Wave Generation from Point Sources: Interference Patterns and Radio Aerials

[poor mystic]

I must be very stubborn, or something, on this because I keep thinking of tens, or hundreds, or thousands of dipoles closer and closer together, and wondering about making a plane resonate in a similar mode.

from an earlier post:
"A dipole in free space will have an impedance of about 72 ohms if driven at the centre.
Two dipoles more than a half wavelength apart will also have impedances of about 72 ohms.
As you bring them close together and parallel to each other, and feed them in phase, their individual impedances will rise, approaching 144 ohms when they get close together."

I am attracted to the idea of an r.f."wave machine", which if I read the above-quoted idea correctly ought be drivable from a standard r.f. amp at ordinary voltages and impedances.
The drawing shows a very sparse version of what I have in mind on the matter of feeders.
I wonder whether the many coaxial feeders driving many dipoles could be replaced by a single distorted planar feeder driving a planar dipole, to achieve a high degree of spatial selectivity.

 

[poor mystic]

and if not, why not?

 

[sophiecentaur]

Thank you very much.

Then is it possible to drive a rectangular plane as a very dense array, whose elements are touching?
I wonder whether copper mesh could be cut to the arc of a circle to feed the plane. By increasing the diameter of the circle the bellying in the path could be made arbitrarily small.
It sounds like easy low-noise comms so far. Surely there's a catch?

I'm not sure what actual layout you have in mind but the "catch" may be in the fact that you have to consider the total path length of signals from feed to each element. What did you want this circular plate to achieve? Perhaps a simple diagram. . . . .

 

[vk6kro]

This is where a simulator can help.

I put 4 dipoles, each 39 inches long and mounted one above the other, into Eznec Demo V5.

At 1/4 wave spacing, 20 inches, there was about 4 dB gain over a dipole even though there was already massive interaction between the dipoles. The two in the middle were most affected and showed poor SWR at the resonant frequency of the other outer dipoles.

I have attached a copy of the EZ file for this. It needs to be unzipped and placed in the ANT directory of EZW in Program files.

Feeding each dipole at 180 degrees relative to the one next to it produces a gain of about 7dB over a dipole but directed in the line of the dipoles (ie up or down in this case).
You have probably seen TV antennas where the feedline went to each element but crossed over to the opposite side along the support boom each time. This is a similar antenna.

The SWR for this arrangement is pretty poor for all dipoles and would need to be adjusted by rearanging the lengths or spacings of the dipoles.

Placing the dipoles 2 inches apart and feeding them in phase resulted in radiation that was mostly along the line of the dipoles but with severe interaction between the dipoles. Gain was less than for a dipole in any direction.

If you can, try to locate a copy of the ARRL Antenna Book. A lot of these antennas have been around since the 1930s.

 

[poor mystic]

I see I am having trouble explaining my idea, so I'll try a new tack on the question.
What happens if (say) 500 dipoles are placed in a row 2 wavelengths long?

If the very dense array I describe works, then a planar aerial resonating in the proper mode should also work.

If a useful oscillatory mode is to be excited in the plane, an EM wavefront from the r.f. amp must reach all points along the side of the plane at once.

If all points along the side of the plane are to be excited simultaneously, then the path length from the r.f. amp to every point along the side of the plane must be equal.

A geometric figure whose radius is the same for all points on its circumference is a circle. Hence a section of a circle can be considered for the geometry of a feeder intended to supply a parallel wavefront to a load.

This inspires me to think that a suitable driver for the plane might be a long feeder, which gradually spreads out, as does a slice of pie, along the course of the path from the r.f. amp. The length of the feeder then determines the arbitrarily nearly simultaneous arrival of a wavefront from the amp along the driven edge of the antenna.

I attach a further drawing.

 

[poor mystic]

attachment came through this time...

 

[vk6kro]

If you did manage to feed it like that, radiation would be along the plane of the dipoles, not at right angles to it as you suggest.

Try the simulation. Even with 4 dipoles, you can see the pattern of what would happen.
In the wires section, you can adjust the spacing of the dipoles just by changing the Z values. Starting at 600 add your first spacing, then the next etc.

 

[sophiecentaur]

I haven't understood why you want such a dense array. Your simulation has shown the high degree of interaction between close elements, which affects the pattern (as well as costing you more in materials). By using in the order of λ/4 spacing your pattern doesn't change much and, for the same number of elements, you can get a bigger aperture and tighter pattern.

 

[poor mystic]

If you did manage to feed it like that, radiation would be along the plate, not at right angles to it as you suggest.

Try the simulation. Even with 4 dipoles, you can see the pattern of what would happen.
In the wires section, you can adjust the spacing of the dipoles just by changing the Z values. Starting at 600 add your first spacing, then the next etc.

Unfortunately I am still very busy but the radiation pattern predicted by the EZNEC simulator looks very like what I would expect from my own investigations.
I am encouraged to think that an increasingly dense row of aerials placed on an axis increasingly more than a wavelength long must obey the superposition theorem and effectively project a signal in an increasingly tight beam.

 

[sophiecentaur]

Unfortunately I am still very busy but the radiation pattern predicted by the EZNEC simulator looks very like what I would expect from my own investigations.
I am encouraged to think that an increasingly dense row of aerials placed on an axis increasingly more than a wavelength long must obey the superposition theorem and effectively project a signal in an increasingly tight beam.

The aperture of the beam will limit the beam width (diffraction limit) unless you start to introduce wildly weighted / in alternating sign current for each element to form a 'supergain array', for which the beam width can be made arbitrarily narrow, but at the expense of sidelobe levels.
As the elements get closer and closer together, the effects of mutual impedance between each element and all the others gets more and more so actually driving the elements becomes harder and harder
Why the obsession with very dense arrays, anyway? They are not good value, I think.
Does the EZNEC simulator include the whole mutual impedance matrix, btw?

 

[poor mystic]

the idea of a very dense array is only that a plane aerial ought be like a very dense array. If this is so, then I can get good directivity using a plane aerial. The advantage would be that there would be no need for the great labour of setting up the many dipoles.

 

[vk6kro]

It is certainly possible to get flat plates of metal to resonate and to radiate. They have to be comparable in size to a half wavelength at the frequency in use or very little of the power supplied to them is radiated.
The problem is, basically, that a flat plate of any kind has a lot of wind resistance and it can produce extra loading on an antenna mast or tower.
There have been attempts at making very compact antennas which are basically a radiating capacitor. Claimed results have mostly been attributed to radiation from the feedline.

EZNEC gives very reliable results, provided you give it accurate dimensions. The impedance at the feedpoint is given over a range of frequencies (at the bottom of the SWR chart as you move the cursor along the graph) and currents in the elements are given in chart form.

I only know the program works by dividing the parts of the antenna up into segments, which are really point sources, and these interact with all the other segments in the antenna.
The free version of the program allows up to 20 segments, which is plenty for simple antennas. Using more segments gives a more accurate result.

The author of Eznec is a regular contributor to the antenna newsgroup
REC.AMATEUR.RADIO.ANTENNA
and his expert comments are fun to read.

 

[sophiecentaur]

Apart from the possibility of Supergain arrangements, which have doubtful benefits, overall, why not use a reflector and a suitable tailored feed? You get a pattern which approaches the diffraction limit in performance, has a good front to back ratio and has an established pedigree. I still see huge difficulties in feedin an array which is densly packed yet such little advantage, if any. If the elements are fed in a way that is easy to achieve, how can the pattern be much different from that of a more sparse array? I presume that you are wanting a realistic solution to the problem - even if you may not want to actually build it.

 

[sophiecentaur]

A diagram would still help. I can't really envision what you have in mind in practical terms.

 

[poor mystic]

Diagrams were included with post 31 and 36. I can re-draw anything that is unclear...

 

[sophiecentaur]

I can see that diagram of a 'wide dipole (or half of it), fed with a tapered line but the EZIP attachment doesn't seem to work for me.

Basically, what I can see gives no control over the currents in the various parts of the radiator. They will just settle down as a form of standing wave, as all radiators do and the arrangement will be like a wide dipole. If your feeder is of a practical length, there will be a phase tilt from centre to edges and such a feeder would be a pretty good radiator in itself.

I just don't see where this is going. You want a beam, why not use a yagi or a dish? They work very well and are predictable. Your array is, by definition, a linear array rather than a two dimensional array so it wouldn't have much vertical directivity.

 

[poor mystic]

Like any conceited fool or ordinary man, I hope to break new ground and accordingly worked on a "broadband wave field" concept. I found a suitable effect predicted for a flat aerial (if it could be made to radiate evenly) or a row of closely-spaced aerials.
If I wanted a link there are much better ways to go about it, I agree.

 

[poor mystic]

Thank-you to everybody who contributed to this thread.
I believe I now understand a lot more than I did, though it is quite possible that I am yet on some path of folly.

In formulating a set of ideas intended to help me define a broadband sound-field, I noticed that since superposed waves are found in electromagnetic fields, the same ideas I was investigating for use with sound might also be useful in radio.
The logical conclusion of the design theory I ended up with for a sound-field radiator is a planar speaker all of which moves at once with no flexing. (Such speakers are suddenly on the market.)
Therefore I became interested in doing the same thing with radio waves - i.e. I would try a planar aerial.

At last I see a reason a planar aerial might not work in the same way as a planar loudspeaker.

The reason I see, that a planar aerial might not work as I would wish, is that the signal received by each section of the copper plate is only partly the signal directly from the mast. Each part of the aerial must also re-transmit the received waves, through the copper at a speed different from that of free space. Therefore confusion and phase mismatch result, and the aerial is useless.

Perhaps, if the speed of the signal through the medium (copper plate) were reduced to exactly half the speed of light there might be something interesting happening.
I'll investigate ways of achieving that.

 

[sophiecentaur]

Interesting.
I think the main snag with your 'equivalence' argument is that sound is a longitudinal wave whereas em waves are transverse. There are a lot of major consequences in the design of a radiating arrays. There is not the equivalent to a continuous planar em radiator except for a reflecting antenna - which is fed with waves which have already been launched.
Let's face it, your picture of a wide single radiator, fed with a long tapered feeder achieves no more than illuminating a reflector using a single feed - except that you actually get directivity with a reflector!

I have seen some flat plate speakers and these certainly do work - although the fidelity is not too good because of wavelengths and dimensions. Making the plate the optimum dimensions and feeding it in the right place gets you a long way towards a usable / cheap / small loudspeaker.

Slow wave structures down to c/2 aren't a problem - even a sandwich of plates with polythene dielectric (stripline) will have a speed of about 2c/3. A crinkly arrangement could easily give you the required transit time reduction. But how will you couple this to a two dimensional array - as you could easily do with a loudspeaker array ?

I have just thought of another significant difference between sound and em radiators. The signal can only be distributed 'within' an em antenna at slower than c, whereas it can be distributed as fast as you like within a sound radiating system (e.g. electrically) compared with the speed of the sound. The sound waves can travel across a flat plate faster than the speed of sound in air, too.

One positive aspect of your 'thought project' is that it has given you a lot of food for thought about antennae in general - it's all good stuff!

 

[poor mystic]

"One positive aspect of your 'thought project' is that it has given you a lot of food for thought about antennae in general - it's all good stuff! "

Very definitely so!

Considering the idea of the physical aerial as containing a sea of electrons held in place by the body of +ve charge represented by the atomic nuclei, I imagined the electron sea as being disturbed by impinging radiation.
Let us consider only those parts of the aerial which are at multiples of half wavelengths in free space from the centre of the aerial. Signals arriving at these places cause ripples in the electron gas which radiate at c for the medium and are superposed throughout the aerial.
At the centre of the aerial, looking from the bottom edge we see a resonant path at the frequency of interest running directly across the aerial. A second such resonant path exists on either side to the left and right.
The cycle of radiation which arrived at the outer aerials one cycle ago, arrives in phase with the new cycle if the distance between aerials is one wavelength at the f of interest in the copper, and if c in the aerial is half c in free space there can be no destructive interference from that source...
but suddenly I'm not so sure that this was the problem

 

[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.