FUNK AMATEUR DK7ZB VHF Yagi Antennas Instruction Manual

AMATEUR RADIO TECHNOLOGY
Stacking of VHF Yagi antennas
MARTIN STEYER – DK7ZB

DK7ZB VHF Yagi Antennas

Obviously, the question of how to connect VHF antennas to form groups causes many radio amateurs a lot of headaches. Theoretical considerations alone are of little use to anyone; practitioners want to be given concrete instructions. In principle, this involves two different problems: One is the question of the correct stacking distance, the other is the practical implementation of the connection.
The question „What is the correct stacking distance?“ can only be answered as ‘It depends’. There is actually no such thing as the „correct“ distance. It is only possible to determine the correct distance for certain cases or purposes. A distinction should be made between two limits, which are already clearly visible when using only two antennas and also apply accordingly to connection to form extensive groups.
If you want the maximum possible gain of approximately 3 dB, the distance is relatively large and the mechanics are therefore complicated; in addition, there are more side lobes compared to the single lobes, but also zeros in the vertical directional diagram.
For best suppression of the side lobes, as it is preferrable for applications such as EME, the achievable gain decreases to 1.5 to 1.8 dB, at much lower stacking distances.
An example should make the dependencies clear: The 7-element Yagi with 10.5 dBd gain and 3 m boom for the 2 m band de-

Figure 1: Directional diagram in the vertical plane (H-plane) of a 7-Ele.-28-Ω yagi according to DK7ZB (gain  10.5 dBd).

Figure 3: Directional diagram in the vertical plane (H-plane) for two 7-element yagis stacked at 2.46 m (gain 13.5 dBd)
scribed in [1] is to be stacked vertically to form a group of two. The radiation pattern does not change in the horizontal plane, but it does in the vertical plane. Figure 1 shows the radiation pattern in the H-plane (vertical) compared to a single antenna. Strong side lobes are visible. These side lobes also occur with very good Yagis and can only be reduced by drastically reducing the gain.  Case 1: The distance is 3.12 m. This gives the maximum stacking gain, the group has 13.9 dBd. Noticeable are the side lobes at ±30˚ above and below the main beam direction, they are suppressed by only 8 dB (Fig. 2). Case 2: The distance is reduced to 2.46 m. The attenuation of the side lobes increases to > 12.5 dB, but at the same time the gain drops to 13.5 dBd. This still appears to be a favorable compromise (Fig. 3). Case 3: The directivity diagram now shows an almost dreamlike suppression of the sidelobes in the range of 40 dB! The distance between the two antennas has shrunk to a manageable 1.14 metres. However, the gain

Figure 2: Directional diagram in the vertical plane (H-plane) for two 7-element yagis stacked at 3.12 m (gain 13.9 dBd)

Figure 4: Directional diagram in the vertical plane (H-plane) for two 7-element yagis stacked at 1.14 m (gain 12 dBd) has dropped to 12 dBd, and the question arises as to whether the effort and the duplication of material costs were worthwhile at all (Fig. 4). At this point, we would like to brief ly discuss the calculation of the distances. If you know the 3 dB opening angle of the antenna, the corresponding value can be inserted into the equation

determine the distance required for the maximum gain [2]. In the formula, α is the 3-dB opening angle in the vertical plane in degrees.

This assumes an ideal radiation pattern without side lobes. If the side lobes are taken into account, relatively complicated interferences between the fields arise, which can only be determined more precisely by computer simulation. If this effect is skilfully exploited, a higher gain than the theoretical maximum value of 3 dB for doubling the effective area can even be achieved as the beam becomes narrower. This leads to the 13.9 dB in case 1 described above, albeit at the cost of strong peaks.
H not only mechanically problematic
In practice, this is not detrimental in the case of vertical stacking. However, the same effect also ccurs with horizontal positioning and leads to an extremely narrow main lobe.
For this reason, one should prefer vertical stacking.

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In practice, four antennas on top of each other are far better than four antennas in an H-arrangement, because the mechanical problems with the “H” quickly become so great that this design can usually no longer be implemented for antennas with a length of 1.5 λ. In addition to the more complicated mechanical design, the high so-called surface moment of inertia of the H configuration can also be a problem. The surface moment of inertia relates to the torque in rotary motion in the same way as the mass relates to the force in linear motion. Since the surface moment of inertia increases with the distance of the rotating mass from the axis of rotation, it is easy to see that (even symmetrically) eccentrically mounted antennas have a much greater surface moment of inertia than vertically stacked antennas with their centre of gravity approximately at the centre of rotation. Anyone who has ever tried to turn a larger Yagi group in H configuration by hand will know that this requires much larger forces com- pared to the same antennas simply mounted on top of each other. For this reason alone, most people will revert to the simple vertically stacked arrangement. It simply takes too long to get the H moving to be useful able to cope with every situation
The same naturally also applies to the rotor at home. It has to absorb (not only) considerably greater torsional forces during acceleration and braking with the H, which quickly exceed the permissible limits of smaller rotators.
Vertical stacking usually more favourable Back to the directional diagrams: The comparison of diagrams 1 and 2 illustrates the effect mentioned above: The interference between the side lobes results in amplification or lower attenuation when antennas are stacked. A significantly increased area of the side lobes can result in interference and terrestrial noise being picked up. For this reason, care should be taken to optimise the diagrams of the individual antennas in EME systems, because poor sidelobe suppression leads to undesirable lobes in an antenna group to a much greater extent. Of course, this effect is not only noticeable in the H-plane, but also in the E-plane if the Yagi antennas are arranged side by side to each other. The only recommendation here is that it is usually best to use two long antennas vertically stacked as a group of two. A group of four in an H arrangement with shorter Yagis has nominally the same gain, but the considerably reduced horizontal aperture angle usually severely restricts the usability for terrestrial traffic. A very low vertical aperture angle is normally preferable because the aim is to focus as much radiation as possible towards the horizon. The only exceptions are satellite radio or Meteor Scatter or Aurora over shorter distances, where a higher elevation angle can be advantageous.

For the radio amateur, who often does not know the aperture angle of his antenna, I have calculated for various (good!) antennas which stacking distance results for two Yagis in the vertical for maximum gain. Assuming that the element positioning and the gain of a long yagi are almost optimal, there is a clear dependency between antenna gain and stacking distance. The opening angles of long antennas only differ so little that the distance can be seen as a function of the gain. I have plotted this relationship graphically (Fig. 5). It can be seen that the specified values lie within a tolerance of 0.2 dB around the maximum gain increase.
Practical hints when stacking Yagi antennas
In most cases, matching problems on VHF are solved with the aid of quarterwave trans- formation elements. Only coaxial technology will be discussed here, although it is not necessarily advisable to use coaxial cables as connecting lines when connecting very large groups with long antennas. In their entirety, they can quickly reach a length of several tens of metres with corresponding additional attenuation. Lowattenuation cables are also heavy and add a considerable amount of mass. For these reasons, specialists in large EME systems use self-made two-wire transmission lines, which are considerably lighter and have low attenuation. However, you have to be prepared for an increase in SWR under wet weather conditions, and even worse in freezing temperatures.
Coaxial 3 splitterdB
Coaxial matching splitters utilise the fact that the characteristic impedance of coaxial lines depends on the ratio of the diameters of the coaxial lines of the inner and outer conductors. The properties of the dielectric, in this case air, also play a role. Basically, the cross-sectional shape of the conductors is arbitrary, which is why the cross-section of the outer conductor can be square even if the inner conductor is round (Fig. 6). This has the advantage that coaxial flange sockets can be easily installed, which is not so easy with round conductors. Fig. 7 shows the schematic structure of such a matching splitter for two antennas. The ratio D/d determines the impedance of the arrangement. It can be determined using the following approximation formula [3]: Z = 138 log D/d + 3.54.
The calculated dimensions must be adhered to relatively precisely, but unfortunately standard commercial pipes and profiles usually do not have the correct diameters. According to calculations by DC9NL in [4], some possible values for D and d are summarised in the table. For a four-way splitter, there is an easily procurable aluminium square profile 25 mm × 25 mm × 2 mm with an internal dimension of 21 mm × 21 mm, which, with a 15 mm inner tube made of copper (standard dimension for heating pipes),  provides the necessary characteristic impedance of 25 Ω.
Fig. 8 shows a model based on this principle for coaxial distributor built for the 70 cm band. To do this, file notches into the ends of the copper inner tube into which the pins of the sockets then protrude so that they can  be soldered in place (Fig. 9). I filed the corners of the bushings on two sides so that the flange of the N-bushings fits on the outer profile. The inner tube lengths are 172 mm for the 70 cm band and 515 mm for the 2 m band. The openings can be closed with PVC plugs as they are used for furniture (DIY store).
Coaxial cable as transformation elements
Figure 10 shows an industrially manufac- tured, coaxial four-way antenna distributor (Andes). It is designed for the 23 cm band and therefore has very manageable dimensions.

As a rule, however, coaxial cables are more likely to be used for groups of two or four in the 2 m and 70 cm bands, which result in fairly simple mechanics. I also prefer cable matching, at least for 144 MHz, because of the unwieldy length of tube constructions. A little maths and commercially available cable standards make it possible to realise extremely inexpensive solutions when building your own!
Vertical stacking of two antennas
Let us first consider the case of two antennas and turn to Fig. 11. At point X, an impedance of 100 Ω must be present for each of the two lines fed in by the antennas, so that the impedance of 50 Ω required for the coaxial cable is created when connected in parallel. For this purpose, the characteristic impedance of the transformation cable is calculated according to the relationship

to 70,7 Ω. A characteristic impedance of70 Ω therefore results in a perfect match but it is no longer easy to procure such cables manufactured earlier. If one accepts aslightly higher SWR of 1.13, it is easily possible to use 75 Ω cables.
The length must be an odd multiple of λ /4 in order to fulfil the transformation condition. In addition, the shortening factor must be taken into account, which varies depending on the dielectric of the insulating material. For solid polyethylene cables, v = 0.667, for cables with a high air content (H 500, H 100, Aircom, etc.) it is higher, usually between 0.78 and 0.85. The manufacturer‘s specifications must therefore be observed. For these reasons, cable lengths of 5 λ /4, 7 λ /4 or 9 λ /4 are used in practice, depending on the distance to the f loor.
For the wiring it is important that you keep the connecting cables as short as possible and takes into account the shielding (with The length must be an odd multiple of λ /4 in order to fulfil the transformation condition. In addition, the shortening factor must be taken into account, which varies depending on the dielectric of the insulating material. For solid polyethylene cables, v = 0.667, for cables with a high air content (H 500, H 100, Aircom, etc.) it is higher, usually between 0.78 and 0.85. The manufacturer‘s specifications must therefore be observed. For these reasons, cable lengths of 5 λ /4, 7 λ /4 or 9 λ /4 are used in practice, depending on the distance to the f loor. For the wiring it is important that you keep the connecting cables as short as possible and takes into account the shielding (with
Interconnection of Four antennas in H-arrangement
Connecting four antennas is even easier, as only 50 Ω coaxial cables are required. To do this, we can visualise the relationships with the help of Fig. 12: The lines leading from each antenna to the points X consist of cables with 50 Ω characteristic impedance. The lengths l1 are arbitrary, but all cables must be identical. Due to the parallel connection at points X, an impedance of 25 Ω is present there. The cable sections l2 transform it to 100 Ω at point Y so that 50 Ω occurs there again after paralleling. A recalculation shows that quarter-wave lines with 50 Ω cable fulfil this task. All lines can therefore consist of the same cable type, only the lengths l2 must be precisely calculated and cut to size. Similarly, subgroups can be interconnected to form larger groups using this method.
Vertical stacking of four antennas on top of each other
If it is possible to mechanically control the vertical stacking of four antennas (single stacking at a distance of 3 m with 2 m antennas already leads to a total height of the antenna group of 9 m), the result is an optimum arrangement in terms of radiation characteristics: very small vertical elevation angle and larger horizontal radiation lobe. For 70 cm in particular, this results in quite manageable arrays with excellent directional characteristics. The same technology as for the H group with 50 Ω cables is basically suitable for interconnection. Since with this arrangement lomnger cables a re required, the use of 75 Ω cables has advantages, as they have a lower attenuation than 50 Ω cables with the same external dimensions.

Figure 13 shows a recommended solution. Just for comparison: With a four-way distributor, all cables must be the same length and orientated to the largest distance. Theuser of three two-way distributors would be even more complex. The individual antennas A1 to A4 with 50 Ω each are provided with 75 Ω transformation cables of the same length l1 . 112.5Ω then appear at points X, which result in56.25 Ω when connected in parallel. Now a transformation to 100 Ω at point Y follows again with 75 Ω cables (l2 ). After parallel connection, you can then connect the normal 50 Ω connection cable to the station at the connection point.
Construction of the coaxial matching cables
Start by soldering the coaxial connectors to the cables; then strip the calculated length from the end of the shielding and expose the inner conductor. For full PE with v = 0.67, this results in 345 mm of cable (length of the shielding) for each quarter wavelength at 145 MHz. A good earth connection and short inner conductor pieces are important at the T-connectors (Fig. 14). If there is no socket there, you can use T-pieces (fittings) made of copper pipe for heating and water installations, which enable a joint-free transition of the braid on the earth side. A test with self-built low- inductance terminating resistors (2 × 100 Ω metal oxide film resistors in parallel, Fig. 15) is informative before connecting the antennas. Check whether the matching results in an SWR of 1.1. If a handheld radio with an extended frequency range is available, the SWR minimum can be determined between 140 and 150 MHz, allowing you to measure whether the SWR minimum actually appears at 145 MHz. If the latter is shifted upwards or downwards, the cable lengths must be corrected accordingly. However, if the instructions are followed carefully, this should not be necessary. Proceed in the same way with cables for 70 cm. An extension cable created in this way for the portable use of two 2 m Yagis is shown in Fig. 16.
Antenna arrangement and practical design
Another important point deserves attention: The arrangement of the antennas must be such that all radiating elements are excited in phase. This means that gamma lines, inner conductors of half-wave balun cables and coaxial cables for the DK7ZB feed must be on the same side (and at the bottom!) of all antennas.

Figure 17: Mechanical realisation of the connection points for pipes for an Hshaped cross with aluminium brackets Photos: DK7ZB
Matching pots are not worthwhile for the 2 m band if you can get clean solder connections for the matching cables. For 70 cm, cable transformers should have slightly higher but still acceptable additional losses. For 23cm only the use of coaxial matching splitters are recommended. In principle, the theoretical values for the gain are higher than one would expect. This is because cables, plugs   and connecting cables with soldered joints  always involve unavoidable losses.
Special attention should therefore be paid to them.

You can also avoid high costs for the mechanics of the connection points for tubes for an H-cross by building it yourself. I will spare the reader a repeated description of the angled aluminium/ exhaust clamp technique, which has also proved its worth for shortwave yagis as an element or support tube attachment. Figure 17 shows it clearly. After final assembly, additional corrosion protection should be provided by spraying several times with plastic spray. Finally, a suggestion for a powerful 2 m/70 cm combination. Two yagis for 2 m and four yagis for 70 cm are combined in an H-cross as shown in Fig. 18. With skilful mechanics, an approximate balance can be achieved despite the asymmetry. The mutual influences are almost zero, in contrast to two nested Hgroups with four antennas each. Last but not least, a word about the costs: The material price for a group of four 10-element Yagis for 2 m from [1] with all parts and matching lines including H-cross is only just over 300 DM; the arrangement has an antenna gain of about 19 dBd. If you consider that this is required elsewhere for a single 3-λYagi, a self-build is definitely worthwhile. In addition, a description in the QSO „Yagi group, completely self-built“ also has a corresponding effect on the assessment by the partner and the builder‘s sense of self-worth, doesn‘t it?

Literature
[1] Steyer, M., DK7ZB:
High performance yagis for the 2 m band using 28 Ω technology,
FUNKAMATEUR 46 (1997), H. 1, p. 72
[2] Hoch, G., DL6WU: Optimum stabilisation of directional antennas, UKW- Berichte (1978), H. 4, p. 235
[3] Weiner, K., DJ9HO: UHF Unterlage, Part I, p. 110
[4] Weiner, K., DJ9HO: UHF Unterlage, Part III, p 571

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