Vertical Stacking for Two Identical Yagis
(c) G3SEK

This example shows how two identical yagis can be stacked so that their capture areas just touch. That distance will give close to the maximum achievable gain.

Points to note

• Stacking two identical antennas can result in 2.5-2.9dB more forward gain - but only if it is done correctly!
• Vertical stacking will reduce the vertical beamwidth and also will introduce extra sidelobes in the vertical (elevation) radiation pattern. When antennas are stacked only vertically, the horizontal radiation pattern of the array will be the same as the individual yagis.
• Wider stacking will make the vertical pattern narrower, and increase the vertical sidelobe levels - both resulting in loss of gain. Wider stacking will also make the antenna bigger and less strong. There are no advantages here, so avoid excessive stacking distance!
• Closer stacking will make the vertical pattern wider, and decrease the vertical sidelobe levels. Although this will result in serious loss of gain if taken too far, it may be a valid trade-off to obtain a cleaner vertical pattern.
• The only way to understand exactly what trade-offs you are making is to run a computer model of the array above reflecting ground.
• Usually you choose the yagis first, and then determine what stacking distance is best for them.
• For long yagis (more than 10 elements) DL6WU has developed a useful formula based on the beamwidth. This gives a very good compromise between extra gain and a clean array pattern:

 DL6WU Stacking Formula for Long Yagis

D = W / (2 * sin(B/2))

• D = stacking distance, vertical or horizontal
• W = wavelength, in same units as D
• B = beamwidth between -3dB points.
  Use vertical beamwidth for vertical stacking (as above);
  use horizontal beamwidth for horizontal stacking.

Horizontal and Vertical Stacking

Points to note

• The capture areas just touch in both the vertical and the horizontal directions.
• The horizontal spacing is greater than the vertical spacing, because the capture areas are elliptical.
• The horizontal cross-arm of the H-frame is in the same plane as the yagi elements, but interaction is minimized because the cross-arm is outside of the capture area of the antennas.
• If the top of the tower extends up to the cross-arm (for mechanical strength) it will be inside the capture areas of the two lower antennas and there may be some interaction. 
• If there are metal guys coming up to the top of the tower, expect some interaction.

Stacking for Low Noise on 50MHz
(c)  OH1ZAA/NN0Y

Reprinted from Cheese Bits, February 1996

Editor's Note: With additional contributions of WA1YHO, WD4ECK, NO0Y, NU6S, WB2KMY and WD8ISK after the KP4XS, W9IP, W7LZP, PA3BFM, WA9JML and OH1ZAA opinions. The following note is an example of the good things that can happen on the Internet mailing lists. It is a summary of discussions that got started on antennas and stacking distances. It grew a bit and although it does not represent an "expert" view on the subject, it represents a lot of real vhf operational experience.

How does this information fit in with the 'capture area' approach used in the rest of this page? See Conclusions.

Sidelobe Noise Power Leaks are Worst from Top and Bottom

If you use an antenna program like Yagi Optimizer with the horizontal (E-plane) plot you really don't know what happens to the top/bottom lobes, since the 3 D-pattern is always at minimum toward the end of the dipoles. Therefore a smooth E-plane plot can show good F/B ratio, but it can hide big lobes in the vertical plane. Therefore I recommend to observe the H plane, and always optimize with that option activated. I only have the old 1988 version of YO but I have seen the newer one, and it is really a marvelous tool. I have also the Antenna Optimizer 6.35 (1994). In clear environments it may be worthwhile for best F/B ratio to slightly adjust antenna dimensions when running a stack instead of a single yagi. On a cluttered tower it's hard to predict all the detuning unless it is completely in the model.

If you know the H plot, you automatically know the E plot, since it is the H plot multiplied with the dipole pattern. Small H plane sidelobes, give still smaller sidelobes in any other 3-D direction. In total integrated noise power this means the that bulk of galactic noise is trying to creep in from over your head, unless your preventive measures are rigid.

0.6 Wavelength Stacking Forgives Poor Designs A Lot (but not everything)

Look at the plot of two in- phase dipoles (in almost any antenna book) with about 0.6 wavelength spacing (like the two driven elements of stacked yagi's). The pattern is compressed enormously to the sides, and gain increases to 4.9 dB over a single dipole. However, the 0 dB F/B ratio does not change.

With stacked yagis at 0.6 wavelength a poor F/B ratio is not forgiven, but anything to the top/bottom sides (and skew) is tremendously attenuated. H-plane sidelobes in wide cones around the Z-axis are virtually eliminated. However, the more complex mutual coupling due to parasitic elements limits stacking gain to lower values than with dipoles, but with very short yagis the 3 dB mark can even be slightly exceeded.

There are two simultaneous benefits: Overall parasitic noise power is greatly reduced, and mostly nearly 3 dB additional gain is produced with the stack. The net S/N ratio gain with uniform noise from all directions is at least 5 dB, but with the cosmic hot spots much bigger contrasts occur. Remember also that the earth turns with a speed of 1 degree in every 4 minutes, so that certain azimuths are not "jammed" all the time. The sharper your main lobe, the shorter the suffering. We need someone with a good "electronic noise map" (meaning a sky noise data map on a PC) to calculate the advantage for a specific stack (when compared to a single yagi).

0.6 Wavelength and 1.2 - 1.4 Wavelength Stacks for Maximum Gain

Stacking at 0.6 wavelength always assures the noise power cancellation, but if booms get long (say longer than 8 m (27 ft), the stack starts to look as a single yagi gain-wise. The stacking gain may fall well under 2 dB (which is still a lot), but if the single yagi pattern is relatively clean it is better to go to for 1.2 wave stacking for moderate length yagi's and 1.4 wavelength stacking for the long ones. This is just due to the mutual impedance: a 0.8 wave separation is always poor for gain and sidelobes (see the consistent gain dips in W2PV's YAGI book).

With four antennas it is superior to use non- uniform stacking: first stack 0.6 wave with each pair, and then allow the two bays to cancel the residual sidelobes of the separate bays (then there will be hardly any noise power from any unwanted direction). For maximum gain shortcuts can be made, but due to the S/N issue on 50 MHz, I would never neglect the 0.6 wave basic cell as building block for optimal listening. This is also the reason why VE7BQH's collinears on 144 MHz work so well. Close spacing and careful current balancing eliminates all parasitic noise leaks.

Combining Low/High Antenna Patterns with Wide Spacing

It is a fairly widespread misunderstanding that you can simply connect a low and high antenna to one cable and that the coverage is then the same as with each one separately. Remember that the pattern is a summation of FIELD VECTORS and that the combination generally forms a ZERO field in at least one angle of takeoff where both antennas would launch a considerable field, when used one at time. Also the result is 3 dB worse at an angle where one of the antennas has a pattern null due to ground reflection (since the power has been shared; half lost).

Also stacking of two antennas does not lower the takeoff angle, but it will correspond to the AVERAGE height of the two (when fed in phase). Therefore the maximum field of the higher antenna will peak at a lower angle, but the higher gain of the two makes that the combination will still produce a stronger field at this same lower angle, though the peak strength of this lobe is a bit higher.

Varying the phase between the two yagis gives new orders of freedom, but it always weakens the field in an initial maximum (any new formed field maximum will be lower in strength and offset in elevation)

Terrain Analysis is Not Sufficient in One Dimension

A relatively flat environment (or sea/lake) will produce a fairly neat analysis assuming that things are fairly homogeneous over the penetration depth of the wave (this is a completely neglected issue, since a thin layer of wet clay over rocky ground may not suffice as a real substitute on lower frequencies). Most hilly landscapes tend to act like optical lenses, but it is hard to get into a clean focus. The problem about a focus is that when that makes a signal terribly strong in one place, it must be weak somewhere else. This is why a Fresnel zone is always an area and has to be considered in full for a even a two-dimensional far field analysis.

A nice example of the preceding is the story of VK3UM, who used to drive around in Australia (probably on his motorcycle), while listening to the BBC transmissions. When he finally found an area where signals peaked awfully high, he bought his new QTH at the hot spot. I remember working him on 14 MHz, while turning my power down to about 20 milliwatts, and still got a 57 report (loud and clear). My sea reflection was a big help too (though only 20 mS/m at best, but near perfect on 14/50 MHz h-pol.).

Pileups, S/N Ratio and One-way Propagation

Most so called one way propagation I tend to explain with local S/N ratio and the fact that signals from small antennas tend to drown in the noise, but big signals keep at least head and shoulders dry. A pile-up is the most brilliant example of that. Why is one calling for 8 hours without results, and the other makes it with one shout, while both receive the DX at reasonable strength? It is no one-way propagation at the DXer's end, and even less on yours!

On receive, think about the pile up as the cosmic noise and a weak DX as the new DXCC you need. Your stack pushes the noise floor down to get one more, and otherwise you would witness a dead band.

No one can understand the difference of a few dB unless he has worked a couple of years with a piece of wire, and is then allowed to work with a 6 el monoband yagi for a day or two. The contrast will be finally clear when returning to his own setup (this is why newcomers should always play first with a simple antenna, albeit just for a while). Due to the inflation of S meter scales, most reported differences of a few S units is not more than those few dB's, but in S/N ratio those values may often approach the truth.

Ordinary and Extraordinary Ionospheric Modes

With microwave equipment, Magic T's and the like are used for one-way propagation (isolators etc.). These mostly require magnetic fields and coupling of different modes. In geophysics we may expect one-way propagation when the geomagnetic field is ready for the game. That is when the magnetic field is perpendicular to the movement of free electrons induced by the impinging radio wave. Therefore there are ordinary and extraordinary waves in ionospheric propagation, and the MUF is about 1.4 MHz (the gyro frequency) higher for the highest extraordinary mode.

This may explain an effect like WD8ISK's vertical beating a 6 el yagi, but there it could as well happen that the elevation of the yagi was proper to make a null for the vertical angle of arrival. A polarization rotation is also possible, but will gradually continue to the other polarization in time.

One way propagation may occur when the extraordinary wave is excited to the one direction of the path and inhibited to the other. The cause may be the initial state of polarization. Since waves tend to gradually change polarization in ionospheric layers (Faraday rotation effect like in EME) it is not that simple, and we may again play with the idea of crossing marginal S/N levels, when it seems to appear. This means that the process is there but it is not completely ON/OFF. The stack will again provide there rescue close to the near off state.

Brewster and Polarizations

For poor ground the Brewster angle is high and this makes patters of horizontally and vertically polarized yagis or groups very similar for the DX angles. Mainly at the ocean shore ("liquid copper"), the maxima are interlaced to cover practically all angles, while switching between the two polarizations. Therefore, just switching the polarization is not sufficient to cover all angles inland. Antennas are required at least at two different heights, and should also have provision to operate separately. The vertical reflection coefficient from poor ground is worst at the Brewster angle (with a 90 degree phase shift) and is always weaker than the horizontal coefficient.

Common Volumes with Scatter

With sliced patterns due to high antennas and good ground reflections, there will be a multitude of common slices in the cross section. The total common volume and the scatter angle determines average levels (height is a bonus, even on one side).

Tilting Mountain-top Yagis

I remember a Boulder Foothills Field Day in Colorado with the W0DK group in 1985. It was a steep down- slope so ground reflection was not useful. The city covered most of the below horizon angles, and most noise was spiky man-made. Since the main lobe of a single yagi is fairly wide, tilting did not help much. Any 0.6 wave stack would have been the answer (and partly hiding behind the edge, if the top had been wide enough with a proper flat tilt for ground reflection gain).

Conclusions (by G3SEK)

How does this information fit in with the 'capture area' approach used in the rest of this page?

Quite simply, if you want to use the favourable stacking distances of 0.6, 1.2... wavelengths for low noise, you then need to choose yagis with capture areas that 'like' to be stacked at that distance. For 50MHz that limits you to around a 1-wavelength boom for 0.6 wavelength stacking, jumping to about a 2-wavelength boom for 1.2 wavelength stacking. Boom lengths between those figures (e.g. around 1.5 wavelengths) will not be very suitable because 0.6 wavelengths is too small a stacking distance, and 1.2 wavelengths is too much.

For arrays of longer yagis, the pattern of the individual yagis can be made very clean, which means that the vertical sidelobe levels will by OK at any stacking distance - 'special' fixed stacking distances are not necessary. See the DUBUS designs, for example. The stacking principle then is to control the levels of the first sidelobes each side of the main beam, and for this you can use the DL6WU formula or computer optimization.

Stocken zu Gruppen
(c) DK7ZB

Zwei verschiedene Varianten bieten sich an: Jeweils in der Vertikalebene übereinander 2 Yagis  (optimaler Abstand 2,40m) oder übereinander 4 Yagis (optimaler Abstand 1,60m je Ebene).

Besonders die 4er-Gruppe stellt schon eine Hochleistungsanlage dar, die für Konteste bereits voll tauglich ist und mit 15dBd Gewinn einen großen horizontalen und einen kleinen vertikalen Öffnungswinkel besitzt.  Möglich ist auch eine Anordnung von 4 Yagis in  H-Form, diese ist aber elektrisch ungünstiger als die übereinander angeordnete Variante.

Bild 9: Stocken von zwei Yagis mit 75-Ohm- Koaxkabeln

Da eine Zweiergruppe einfach zu stocken ist, wird dies kurz beschrieben. Man benötigt zwei 75-Ohm-Kabel (Bild 9) mit einem ungeradzahligen Vielfachen von Lambda/4. Unter Berücksichtigung des Verkürzungsfaktors bietet sich eine Länge l1 von je 172,5cm an (RG-59B/U, 75Ohm, V=0,667, 5/4-Lambda). In der Mitte werden die beiden Kabel in einer kleinen Dose zusammengeführt und eine Buchse eingebaut. Hat man an jedem Ende zwei Stecker, kann problemlos bei Portabelbetrieb die Antennenanlage auf- und abgebaut werden. Theoretisch sollte das Aufstockkabel 70,1Ohm Wellenwiderstand haben, die zusätzliche Fehlanpassung liegt bei <1,2 und kann absolut vernachlässigt werden. Das am Kabeleingang gemessene SWR ist immer deutlich besser als die theoretischen Werte, wenn man alles richtig dimensioniert hat.

Abschließende Betrachtungen

Wer durch den Nachbau auf den Geschmack gekommen ist und längere und leistungsfähigere Yagis nach dem gleichen 28-Ohm-Prinzip bauen möchte, kann  ein gepacktes File mit den Antennendaten und -abmessungen für die Bänder 6m, 2m und 70cm diverser erprobter Hochleistungsantennen bis hin zu EME-fähigen Ausführungen als Yagi.zip  herunterladen.