One of the first antennas I ever built was a 1/2 wave dipole for 2m (FM segment). I chose this as it seemed like the simplest antenna to build and get going. And indeed it was.

The idea is simple and execution is simple:

1) Figure out what half the wavelength for the band you want is;

2) Figure out what half of that is, as that’s the length of each of the two legs you require;

3) Support the two legs a bit apart, connecting the coax (via a balun – or without, although not the recommended) to the two legs – centre conductor to one leg, braid to the other leg;

4) Connect to a transceiver via a SWR meter and then trim until you get as close as possible to an SWR of 1:1.

Easy, and generally you end up at an SWR at 1:1 or close.

But lately I’ve found that to model a dipole in 4nec2 and obtain an SWR of 1:1 is impossible! There, I’ve said it. It’s impossible to get a 1:1 SWR for a dipole in 4nec2. I’ve run it through the optimiser and optimised on pretty much every parameter I could think of.

In the end, the best SWR I can get is ~1.4:1.

So if that’s not enough to get an F call wondering, what is! Well from there I’ve been reading and reading and reading, and have found some interesting things.

First, there is a slight extra bit one must do to figure out the length of a half wave dipole. The formula is:

l = ((c / f) / 2) * k

Where:

l – length in meters of 1/2wl dipole

c – speed of light: 299.8

f – frequency of desired band

k – ‘k factor’: normally in the range of 0.9 to 0.98

What!? ‘K factor’, what’s that doing in there. Ahhh! Well, that’s the additional bit. The K factor is used (varies) to accommodate for the diameter of the conductor/wire. This is interesting…

Fred Swainston in the Radio Theory Handbook (section 21.8) further describes this as:

“At the open circuit end of an antenna, a small amount of capacitance coupling to the environment exists. This capacitance allows a small amount of current to flow from the end of the antenna, thereby reducing the impedance at the end of the antenna from a theoretical infinite. This is termedend effectand will cause the impedance of a centre-fed dipole to be reduced. It is a contributing factor to the k factor when calculating the physical length of a dipole.”

Ahh, so that explains why I always seem to have to trim so much off my dipoles before I arrive at a reasonable SWR – though normally near 1:1. But still, how come I can get an SWR of 1:1 but I still can’t model that.

Well, that comes to the next bit I found. What is the typical impedance of a model dipole?? Well, it turns out things are not as simple as I thought and that 1/2 wave dipoles actually have a typical impedance of ~73 Ohm. That’s right, a better match for 75 Ohm than 50 Ohm. So this means we should normally at best be expecting an SWR of:

73 / 50 = 1.46:1

Further, as supporting evidence, that explains why the impedance of a folded dipole is a multiple and has a typical impedance of ~300 Ohm (4 x 73 = 292). As the formation of a folded dipole is said to result in an impedance transformation of 4:1 – and hence why you use a 4:1 balun with a folded dipole.

Alright, so there’s two additional bits of detail:

– k factor to accommodation for wire thickness and capacitive coupling to the environment;

– typical impedance of a dipole is ~73 Ohm and thereby typical SWR would be 1.46:1

That then tells me that my 4nec2 models are probably fine, but it doesn’t explain how in the real world I get a SWR of close to 1:1 for my dipoles.

Further reading though tells me that environment can have a big impact and one of which is the ground. Fred Swainston again comes to the rescue (section 2.16) when considering the ground with this statement:

“A horizontal half-wave antenna should be no less than 0.15 of a wavelength above the ground otherwise the feed point resistance will be less than 40 Ohms.”

So in theory if I started at 73 Ohm in free space and then headed down towards 40 Ohm when I added a ground I should be able to reach an SWR of 1:1 surely. Well, unfortunately I’ve still not be able to model this, however ground is not the only thing to consider. Another great one I looked into was transmission line loss and saw how that could also have an impact. So bit by bit, I could see these things adding up and lowering the impedance and thereby correcting the SWR.

In the end then maybe when many factors of the real world are combined – oh, how about conductivity of the materials used – then I guess an SWR of 1:1 is eventually achieved.

BUT, at what cost. I also noticed that when adding in the ground to my model and having it at a height of 0.15wl that the radiated efficiency plummeted to 32%! So I do wonder how _efficient_ my 1:1 dipoles are…

Couple of bits of online reading you might like:

Wikipedia

VK1ODs Optimised Dipole Efforts:

Also, included below is a 4nec2 model I’ve made with lots of symbols so that you can ‘configure’ and optimise it to your hearts content. As well as a couple of comparison SWR graphs for the dipole with real ground, and in free space.

Enjoy!

Details of graphs:

1. Dipole in freespace;

2. Dipole with model ‘real ground’.

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