For a horizontally polarised antenna the E-Plane (electrical field vectors) is horizontal = Azimuth Plot,
the H-Plane (magnetical field vectors) is vertical = Elevation Plot. And vice versa for a vertically polarised Antenna.
For stacking similar to VE7BQH G/T Table use
which also should be used in the model to derive the half power beam widths with.
In any case the frequency used in NEC and DL6WU formula should be similar for best results.
Image: © Dr. Tanja Kurzenknabe
Stacking Formula acc. DL6WU
• W = wave length [m]
• c = Speed of light in vacuum (299,792,458 m/s)
• f = Frequency[Hz]
• D = Stacking Distance [m]
• B = -3 dB Beam Width = Half Power Beam Width (HPBW)
From what boom length on is it valid?
The 6WU stacking formula is said to give valid results from a boom length of 2wL on. Why so? Because DL6WU measured on 1296 MHz Yagis and the shortest one he published just had 10 elements. As time goes by the radio amateur community takes this number as given and there we have it!
However, when investigating stacking Yagis below 2wL with 4nec2 or EZNEC we find that
• Yagis E-plane: the formula gives a very close approximation from about 0.7 wL of boom length
• Yagis H-plane: the formula tends to produce too close spacing by approx. 0.1 wL for Yagis less than 2 wL of boom length
What gain to expect?
Increase in gain due to stacking to double number of Yagis in either plane with distances according this formula results in measured max. extra gain of 2.9 dB (cable and transformation losses excluded). Here Peter V. Viezbicke and DL6WU give same number. Their measurement charts look similar too.
Here is an original chart, drawn by the hand of the very Günter Hoch himself
Source: by courtesy of DL6WU
• x-axis is stacking distance D/λ what means distance quoted in wave length; y-axis is resulting gain in dB
• The chart line marked '+' is his NEC simulation, the one marked 'o' the measurement results
• The vertical line named D-opt is the stacking distance his formula delivers
• Φ is the Yagis -3 dB Beam Width.
As there are quite differning designs with varying side and rear lobe levels the DL6WU formula can not serve all right to full extend and all occasions. As nothing but the main beams -3 dB width is ingoing nothing else counts here.
Nevertheless D-opt rightly suggests optimum distance as a compromise between extra gain and increase of side lobes i.e. noise level for very most of designs. When optimising a stack to the max the DL6WU formula can not always deliver on the last quantum. Here we use NEC and TANT in combination to find best match for whatever goal we have put up.
For best reception sufficiently low Antenna Temperature of the stack or mostly best G/T are recommended. The weighing between both much depends on the local noise level.
For hardest punch of our TX signal slight over stacking i.e using up to 10 ... 15% larger stacking distances then the 6WU formula suggests may be a good choice.
Those who want to learn more about stacking and its optimation may find further details here.
The issues of the Dubus magazine can all be ordered as single issues, it does not take the annual abonnement for this
My Articles on Stacking in Dubus-Magazines
Stacking beyond DL6WU - Part 1
Basics like phase shift in the Yagi-Uda Antenna, pattern qualification for various stacking goals, background on DL6WU formula and analogy to Wave Optics. Pictured explainations on Effective Apertur Area in context to stacking and more
Dubus 4/2013 & Dubus Technik XIII
Stacking beyond DL6WU - Part 2
Diamond Stacking compared to DL6WU by normalised effective aperture areas (with Slobodan Bukvic, YU7XL), an introduction to phase shifted stacking schemes, Phased Arrays, Stagger Stacking in pairs and larger groups with explicite notes on how to feed such systems
Dubus 1/2014 & Dubus Technik XIII
Stacking beyond DL6WU - Part 3
Antenna G/T wise advantages of vertical 4 or 6 Yagi stacks on UHF against common H-frame arrangements for extraterrestrial communication
On the Internet online
How to build a 4 Yagi array in NEC in compliance with the VE7BQH G/T Table (with VE7BQH) plus a detailed
view on all parameters in the G/T Table
For download as PDF at EA6VQ's www.DXMAPS.com 9/2011
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73, Hartmut, DG7YBN