Loop Antennas or Variations on the Quad Loop
The square loop is widely used by itself and as an element in multi-element quad arrays. What I shall discuss in this series of articles are variations on this basic loop which will enhance its performance. In this first article I shall confine myself only to single loops in free space. The next article will go into how to make these antennas perform optimally over real ground. The last one will show you how to put these elements together into multi-element arrays.
For the sake of simplicity, all antennas discussed here are horizontally polarized and designed for the center of the 2-meter band at 146 MHz. However, when appropriate, I will discuss how they can be scaled to the lower bands and briefly discuss what other variables enter the picture when these antennas will be used over real ground. Also, since all of the antennas will be modeled with relatively thick .5″ (12.7 mm) wires their performance will be the best that can be hoped for. L. B. Cebik, W4RNL in another new series of articles in antenneX will show you how you can come close to this level of performance on the lower HF bands.
Figures 1-6 demonstrate a variety of antennas based on the rectangular loop. These range from the common “quad” or square loop (Figure 1) to the rectangle (Figure 2), the two variations on the double rectangle – the ADR (Figure 3) or asymmetrical double rectangle and the SDR (Figure 4) or symmetrical double rectangle—and the multi-loops which can have as many loops as you care to attach to one another. As an illustration of the latter, we have a S4R or symmetrical quadruple loop in Figure 5. Figure 6 is another variant of the quad loop—the “diamond”. For our discussion, we will begin with the simple square loop and then go on to all its kindred. Our main goal will be to increase antenna gain and we will see what price we have to pay for it, if any, with each type of loop.
Bandwidth Considerations
Let me digress for a moment and discuss the necessary bandwidth (BW) needed for the amateur bands. In the U.S. the widest amateur band is 80 meters which, extending from 3.5-4 MHz, requires a BW of 13%. There is no gain antenna that will fully cover this band. The next widest band is 10 meters – 28-29.7 MHz – and the necessary BW is almost 6%. In the U.S., but not in the rest of the world, 40 meters is available from 7-7.3 MHz and spans about 4%. 2 meters and 20 meters are similar in requiring BW’s of about 3%. 15 meters needs about 2%. The WARC bands are so narrow as to have virtually no BW limitation.
Because of all this, the type of antenna that you can use and its dimensions must be tailored to the band that you need it for. You can get away with very high gain but very narrow-band antennas for the WARC bands but will have to sacrifice some gain to be able to cover the full range of 10 meters. Similarly, 40 meters will be difficult to cover without making some sacrifices. Amateurs in the rest of the world, however, can afford to use a more narrow-band antenna with higher gain. On the other hand, 80 meters may not be a problem. My personal feeling is that, since you cannot cover the whole band in any case, you can tailor you antenna to cover the narrow segments that you will actually be using and try to squeeze as much gain as possible from it. For instance, in the U.S., 30 kHz is adequate to cover either the SSB or CW DX “windows”. At any rate, the way to relate my 2 meter figures to the other bands is the following: an antenna with a BW of 4 MHz (144-148 MHz) on 2 meters would cover from 14-14.4 MHz and one with a BW of 8 MHz on 2 meters (142-150 MHz) would cover the whole 10 meter band – if the antenna can be properly scaled.
From the point of view of antenna BW, the one principle that I have gleaned from studying all of the antennas that we will be discussing is that BW is directly related to the size of the radiators. Anything that widens the radiators increases the BW and anything that narrows them also narrows the BW. This also holds true for the front-to-back ratio (f/b) BW of multi-element arrays.
The Square or Diamond Loop
This quad, seen in Figure 1, which I am sure many are familiar with, has been known since the early 1940s. It is nominally 1+ wl in perimeter but this is a function of the frequency and the wire diameter. L. B. Cebik, in an earlier article in antenneX (now in Archive III), provided formulas for determining the actual perimeter depending on these parameters. To summarize: the thicker the wire the greater the perimeter, the higher the radiation resistance and the wider the bandwidth.
Table 1 lists the parameters for all of the antennas we will examine in this article. The quad or square is the first one. The height is that of the top horizontal radiating wire—the bottom wire for this and all of the other antennas has arbitrarily been set at zero.
The quad functions as if it were two .25+ wl dipoles which are fed in phase by a pair of .25+ wl transmission lines. The gain of a thin-wire quad is about 3.3 dBi or approximately 1.2 dB over that of a single dipole. This is the result of the “stacking gain” due to the mutual interactions of its two elements which are separated by about .25 wl. Its radiation resistance is about double that of a dipole.
For an equilateral loop of approximately .25 wl+/side it does not matter whether it is in a “square” or the “diamond” configuration seen in Figure 6. But, as we shall see later, when we attempt to stretch the height of these antennas for more gain, this analogy holds only for the equilateral case.
The loop dimensions, carried down in the ham literature for many years, are basically incorrect because, as L. B. Cebik has pointed out, they do not take into account the relationship of the frequency the antenna is being designed for and the wire diameter as they affect the loop perimeter. More importantly, while we have always designed Yagis using thick elements, the wire size suggested for quads has been very thin—usually 14 AWG. This certainly limits the bandwidth of single loop quads at HF and seriously affects the performance of quad arrays which suffer in not being able to maintain high front-to-back (f/b) ratios over the same frequency ranges as well-designed Yagis.
To address this problem, L. B. Cebik, in his new series of articles, will show us how to overcome these liabilities by using “thick wire equivalents” (my term) or simulating thick wires with multiple thin ones.
The Rectangle
Now that we have summarized the starting antenna, the square loop, let us see what happens when we stretch it out by making the antenna taller and narrower. That is, we make the two transmission lines taller and the two radiators narrower as in Figure 2. We do this because we are always searching for more gain.
As I have summarised in earlier articles, stretching out a rectangle separates its radiators and, due to the mutual interactions between radiating elements, results in greater “stacking” gain than you have with the quad where the radiators are separated by only .25 wl+. Theoretically, with lossless loops, you can stretch out the transmission lines between radiators to .5 wl and approach a maximum gain of about 6+ dBi or almost double the quad’s. This antenna is impossible to build since its radiators at that separation are isotropic or point sources while the radiation resistance approaches zero ohms. In effect this model is that of a .5 wl transmission line shorted at both ends.
Gain has to come from somewhere; azimuthal narrowing, elevation lobe narrowing or both. With Yagis the gain comes from the narrowing of both lobes. Due to the shorter radiators of loop antennas there is really no azimuthal narrowing but there is substantial elevation narrowing. With horizontally polarized antennas this is extremely useful. Even a narrow rectangle has almost 90 degrees of azimuthal beamwidth (at the -3dB points) and the narrowing of the elevation lobes decreases its responsiveness to high-angle interference.
Let us look at Table 1 again beginning with the 28″ rectangle and ending with the one 36″ tall. We see that the radiator width decreases as the antennas are made taller, the radiation resistance decreases at a slightly faster rate and the SWR BW decreases even more rapidly.
On 2 meters, if we wish to, we can construct a rectangle, seen in Figure 7, which is 36″ (.45 wl) tall and with a radiator width of 7″ (.09 wl), which will have a gain of 5.5 dBi – or almost the maximum attainable – and a “matchable” feedpoint resistance of 10 ohms. But the price to be paid for such an “extreme” rectangle, besides the low radiation resistance, is extremely narrow BW – only 1.5 MHz or about 1%.
Nevertheless, as noted above, there are a host of antennas for 2 meters that provide greater gain than the square loop, have a wide enough BW to cover the band and have practical feedpoint resistances.
The 28″ (.35 wl) and 30″ (.37 wl) tall rectangles have more than enough BW to cover even 10 meters while the 32″ (.4 wl) rectangle will easily cover 20 meters when properly scaled. These antennas are easily scaled for UHF and higher and will have wider BW’s due to the relative thickness of the wires with respect to wl.
Even the highest gain rectangle has sufficient BW to cover any of the WARC bands – if you can deal with its radiation resistance. However, because of the overall height of such a rectangle and the proximity of the lower radiating wire to the ground you will find that the best antenna for gain at a low elevation takeoff angle (TOA) will actually be one that is shorter. This tradeoff between the highest gain in free-space and the highest gain that can be attained at the lowest elevation TOA over real ground is discussed in detail in my article on the 30 meter loops. I will go into this subject, on a band-by-band basis, in the next article in this series.
The last point that I want to make with respect to practical antennas over ground is that, the higher up you go in frequency, the taller an antenna that you can use because the TOA is dependent on the proximity, in wl, of the lower wire to ground – or on the average height above ground of all the radiators. This point is important to bear in mind when we will be discussing even higher gain symmetrical double loops which are, at the smallest size, twice as tall at over .5 wl. It is also clear in my mind that the multi-loops composed of 3+ loops are only useful at VHF and higher.
We will finish the topic of the stretched out single loops with a short discussion of the “diamond” seen in Figure 6. As I mentioned earlier, the “diamond” and “square” equilateral quad loops perform about the same. This does not hold when you stretch the antennas by making them taller and narrower. When you do so, because of the current distributions and phasing along the wires, the diamond never gets close to the gain of a rectangle while its radiation resistance drops more rapidly as the antenna is made taller. The end result is that an elongated diamond is not a useful antenna.
The Symmetrical Double Rectangle or SDR
As I mentioned in an earlier article, this antenna has been called by many names: the skeleton slot, the DMS or double magnetic slot and the H-Double Bay. Since it consists of two equal-sized rectangles or squares I have adopted L. B. Cebik’s more descriptive term, the SDR. This term is useful also in differentiating it from another antenna, the asymmetrical double rectangle or ADR.
Here we have two equal-sized loops attached to each other. There are 3 radiating elements which are co-planar. The gain of such an antenna averages 1 dB more than that of the simple rectangle which composes one of its loops. In addition, because of the impedance transformation caused by the addition of a second loop, the radiation resistance at one of its end wires is much higher than that of one of its component rectangles. It can be fed at either end wire or at its center.
However, in the specific case of a SDR of two square loops and built with thick wires, it must be fed at the center wire. This is because the end-wires cannot be resonated due to the phase of the currents in the loops and there will always be a negative reactance at the feedpoint. The problem disappears if we make the loops slightly more rectangular—that is taller and narrower. Also, the problem does not exist in practice if we use relatively thin wires on lower frequencies. The reason for this inability to resonate a SDR with thick wires relative to frequency is because the loop perimeter is greater with increasing wire thickness. This leads to a widening of the radiators and creates the particular current conditions leading to this phenomenon.
Also, when using thick wires and feeding the end radiators, the antenna squints. That is, the elevation pattern noses up from the horizon. This is barely perceptible with the SDR but becomes more obvious with end-feeding multi-rectangles composed of 3 or more loops.
As for its utility the SDR is most useful from 15 meters on up in frequency. Note in Table 1 that an SDR composed of two square loops has a BW greater than the quads. On 10 meters such an antenna will be about 17′ or 5 meters tall. On the lower HF bands its bottom wire will be too close to ground to yield the best gain at a TOA of 5 degrees or less unless the supporting structure is very tall. (This criterion is just my own arbitrary definition of what is the best elevation angle for DX’ing).
Lastly, this antenna is excellent in multi-element arrays and as a basic pair of elements in VHF-UHF quagis. Arrays are extremely “well-behaved” with very high gains and wide SWR and f/b BWs. I have a particular 2-element antenna, to be discussed in a later article, which has a very high feedpoint resistance and extremely small changes of reactance over a wide band of frequencies. This type of antenna, as L. B. Cebik has pointed out, is very useful at UHF where feedline losses mount rapidly with SWR.
The Multi-loops
There is no theoretical limit to how many loops can be joined to each other. Figure 8 shows the gains of single element multi-loops of up to 6 conjoined rectangles where each rectangle is varied in height from .3-.45 wl. The gain curves plateau because the total gain is a function of the log of the number of radiating elements, which in the case of loops is always one more than the number of loops.
My preference is for using even-numbered loops with odd-numbered radiators. This is because the currents are balanced at a radiator which is at the geometric center of the antenna and you avoid the squint problem. On the other hand, and another topic for the future, is that the squint may be useful to some. If so, I have some models where the nulls in the elevation pattern from a center feedpoint are filled in by the squint lobes from an end-wire feedpoint. So, in essence you can steer the antenna vertically by changing its feedpoints.
Multi-loop antennas in compact arrays have tremendous gain but it is obvious that their overall heights make them useful only at VHF or higher. David Jefferies and I wrote an article about them in antenneX[iv] based on preliminary work in order to stimulate interest and further studies. As far as single element antennas go, I do not think there is a planar antenna which can come close to the gain of these other than the grid arrays used at microwave frequencies.
The Asymmetric Double Rectangle or ADR
This antenna has been known for almost 30 years as the Hentenna. It is a shame that its theoretical underpinnings have not been worked out in detail earlier because it is an extremely useful antenna. It consists of a square or rectangle to which you attach another, smaller, one. I call the larger loop the primary loop and the smaller one the secondary loop. It is pictured in Figure 4. There are 3 radiators, each of which can be fed. However, based on my experience with the impedances at its radiators, I recommend that you feed the wire farthest from the center. This is for two reasons; the radiation resistance is more stable as you vary the relative sizes of the two loops and there is slightly more gain. By the way, it makes no difference how this antenna is oriented. In practice, it is preferable to turn it so that the far-wire, or the wire most distant from the center wire, is the lower one. This makes feeding it much easier.
Many good things happen when you join two different sized loops and the only minor disadvantage is that of complexity. These antennas have more gain than the larger rectangle they are composed of (the primary loop), have higher feedpoint resistances and wider BW’s. The secondary loop is the key to overcoming some of the liabilities of simple rectangles. Please note that, in Table 1, you see two dimensions specified for the height of a ADR. For instance, the ADR of height 30/7 refers to one with the top wire at 30″ and the middle one at 7″. The lower one is always at zero height.
Let me summarize how this antenna works. The secondary loop is essentially an impedance step-up transformer. When you attach it to a resonant rectangle the impedance of the rectangle becomes highly negative. In order to resonate the new antenna – at any of the 3 possible feedpoints – you must increase the perimeter of the primary loop. You can do this in two ways. The first is by making it taller and increasing the height of the primary loop while keeping the width constant. Or you can do it by keeping the height constant and increasing the widths of all 3 radiators. There is extra gain to be had either way.
If you resonate the antenna the first way, by keeping the radiator width constant and by increasing the height of the primary loop, it results in more gain but, because of the constant width, there is no increase in the BW. However, this is the perfect antenna for a WARC band such as 30 meters because BW is not a problem and the increase in overall height is small enough such that the ground proximity effects do not steal low-angle gain. On 30 meters, this was the antenna that I found to have the highest gain at low elevation angles.
The second way to resonate the antenna, by making it wider, is the cure for the ills of the tall/narrow rectangle. Widening the radiators also results in extra gain but not quite as much as with the first method. But there is a large increase in radiation resistance and BW.
Let us look back at Table 1. Compare the simple square loop to one to which we have joined a small secondary loop – the antenna labeled 30/7 which has a primary loop of 23″ (about the size of the quad), a secondary loop of 7″ and an overall height of 30″. The ADR’s radiator width is now much greater at resonance and we see the expected increase in gain and radiation resistance. But look at the BW. The impedance transformations taking place along the two transmission lines of unequal length which connect the radiators result in an overall impedance stability over an enormous frequency range of 51.5 MHz or 35%. Moreover, the gain BW, defined as within .5 dB of the gain at the design frequency of 146 MHz, is also the same.
If we now make the secondary loop 1″ taller, while keeping the primary at 23″, we get the next ADR I want you to look at – the 31/8. For various reasons, which I am presently studying, the SWR BW increases to almost 100 MHz (97 MHz or 66%) while the gain BW is 59 MHz or over 40%.
This antenna should cover the range of 21-30 MHz or three ham bands. L.B. Cebik was kind enough to scale and model this for me over that range and it works. The only problem now is that of wire size and I will be applying his method of simulating large diameter wires with multiple thin ones to see if we can come up with a practical antenna for this range. Or for 14-21 MHz.
As for curing the ills or liabilities of the rectangle let us look again at Table 1, starting with a 32″ tall rectangle. You can see that its BW is under 6 MHz. Now let us add a 4″ secondary loop to it and note the results under ADR 36/4. The gain increases by .18 dB, the radiation resistance by about a third and the BW to a little under 8 MHz. It provides a decent match to a 50 ohm feedline over a BW of 7 MHz. With minor “tweaking” it we should be able to scale it to cover the entire 10 meter band.
This antenna is 36″ tall and it is interesting to compare it to the simple 36″ rectangle in Table 1. The rectangle has about .3 dB more gain but its feedpoint resistance is only 10 ohms. And its BW is about 1.5 MHz. If you opt for the ADR you pay a small price in virtually “useless” gain and a large return in “feedability” and BW.
With respect to the bands that this antenna can be used on, there is no limitation. On its side and vertically polarized it can be constructed for 40-160 meters. In its horizontally polarized state it is the antenna of choice in the10-30 meter range when you are height limited or when you need a very wide BW. We will see in a later article how it plays as an array element. I’ll give you a clue – it is great.
The last point I wish to make with the ADR is in how it tunes. As I mentioned earlier, the only cost in constructing it is a slight increase in complexity. The ability to tune it more than compensates for this. To increase its resonant frequency, simply move the middle wire towards the geometric center of the antenna. To decrease it, move it away from the center and closer to the near radiating wire. No pruning, no stubs.
Summary
We have looked at a number of different kinds of solitary loops – all variations of the rectangle – and have discussed the advantages and disadvantages of each. All the variants have greater gain than the quad or square loop.
The rectangles can be used as gain antennas over narrow BW’s but the ADR is a better antenna from 10-80 meters. We shall see in the following article that, over ground, the ADR is preferred because it has a higher attainable low-angle gain and because it is easier to tune. In arrays, it cures the major ill of multi-element quads, that of a narrow f/b BW.
At 10 meters and higher in frequency, the SDR comes into its own and has even higher gain. As we will see in a later article, it performs well in multi-element arrays.
The multi-loops, consisting of 3 or more conjoined rectangles, deliver extremely high gain, have easily matched feedpoint impedances and are useful from VHF on up. They form the basis for very high gain arrays. Until next time,
Originally posted on the AntennaX Online Magazine by Joel Dan Handelsman, N2DT
Last Updated : 25th May 2024