Stacking of Yagis and antenna effective aperture

The matter of stacking Yagis for improved gain is it seems a bit of a black art (and it should not be).

A common piece of advice is to visualise the capture area of the individual Yagi, and to stack them so that their capture areas just touch… with the intimation that if they overlap, then significant gain is lost.

Above is a diagram from F4AZF illustrating the concept. Similar diagrams exist on plenty of web sites, so it may not be original to F4AZF.

Now Capture Area or Effective Aperture Ae is a well known concept in industry and explained in most basic antenna text books. In concept, the amount of power available from a plane wave by an antenna is given \(P=S Ae\) where S is the power density of the wave (W/m^2) and Ae is the Effective Aperture. We can calculate \(Ae = G \frac{ {\lambda}^2}{4 \pi}\).

So, let's consider a 17 element DL6WU for 144MHz, with a gain of 16.7dB (G=46.5) and optimal stacking distances of 4.133m and 4.332m (Estimating Beamwidth of DL6WU long boom Yagis for the purpose of calculating an optimum stacking distance).

Let's calculate the area of an ellipse of those optimal axis dimensions as \(A_{se}=\frac{\pi}{4} \cdot 4.133 \cdot 4.332 = 14.1m^2\).

We can calculate Ae to be \(Ae = G \frac{ {\lambda}^2}{4 \pi}=16.1m^2\). If this figure were used to drive the stacking distances, an issue is what aspect ratio to choose for a particular antenna, the diagram is not good guidance. For comparison with the example antenna, if we used the same aspect ratio as the optimal stacking distance mentioned above, each axis would be larger than optimal by a factor of \(\sqrt \frac{16.1}{14.1}=1.07\) in this scenario.

Clearly, the concept is flawed. It is another of those simplistic explanations that is appealing at first glance… but flawed.

Update 20/10/2020: this article contained a serious computational error which is now fixed.