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 \(Ae = G \frac{\pi {\lambda}^2}{4}\).

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).

We can calculate Ae to be \(Ae = G \frac{\pi {\lambda}^2}{4}=157.9m^2\).

Let’s calculate the area of a rectangular stacking box \(A_{sb}=4.133 \cdot 4.332 = 17.9m^2\).

So, how do you possibly contain the 157.9m^2 capture area within the 17.9m^2 stacking box, no matter what shape you make the capture area.

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

Popularity does not determine fact… well in science anyway.