADR looks like. For each element we have taken a nominal 1 wl loop and added a smaller loop on to it. These antennas are fed at the center of the wire the farthest from the center wire of the driven element. What have we accomplished?
Look at Figures 1 and 5 which compare two antennas – a quad array and an ADR array. These are designed for 10 meters and use “practical” 2.5 mm wires (#10 AWG). The graphics speak for themselves and we will discuss these in detail shortly.
3 versions of ADR 2 element arrays: Dimensions in wl and meters
First let us clear up some details in nomenclature. The element spacing and loop widths are straight forward. The element height is the distance between the two end wires or the top and bottom wires. The secondary loop size is the distance between the center wire and the nearest end wire or the top wire in this case. The primary loop is the larger loop and is defined as the distance between the center wire and the farthest end wire or the bottom wire – this is the feed wire.
The resonant frequencies of the ADR loops are largely determined by the sizes of the primary loops. The antennas can be tuned by moving the center wire. Moving it closer to the far end wire makes the primary loop smaller and the resonant frequency goes up. Moving it closer to the near end wire enlarges the primary loop and lowers the resonant frequency. As you can see, the reflector is much larger than the driven element – due to the great difference in resonant frequencies between them. I deliberately kept the driven element’s center wire at less than the geometric center to enable some tuning leeway if the resonant frequency had to be changed. You only have the capability to tune it to the geometric center of the antenna. Once this wire is centered then you must prune wires to tune it.
Table 4 compares three ADRs. The first is the first one I was able to make work after playing with dimensions. This is the antenna I used as the ADR reference in Figures 1 and 5. The next two were modeled after I had developed some “feel” for these antennas. If you compare #2 to #3 you may notice that the change I made was to make the loops narrower. At the same time I increased the center wire spacing or secondary loop size and made the antennas taller. Interestingly, and not explained as yet, is the fact that the Rin increases with the taller-narrower loops. This is contrary to the way the single loops behave and is beyond that expected from the increased element spacing which results from the height related increased coupling.
Now let us at Figures 6 and 7. These compare the f/bs and gains of the 3 ADRs whose dimensions are given in Table 4. ADR #3 is at the maximum limit for gain given this thin wire diameter. All the ADRs have a gain fall off – over the 1.7 MHz BW – which is considerably less than the quad’s as is seen in Figure 5.
Figure 8 (quad) and Figure 9 (ADR) show the SWR over the full BW of 10 meters. SWR is not an issue with either but the BW is better with the ADR. With its very high feedpoint Rin we would expect the ADR to be less susceptible to detuning with rain or ice.
Note the resonant frequencies of the two loops of each array. These frequencies are the means by which you can tune these arrays.
As to the major reason for the increase in the f/b BW of the ADR array, David Jefferies, G6GPR has suggested that it may be due to the double-tuned circuits in each element. The asymmetrical double loop elements each consist of two loops of very different inductances which “stagger tune” them. There is no question that this is in effect with single loops and their gain and SWR BWs. You can stagger tune the frequencies of the primary and secondary loops to get astonishing BWs.
Front-to-back and front-to-rear ratios: Two last points with reference to the ADR array. One, as with all loop arrays, the front to rear ratio (f/r) is never as good as the f/b at the extreme upper end of the frequency range due to prominent rear quartering lobes. The worst case with this antenna is a f/r ratio of 13.5 dB which occurs at the high frequency end. The second point I would like to make is how short the boom length is – the largest is 1.423 M or little over 5 feet.
Tuning the ADRs
As a lot of us have already found out it is hopeless to tune even a simple quad array by pruning or with stubs. We can resonate the antennas quite easily by tuning the driven elements. It is virtually impossible to tune the reflectors. Why? Unless one has a power or receiving source at a distance and along the bore sight axis and an incredible amount of time you cannot come close to quantifying a null to the rear. And even if you are close how can you discriminate in fractions of a dB let alone even a whole dB?
I have developed a method of tuning my 2 meter ADR array which should work with all of them. Open up the reflector also with a “feedpoint” at the center of the bottom wire. Place UHF or “N” female connectors at the feedpoints of both driven and reflector elements. I used a commercial dipole connecter which was made of plastic and was waterproof.
Tune each element to its design frequency by alternately feeding it with the other in place but open circuited. Then put a shorting male plug into the reflector’s feedpoint. Of course you have to tune each element at the height where you want the antenna.
Start with the “ball-park” dimensions above or model the antennas to arrive at the dimensions. I can assist with any questions. Then move the center wire up or down to tune the loops. There is no question in my mind that, if you use insulated wire with a lower Velocity Factor than that of bare wire, the loops may tune slightly lower in frequency. No problem—just move the center wire. I have left plenty of leeway in the driven element’s center wire position to enable movement towards the center axis to move the resonant frequency higher.
Construction
Build the antenna as if it is a quad. Use spreaders and connect the end wires to them. Leave the middle wire free for tuning. Then spray and waterproof the connections. I would strip the insulation of the verticals at about where I plan to attach the center wire and would use alligator clips or another type of temporary clamp to connect it. After tuning, the connection should be soldered. Unlike the Hentenna, the feedpoint is not at the center wire and you do not have to worry about it being weighed down with a connector and cable.
Conclusion
The ADR may be the most “perfect” loop element to date. As an array element, it overcomes the major deficiency of the cubical quad antenna and is easy to design using thin wires to cover the entire width of 10 meters. It is not any more difficult to tune than the quad and is easy to match and feed over the desired BW.
The next article in this series will show you how to design 3 and 4 element ADR arrays for 10 meters and higher. Until next time:
Originally posted on the AntennaX Online Magazine by Igor Grigorov, RK3ZK
Last Updated : 30th May 2024