# Two theoretical optimal antenna questions

Discussion in 'Antennas, Feedlines, Towers & Rotors' started by M0AGP, Jul 28, 2020.

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1. ### M0AGPHam MemberQRZ Page

Question 1: say you have an area for antennas that is a square with dimensions L by L feet and the frequency is f. You are allowed to have as many 1/4 wave verticals as you want, but the total power input is a fixed amount, so you are splitting power to all the verticals. You can place any number of verticals in the L by L square.

For simplicity, say you can feed each vertical with any percentage of the total power and any phase you want. Feedline loss is zero and ground is perfectly conducting to the horizon to simplify the problem. (Hopefully not so idealized that the answer is useless!)

We ignore SWR issues, assuming we can somehow feed the verticals efficiently.

What array of 1/4 wave verticals would you choose, how would you split power between them and what phases would they get in order to achieve "a really useful gain pattern for DX"? And what does the far field plot look like?

For “a really useful gain pattern for DX”, this is debatable, but let’s say we want to maximize the total radiated power “from desired heading plus or minus 10 degrees, and at a take-off angle between zero and ten degrees.”

Feel free to substitute a better definition!

We could narrow down the parameters to be the 20m band and a plot of land 20m by 20m as a concrete numerical example.

This might (once made practical) make for a nice compact antenna with gain for hams with antenna height restrictions (like in the UK where antennas require planning permission and your neighbors can easily block you, potentially taking delight in said activity...asking for a friend...).

Question 2: what if you are allowed to have some vertical elements parasitic instead of driven, and with slightly varying lengths (as in a Yagi)?

In the second example the answer might look a bit like “horizontally stacked” Yagis?

A recent YouTube video by Callum M0MCX (of DX Commander fame) discussed a partially parasitic vertical array for 40m - this is the inspiration for this question.

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2. ### AK5BHam MemberQRZ Page

One of my "dream antenna scenarios" is elevated four-square arrays for 40, 20, 17, 15 and even 10 meters. Realistically I might be able to accomplish that with one of the higher bands at our new QTH (but other verticals in the same area might interfere too much for it to be a worthwhile endeavor).

W8PW has a fantastic four-square array he took two years to build---and he did so very well---check out his QRZ page that has details and photos. "Antenna Surrounds Wife"

Good question and this is going to be a thread of special interest to me; thanks for posing such questions.

73

Jeff

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3. ### M0AGPHam MemberQRZ Page

Hmm ... I suspect this is a hard question to answer. There are a lot of degree of freedom to play with here.

Focusing on the example of the 20 meter by 20 meter back yard, in the case in which we are allowed to use parasitic elements, let's say we want to set the thing up for a single beam heading. Let's assume for convenience that the back yard is "pointing" in a useful direction.

In this case we could create three horizontally stacked vertical beams, each with a one wavelength boom, and with a half wavelength between the Yagis. Let's say a single yagi with a one wavelength boom has about 9 dBd gain. Then hopefully we get a bit over 12db gain from this backyard full of verticals with the ground plated with lots of radials.

How do those figures sound?

4. ### K0UOPlatinum SubscriberPlatinum SubscriberQRZ Page

Get John's 0N4UN's book Low Band DXing
It concentrates on 40 and lower but the same information can definitely be applied on other bands/ he goes into detail on four squares and phase antennas.
I followed his information when I built my 4 square's for 160 and 80 years ago.
I'm using elevated radials along with an extensive ground system which is primarily for lightning protection.

The 4 sq is also using Collins type power dividers for phasing/ but I have used phasing line and DXE boxes in the past

Yes you can use Verticals in line with parasitic and reflecting elements.
I'm currently playing with a fix full size 6 element 40 meter vertical beam centered at 100 feet high (1/2 wave elements wave spacing +90ft hung off my tower with a catenary line. This antenna has a wider beam width than a horizontal beam with somewhat less gain.

Last edited: Jul 29, 2020
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5. ### M0AGPHam MemberQRZ Page

Wow those antennas sounds amazing! Your QRZ page is also amazing. I will definitely get that book and learn - thanks

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6. ### AA5MTHam MemberQRZ Page

I haven't done this yet, but I will 'someday'. My vertical will be mounted on a lazy susan type support. Why would I want to turn a vertical? Because I will put an electric lift on it to change the take off angle! This makes it bi-directional, and steerable like a beam. The changeable take off bypasses holes in a standard take off pattern lobes.

I will start with a single band short dipole like MFJ makes, to keep the price down, with the small tv rotator they have also. This way, I don't have to worry about a ground screen, although this would not be a problem with most verticals.

When laying flat, is becomes a NVIS antenna, and steerable.

Tom

7. ### AK5BHam MemberQRZ Page

I am confused about your above idea; could you please post a sketch of your Lazy Susan vertical design? Is it a horizontal dipole that becomes a vertical dipole or is it an array of monopoles somehow? Thanks for clarification.

73,

Jeff

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8. ### M0AGPHam MemberQRZ Page

Tom - are you thinking of tilting the groundplane and vertical element together, with the idea being that you could concentrate more energy toward the horizon in the direction of the tilt? And then rotating the tilted vertical to get the "low part" of the radiation pattern in the desired direction? Not sure about others but I have never heard this idea before (old timers will no doubt have heard of it!). I don't know how well that would work. I guess it could be modeled most easily in EZNEC by putting the whole thing up in the air as an elevated groundplane vertical and then tilting the entire antenna towards one direction.

Interesting - someone good at the software might want to try this to see if tilting the vertical gets more radiation towards the horizon!

9. ### M0AGPHam MemberQRZ Page

I have had a look at ON4UN's book - wow that is a great resource - so interesting!

I read some of the phased vertical stuff and I think that the art of this ends up being in three main parts: decide what current levels and phases you want at each vertical, figure out how the heck you will actually build that in a practical manner and then build it. The easiest part I expect is probably the first part where you decide which currents and phases you want. The engineering and construction of the the real thing looks pretty complex indeed, especially on low bands. I tip my hat to those who have done it!

A little calculation I put together is an incorrect but heuristic one that adds up the interference pattern contributions from the verticals so as to show the kind of radiation patterns achievable. I first tried it on the four square array and surprisingly got realistic-looking azimuthal patterns. One very surprising thing is that I got an optimal solution that looks close to WA3FET's optimal solution for max gain for a four-square array. That is no doubt a numerical coincidence!

I also set it up to tackle the 8-circle array which consists of a circle of 8 verticals, each a quarter wave from the next and arranged like the "corners" on a stop sign. I assumed equal currents in the verticals and used the amazingly good "Solver" in Excel to optimize the phase lags of each vertical so as to get maximum gain. I think the 8-circle is usually used in a way that only uses 4 of the antennas at a time, but I tried to work out the radiation pattern that would optimize the forward gain using all the elements. The solution I got sort of repeats as you go around the circle, but the second half of the circle has the negative of the phase lag of the first half.

[I clumsily can't figure out how to insert a picture as it wants a link - will come back and post the pic of the radiation pattern if I figure it out]

My super-simplified calculation method
I assume that at some far-field point R the radiation will be the sum of contributions from all elements. I assume that the contribution from a given vertical is proportional to the current at the base of the vertical and also to a complex number representing the phase factor. So for example, say the distance from vertical 1 to R is called d1. Then the real part of the phase factor looks like I(1) * cos(k*d1 +phi(1)) and the imaginary part looks like I(1) * sin(k*d1 +phi(1)). The quantity phi(1) is the phase lag to vertical 1. The quantity k is the wave vector equal to 2 * pi / wavelength.

We add up all the real and imaginary parts to get a single complex number (analogous to a field strength) and then the power is I think proportional to the absolute magnitude of the complex sum (number times its complex conjugate).

Doing this in a spreadsheet is very easy, it turns out, and can be used to produce pretty patterns that look like real radiation patterns. But of course such an oversimplified calculation will only produce a vague picture of what a real array's radiation pattern would be.

Why my calculation is wrong:
1. It is not solving Maxwell's equations: it is just adding up an interference pattern from a bunch of emitters
2. The emitters do not interact with each other: in reality each vertical would absorb energy from other verticals and reradiate some of it- this is fully missing. My calculation method could not tell a Yagi from a dipole!
3. It is two dimensional, in the sense that all radiators are isotropic and we only look at the pattern in the "xy plane" (it could be extended to three dimensions in a straightforward way...hmm...)
4. There are no losses anywhere apart from the 1/R^2 drop in power from the antennas
5. There will be numerous other reasons why it is wrong
In any case this was educational for me: I got something of an appreciation for how difficult solving the real physics and engineering problem is!

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10. ### AK5BHam MemberQRZ Page

Long story short; I'm afraid things don't work that way. If tilting a Marconi would shift radiation considerably, we'd all have crooked and cock-eyed antenna farms, mate!

73,

Jeff

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