Amateur Radio (G3TXQ)- HexBeam shape

In the quest for physically-small antennas, designers have tried many ways to shorten elements without sacrificing too much performance - bending the dipole element into a "inverted W" is just one approach amongst many. If you remember your High School maths you will be able to work out that, by making the included angles of the "inverted W" 60 degrees, the length of the antenna is halved compared to a linear element. However, it's an unfortunate fact of life that there is a price to pay for making antennas smaller: the "inverted W" shape produces 0.4dB less gain than a linear half-wave dipole, and at resonance its impedance is a rather low 23 Ohms. The low impedance matters because it increases the "Q" of the antenna and hence narrows its performance bandwidth. It should therefore come as no surprise that a beam formed from "W" shaped elements has less gain and a narrower bandwidth than the more usual "linear" designs.

You may wonder why bending the element into this shape should cause such a large reduction in its input impedance. Here's a simplified explanation:

In this magnified drawing of the centre of the "W" shape a current "i" is flowing. This current can be resolved into orthogonal X and Y components with magnitudes i*cos(60) and i*sin(60)as shown. Notice that the Y components are in vector opposition to one another and so cancel one another out. Only the X component - equivalent to half the current in the radiator - contributes to the radiation. Put very simply, although a current of i is flowing in the "Inverted W" dipole it is equivalent to a linear dipole with only i/2 flowing at its centre.

We would therefore predict that an "inverted W" dipole would have a Radiation Resistance one quarter that of a linear half-wave dipole, or 18 Ohms. In practice, complete cancellation of the Y components only occurs at the centre of the element where the opposing currents are very close to one another; this causes the radiation Resistance to be higher than the predicted 18 Ohms - in fact it is about 23 Ohms.

It is interesting to compare performance parameters of the "Inverted W" dipole with those of other physically-short dipole shapes. The following figures show the Gain, resonant feedpoint Impedance and 2:1 SWR bandwidth of various shapes. Some of the shapes have a vertical component - for example, the quad loop - so although the turning radius is quite small you have to remember that they also occupy vertical space.

A clear message from these results is that you don't get "something for nothing" - generally, the bigger the turning radius the higher the Gain, Impedance and SWR bandwidth. There's quite a lot of "scatter" of the points, but in the case of Impedance there's almost a linear relationship with turning radius.

To conclude:

The performance of the "Inverted W" dipole is pretty much consistent with its size - no better and no worse than you might expect from a dipole with a turning radius of 9.3 ft !