Stacked Antenna Arrays

Authored by: Basu (VU2NSB) on October 31, 2019.

How do Stacked Antenna Arrays work?

Stacked Antenna Arrays or Stacked Array is usually referred to as a set of directional antennas like the Yagi, the Cubical Quad, or the Helical antenna being placed in the vicinity of one another while being driven by a common RF transmitter. This scheme would result in additional forward gain beyond what is available from a single constituent antenna. This is the type of Stacked antenna Array that we are going to investigate in this article.

Although, antennas like the Yagi, Multi-element cubical Quad, collinear antennas, etc are technically also antenna stacks. Most of these antennas are created by stacking several dipoles or monopole antenna elements. There are essentially two types of antenna stacks based on their radiation pattern directions. Those antennas which radiate in a direction along the stacking plane of the antenna elements are called Endfire antenna arrays, while those which radiate perpendicular (orthogonal) to this plane are called Broadside antenna arrays.

Typical examples of the end-fire antenna array are the Yagi, LPDA, Multi-element Quad, etc. Typical Broadside antenna arrays are the Collinear antenna, various types of curtain antennas like the Sterba Curtain, etc. We continue to deal with all these types of basic antenna arrays in other separate articles on our website that are dedicated to such antennas.

Getting acquainted with the Stacked Antenna Array

Typical deployment of a 2×2 stacked antenna array.

As we said before, the Stacked antenna Arrays that will we now discuss are the ones that are formed by stacking of other basically stacked dipole arrays like the Yagi, etc. Stacking of several Yagi antennas, crossed-Yagi, axial-mode helical antennas, Quads, Quagis, etc ar most common among radio amateurs operating on HF, VHF, or UHF bands. On the HF band, for terrestrial radio communication, a stacked Yagi antenna array is perhaps the most common format. Though a stacked antenna array is quite a large physical structure and thus not practical for most radio amateurs on account of space constraints, we still see several operators around the world who do manage to deploy stacked arrays by overcoming various challenges.

Before we continue further, let me also say that the purpose of stacked antenna arrays is not only to achieve higher gain. They may also be used for beam steering which means that the direction of the forward beam may be made to point in a direction other than its typical forward direction without physically rotating the antenna. This is achieved electrically by controlled alteration of the phase of the drive to each of the constituent antennas in the stack. Such beam-steering antenna arrays can swing their beam direction very rapidly and literally scan from one azimuth or elevation direction to another. A typical real-world example of a beam steering stacked array is the active electronically scanned array (AESA) which is nowadays being quite extensively being used as a Radar antenna on modern military aircraft. AESA also finds application in ground-based air defense and fire control radar systems.

Amateur radio operators do not seem to leverage the beam steering attribute of stacked antenna arrays, perhaps due to the relative complexity of the antenna feed system that provides a smooth phase shift at the TX power level. It could also well be that since no commercial amateur antenna manufacturer so far offers phase steerable antennas, nobody uses them. Whatever might be the reason, a steerable beam stacked array of this nature would in many cases allow a fixed and non-rotatable structure to cover large parts of the world for radio communication. Though electrical azimuth beam steering for HF antennas may have some limitations, yet it definitely broadens the area coverage. On the other hand, elevation beam steering will allow the operator to control the optimum radiation take-off angle and hence let the operator tailor the antenna lobe on the fly, either for DX, or short, or medium-range contacts, whatever is desired.

Stacked Antenna Array structure and its salient features

A representative configuration of a wide-spaced stacked array.

Typically, multiple Yagi or any other directional (either unidirectional or bidirectional) antenna may be arranged in a stack. The stacking may be either along the horizontal plane, a vertical plane, or even a hybrid combination of stacks that contain constituent antennas stacked in both the horizontal as well as the vertical plane. The stacking may consist of 2, 3, 4, or n number of antennas. If the n number of antennas is stacked horizontally then we call it (n)x horizontal stack. Similarly, vertical stacking is designated as (n)x vertical stack. A hybrid stack comprising of both n number of horizontal and m number of vertical stacking order is designated by (n)x(m) stack.

Typically, uniplanar HF stacked arrays are preferred by radio amateurs for vertical stacking and normally we might use 2 or three antennas in a vertical stack. A bi-planer hybrid stack for HF bands may often be a 2×2 stack. However, on VHF or UHF bands we may often come across 4×4 or even larger stacks. Such biplanar stacks may often be asymmetrical where the number of antennas placed horizontally or vertically may be different. This helps in further tailoring the radiation lobe pattern of the stack. Various different communication applications use different stacking orders to achieve their unique objectives.

As a general rule, the more the number of antennas stacked in the horizontal plane, the greater will be the lobe compression in the azimuth and hence a narrower azimuth beamwidth. Similarly, the more the number of vertically stacked antennas, the narrower will be the elevation beamwidth. In free-space, symmetrical stacks will produce a more-or-less circular wavefront beam cross-section. However, an asymmetrical stack like a 4×2 stack will produce a beam that will have an elliptical cross-section.

Here are some of the salient features of a typically Stacked Antenna Array. We will expand on the important attributes as we progress through this article.

2.7-3.0 dB additional gain is produced each time we double the number of antennas in the stack.
Wider the stacking distance greater would be the additional gain while closer stacking will yield lesser additional gain.
The constituent antennas forming a stack must all be identical with minimum spurious lobes and a clean pattern to be able to achieve a clean stacked array radiation pattern.
Wider stacking will produce larger undesired sidelobes while closer spacing will produce a cleaner pattern with smaller sidelobes.
At a low height above ground, there will be some pattern distortion while stacks deployed high above the ground will mitigate the problem.
An Excessively small stacking distance will result in significant mutual coupling which will alter feed-point impedance and cause gain loss.
If constituent antennas (Yagi) in the stack have moderate beamwidth then the optimum stacking distance will be closer while narrow beamwidth constituent antennas will require wider stacking distance.
Best stacks are monoband stacks though multiband antennas can also be stacked but there will be a performance compromise since a multi-band stack will perform sub-optimally on several bands.

Effects of ground surface proximity on stacked arrays

Clean elevation lobe pattern due to proper stacking distance.

So far so good… However, when we deploy a stacked antenna in close proximity to the earth’s surface, then the simplistic nature of clean radiation lobe patterns that we explained for the case of free-space, primarily the elevation lobe pattern, largely goes for a toss. The azimuth pattern remains more-or-less unaffected, The presence of the earth’s surface and consequent reflections from it is the cause. All terrestrial stacked antenna array deployments (barring a purely horizontal stack), especially on HF bands must take the factor of ground reflection into account. Though the elevation lobe pattern of almost all antennas (barring a vertical with an integrated ground plane) alter due to the earth’s surface proximity, the lobe patterns remain clean. In the case of a typically stacked antenna array, not only does a similar elevation pattern change occur, but the additional distortion of lobes tend to happen which may not be always bad but could often produce undesirable effects. Please note that this kind of distortion does not apply to uniplanar horizontal stacks.

The VHF/UHF stacked arrays suffer minimally on account of proximity to the earth. Normal deployment heights of the stacks are several wavelengths above ground. However, HF stacks are less fortunate. The height of a typical HF stack above ground may practically just only be a few wavelengths (if mounted on a tall tower), otherwise, it may even turn out to be as low as a fraction of a wavelength, depending on the operating band, while the stack spacing may be comparable to the height above ground or at times may even be greater.

One might ask, So what? Why does it matter for a stack and not so much for a standalone Yagi? Fair question… The answer is that for a stacked array to produce a clean, predictable, and a gain enhanced radiation pattern, the constituent antennas that we use to form a stack are usually identical antennas. This means that individually the characteristics of all the constituent antennas are identical, including their radiation patterns. In free-space or at significant height (in wavelength) above ground, all is hunky-dory. All the constituent antennas of the stack behave identically.

Effects of Stacking Distance to Height (S/H) Ratio

Poor elevation lobe pattern characteristics due to incorrect S/H ratio.

Now, if we lower the stack and bring it closer to the ground, or we do not physically lower it but if the stack is designed for a lower frequency (longer wavelength) band with a larger stacking distance (spacing between the antennas in a stack), then the effective electrical height of the stack in wavelengths becomes less. To add to the woes, the stacking distance becomes comparable to the stack height. This brings us to a new term, the Stacking distance to Heigth ratio (S/H). The lower the S/H ratio for a stack, the lesser is the stack pattern distortion, while on the other hand, as the S/H ratio increases beyond a point, the elevation radiation lobe pattern starts getting distorted more and more. That is why a VHF stack at a particular height will work great due to a far lower S/H ratio resulting from the height (H) being large in terms of wavelengths. On the other hand, an HF stack (operating at a longer wavelength) at the same height measured in meters (or feet) translates to a far lower height in terms of wavelengths. Hence, the S/H ratio may rise through the roof, thus it might produce significant distortion of elevation lobes.

Let us examine why this happens. Unlike a single standalone Yagi which has a uniform height above ground for all its elements, in the case of a stack, it is different. A stack comprising of vertically stacked Yagi antennas has them all at different heights above ground. Now, if we were to look at each of these vertically stacked Yagi individually, we find that the elevation lobe pattern of each of them (on account of different heights above ground) will be differently shaped from that of the one below or above it. In other words, they are no more identical antennas in terms of their radiation patterns. This is the reason for the distortion of their combined pattern in a stacked array configuration.

As we mentioned before, the elevation pattern distortion on account of the above factor may not always be detrimental. For instance, a small distortion may actually tend to fill up the inter-lobe nulls and make them less deep. This would mean that the overall performance of the stack at various elevation angles may become a bit more uniform. On the other hand, if the S/H ratio is too high, it may result in excessive distortion. This may lead to creating several low amplitude secondary lobes across the elevation plane to produce a poor performance at those angles. Even the gain enhancement of the main lobe may be negligible despite stacking.

Gain enhancement and Stacking order
Let us now see how much more gain can we expect from a stacked array antenna in comparison to a single unstacked antenna. Theoretically, we may achieve a gain enhancement of 3dB each time we double the number of antennas in a stack. For instance, if 2 Yagi antennas were to be stacked (either horizontally or vertically), then we might achieve a 3dB additional gain over a single Yagi. Now, if we were to double the number of Yagi antennas to 4 to form a typical 2×2 stack then we will get another 3dB thus making the total stack gain enhancement of 6dB. Similarly, a 4×4 stack consisting of 16 Yagi antennas will have a 12dB additional gain over a single Yagi. So on and so forth… Assuming a 3dB gain enhancement by doubling the number of antennas in a stack, the theoretical additional gain (G+) in dB for a (n) element stack can be calculated easily by the following formula.

G+(dB) = 9.966log(n)

However, the practical stacked arrays usually have lower stacking gain that may typically range between 2.7-2.9dB with doubling the number of constituent antennas.

Stacking Order (Stacking format) is not applicable to a uniplanar stacked array but may be used to define the layout of a 3-dimensional biplanar stack. For instance, a stacked array may be configured as 2x2, 3x3, 4x4, etc to form square format stacks. A rectangular format stack may be created like 2x3, 3x2, 4x2, etc. The rectangular stacks allow further tailoring of the overall radiation pattern.

For instance, if the stack is horizontally oriented with more antennas in the horizontal plane than the vertical plane, then there will be a greater azimuth beam compression resulting in narrower azimuth beamwidth while the elevation beamwidth may be broader. On the other hand, a stack with more yagis in the vertical plane with fewer in the horizontal plane will have a narrower elevation beamwidth while the azimuth beamwidth will be relatively broader. However, the overall total gain of the stack nearly remains the same for a stack having an equal number of constituent antennas.

Effects of Stacking Distance on performance characteristics
What should be the ideal stacking distance between antennas in a stack? This is perhaps one of the most vital questions and also could be a bit confusing, especially with so many inaccurate or incomplete narratives floating around on the web space. Not only that, but several articles cite old empirical rules of thumb to determine the optimum stacking distance while there are others that cite different methods too briefly without elaborating enough to provide clarity.

Horizontally stacked array featuring narrow azimuth beamwidth

People often want to know as to what is the best stacking distance? Well, there is nothing as best in this case. One man's best may not be best for someone else. The optimum stacking distance will depend a lot on your objectives. Someone might want to optimize forward gain at the cost of other performance paraments, while another person may want minimum sidelobe magnitude even if that might mean sacrificing some gain. Some people might use a set of broader beamwidth and short boom yagi antennas to create a stack, while another person may use narrow beamwidth high gain Yagi antennas as the building blocks.

This choice in itself is sufficient to warrant an entirely different optimum stacking distance. Then again, the proximity to the earth's surface will usually result in making the individual Yagis in a stack have elliptical aperture rather than an oft assumed circular aperture. We will explain antenna aperture in a moment. This factor may need a different horizontal stacking distance from that of the vertical stacking distance.

So, we see that there are several variables that we need to factor in. Hence, there is no single and simple answer to what should be the optimum stacking distance.

Let us try to bring some clarity to this aspect of the stacking distance of stacked array antennas. Let me first present the old school empirical thumb rule approach and figure out its merits and demerits.

The classic thumb rule for stacking distance states that the spacing should be between 2/3 to 1/2 of the boom length of the constituent yagi antennas used in the stack. It also says if you need more gain use 2/3 boom length approach, while to attain lower sidelobe magnitudes with some sacrifice in forward gain, go for 1/2 boom length spacing.

The advantage of following the above rule is that it is very simple. It also works fairly well if you are stacking 2-4 yagi antennas in the HF band where the constituent yagi antennas are not very high gain and when they are perhaps limited to typical 3-4 element Yagis. The individual Yagis must have moderately wide beamwidths but certainly not be narrow beam antennas. This rule also does not distinguish between circular and elliptical shaped apertures and assumes all antennas to be having circular apertures.

This is unfortunately often not true. The rule is based on boom length and hence might not always accurately address stacking of high gain, narrow beam yagi antennas that are quite often used in VHF or UHF stacked arrays. However, I would not disregard this rule of thumb method because it may be fairly valuable while stacking typical HF antennas especially if you are not too particular about further optimizing any specific performance parameter beyond a point.

Optimizing stacking distance based on effective antenna aperture (A_e)

At this stage, let us now start looking a bit deeper and explore other options to find better methods for determining optimum stacking distance. Earlier in one of the above paragraphs, I had used the term Antenna Aperture. Let us see what it means. Just like photography cameras have lens aperture which determines the quantum of light that is allowed to pass through and reach the lens, we too use a similar concept in relation to antennas. A larger camera lens aperture means more light passes through and pictures can be shot even when the ambient light is low. Similarly, an antenna that features a large aperture is more capable of receiving weaker signals. Hence, an antenna with a large aperture has better performance and is generally preferable.

However, unlike the physical aperture opening as in the case of a camera, the antenna aperture is a notional (theoretical) concept. Barring antennas like the parabolic dish antenna systems which truly have a physical catchment area in the form of the dish, most other antennas do not have a physically visible or tangible catchment area or aperture. Due to the notional nature of antenna aperture, we refer to it as Effective Antenna Aperture (A_e. Despite being notional, A_e is a very useful metric that is not only used to determine stacking distance for stacks but among many other applications, it is also used for calculating the power induced in a radio receiving antenna at the far end of the radio communication circuit. A_e is calculated as under...

where G is gain ratio and not the dB gain.

We notice that the higher the gain of an antenna, the larger is the aperture area. A_e is also proportionate to the square of the wavelength and hence inversely proportionate to the square of the frequency. Hence, high gain antennas will have larger A_e and also higher the frequency, the smaller is the A. Therefore, even a moderate gain HF antenna will have a large aperture while a higher gain VHF or UHF antenna might have a much smaller aperture. At microwave, where the wavelength is extremely small in comparison, the effective aperture of antennas becomes rather tiny. That is why we generally see microwave antennas for long-range communication to almost invariably use a parabolic dish reflector to enhance the effective aperture.

Vertically stacked array featuring a narrow elevation beamwidth.
After having understood the concept of effective antenna aperture, let us now apply it to the stacked array antennas. In a stack, several antennas like the Yagi are arranged in proximity to one another. Therefore the distance between each of them (stacking distance) becomes important. Too close spacing would make them interact unfavorably, while too large a spacing will also produce unwanted side-effects.

So, what is the best compromise? The effective antenna aperture of constituent antennas of the stack helps us to determine the starting point. Take the free-space gain of the constituent antenna and calculate the A_e from the above equation. A_e is the area of the effective aperture. Since the aperture is basically circular shaped in free-space, it is easy to find the radius of the circle formed by A_e. The adjacent antenna in the stack should be placed so that their aperture circles just touch each other. In other words, the spacing between antennas is 2 x radius or equal to the diameter of the A_e circle.

What we get from our calculations above is a scenario that will provide good overall performance from the stacked array. However, there is room for optimizing the stack as per one's need by adjusting the stacking distance around the calculated value. Increasing the distance may provide a marginal increase in stack gain but at the cost of higher magnitude sidelobes. On the other hand, reducing the stacking distance will minimize sidelobes but will marginally reduce overall stack gain. BTW, the additional sidelobes produced due to stacking are also called Grating Lobes because they are produced on account of interference grating patterns of a combination of multiple wavefronts.

HF stacked array antenna designers (with antennas closer to the ground) often need to further account for the fact that the A_e may not be circular in shape. Due to the proximity of HF stacks in terms of wavelength, the aperture shape may often be quite elliptical. Therefore the optimum spacing in the horizontal plane may need to be increased while that on the vertical plane may need to be reduced. But that's another story and we will leave it for another day.

Before concluding, let me state that the transmission line network for feeding every antenna in a stack in proper phase may often become complicated especially for large stacks, we will not dwell into them here. We have a separate section on our website to cover transmission lines where we will discuss this aspect in detail. Several methods or a combination thereof are used, including transmission line harnesses with impedance transforming TL sections, use of power splitters, and various types of Balun or Unun.

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