Wave Generation from Point Sources: Interference Patterns and Radio Aerials

[sophiecentaur]

You seem to be describing what happens in a long wire antenna, in which there is a traveling wave up and down the wire - but, as you are not being specific about the polarisation involved or which direction the currents are flowing in. Why not look at some antenna theory? Wikipedia is a good enough source and much of what you are saying has parallels in standard theory - but not necessarily applied in a 'Kosher' way!
You lose nothing by replacing your "electron sea" by 'currents'. discussing the process in terms of waves and launching into a classical appreciation of the process. If you look at the simplest radiator - a short dipole - fed at the centre there is a boundary condition which says that the current flowing at the end must be zero (it can't be flowing off the end). Yes, you could arrange for a lot of parallel dipoles, very close together, to be fed, in phase, by a set of individual feeders but the presence of the dipoles next to each other is relevant. Waves, launched by one dipole, will reach another nearby dipole and induce currents in it, modifying its effective current. This is due to what we term 'mutual impedance' and gives you an impedance matrix, which describes the relationship between currents and voltages in all the elements in the array. (This. I am sure, is where your last post is effectively taking you). The edge dipoles will be in a different situation from the inner ones and you will arrive at a distribution of 'weighting' across the array.
For an array which is wider than a wavelength, there will be a periodic variation along the width of the array, caused by this mutual impedance. The situation is less of a problem when you are firing broadside because the symmetry of the system tends to balance out the effect but the edge elements will still be affected and you will not have the aperture that you might expect.
The only way to eliminate / reduce this effect is to make the dipoles very short (reducing the mutual interference) and 'forcing' the desired currents into each feedpoint. This is highly inefficient as the resistance of the feeder and elements becomes comparable with the radiation resistance of the element (that is the resistance presented at the feedpoint, corresponding to the actual radiated energy).
This applies to the antenna when used to receive, too. Only, if you are not pushed for received signal strength and just want to reject interference, you can design effective receiving arrays using 'active' antennas, which act as 'probes' rather than as resonant elements.

 

[poor mystic]

For clarity, again there are no individually-driven dipoles in a planar aerial.
Please refer to the diagram

 

[poor mystic]

I think the explanation loses little enough couched as a sea of electrons and needs smaller words

 

[sophiecentaur]

I think the explanation loses little enough couched as a sea of electrons and needs smaller words

Except that, to describe 1. What the electrons do to each other and 2. How the electrons are involved in producing a coherent wave, you need quite a bit of detail. Just saying that Volts make the electrons move about is hardly enough. That theory is a bit incomplete and can't necessarily be relied on to predict what will happen. Why do you think people use classical em theory to do em calculations? You need your own personal re-jigging of Maxwell's Equations if you are to get anywhere, I think.

 

[sophiecentaur]

I now see the diagram and would agree that (allowing for the Earth, implied) underneath) the arrangement will launch a wave, radiating outwards with a Horizontal Radiation pattern that is not easily to determine (could have maxs and mins in all sorts of places) and a VRP which will have a minimum vertically.
To determine the pattern accurately, you would need to know the currents, phases (and directions, I suspect) all over the plane. Not a trivial exercise.

In many ways, splitting the array up into insulated vertical strips makes the calculations much easier - but you need a lot of feeds for that.

 

[poor mystic]

Thank you very much for your continued attention through a difficult exercise.
I now wish to find a way, using the wave field theory I have so hardly developed, to simplify the difficult calculations you describe.

For an infinitely long plate, the only resonant circuit for f is the notional dipole between the feed and a point across the plate, hence radiation is confined to that path.

In my diagram of the aerial I unwisely chose a resonant length for the plane. Please refer to a new diagram attached, in which I attempt to address the issue of longitudinal excitation of the aerial by gradually decoupling the radiator from the (non-existent) ether.

 

[poor mystic]

"You need your own personal re-jigging of Maxwell's equations if you are to get anywhere, I think. "

Free space is like the secondary of a transformer driven by the primary, which is the aerial. Why make it any more complicated?

 

[poor mystic]

Perhaps there is now enough for a decent experiment with a chance of achieving a directional aerial. The main thing I'd like to improve before I start is the tail-off at the ends of the aerial. I don't believe I have the right notion there yet.
A perfect match into a complementary load seems wasteful. not to mention difficult to calculate, but it may be that the ends can be gradually led into a wire and terminated there.
I'd like to try about 21 notional dipoles.

 

[sophiecentaur]

Just to clarify things: how "directional" are you hoping for?

 

[poor mystic]

Well, the simulations are ridiculous. Nothing could be that good, et cetera.

 

[sophiecentaur]

How did you specify your model? What units were you using: wavelengths / m / inches?
It could be a GIGO thing. Happens to me all the time.
Seriously, what beamwidth were you expecting for a 2λ wide array?

 

[poor mystic]

"what beamwidth were you expecting for a 2λ wide array?"

Using a variant of the same routine with which I got a very surprising result, and simply looking at the graphed output, I get about 80 degrees bidirectional spread.
This is calculated at a distance of 250 wavelengths from the radiator axis.

 

[sophiecentaur]

It is normal to describe beamwidth in terms of angle between 3dB points and I imagine your 80^o figure is between first nulls.
For a 2λ wide parabolic antenna, the 3dB beamwidth is about 70λ/d - which would be 35^o, so what you got doesn't seem out of this world for that sort of aperture.
I suggest this http://www.kyes.com/antenna/navy/basics/antennas.htm" might give you some ideas about performance, based on conventional practice.
Of course, it is normal to calculate the far field values, rather than what you have done. It normally makes the sums easier, too.

 

[poor mystic]

No, I used the half power point just like everyone else would.
It probably seems arrogant of me but I'm not actually interested in conventional practice. I only like it when I can make people go "wow".

My next task then is to consider the feeder arrangement. I think that with a resonant feeder it might be possible to tap standing waves to power each notional dipole and provide a correctly-phased sum of signals to a receiver.
I expect I can think of a resonant coaxial feeder as a tank. Then the same current excites the entire circuit; the same potentials exist at every node. Each notional dipole receives equal power.
If I could clearly see how to calculate the impedance of each dipole I'd feel better. Naturally, I hope to find a simplifying trick.

I attach a plot showing a slice of the wave field for 21 dipoles.

 

[poor mystic]

I ought have some grace, and act embarrassed; sometimes it's good to look, then jump. I see that the "first null" is probably something you read on a meter, and means 3dB point. Is it a ham term?

I know it's usual to calculate far field but I couldn't locate my polar plotting routine, and had to grab a slice from a full-field plot. I didn't want to wait forever so I made the slice as close as I dared to hope might yet give a notion of far-field patterns.

Really astonishing wave fields are predicted to come from very many - say 500 - dipoles , or notional dipoles. I have generated graphs I fear may draw scorn and disbelief, you may generate them for yourself I guess.

I don't have much real experience of the sort I need in radio. I've gained an idea of how one matches a signal to this unfamiliar bearer (I understand information transmission practice very well everywhere but radio) and most of what is in the link is quite obvious to me, but knowledge of aerial impedances is something I do not presently have

I really think I should be up to the challenge of working things out on the hop if I need to, but some days it's like it has been all day for me today - I must have thunk too hard last night working out how to make the rectangular piece of copper into an array, and today thinking about a feeder.

Do you like the feeder?

 

[poor mystic]

please see attachment