Wave Generation from Point Sources: Interference Patterns and Radio Aerials

[poor mystic]

Hi Everybody!
I have been wondering about wave generation from point sources, and interference.
I have noticed that if several point sources are sited in a line much more than one wavelength long, a very directional interference pattern develops. The closer the sources and the longer the line, the better the directionality.
Can radio aerials be set in such an array?

 

[berkeman]

Hi Everybody!
I have been wondering about wave generation from point sources, and interference.
I have noticed that if several point sources are sited in a line much more than one wavelength long, a very directional interference pattern develops. The closer the sources and the longer the line, the better the directionality.
Can radio aerials be set in such an array?

Absolutely. Antenna arrays are commonly used for controlling directionality of the radiation pattern. The element spacings are generally less than a wavelength, though.

http://en.wikipedia.org/wiki/Antenna_array

http://www.google.com/images?hl=en&source=imghp&q="antenna+array"&gbv=2&aq=f&aqi=&aql=&oq=&gs_rfai=

.

 

[waht]

VLA in New Mexico

http://en.wikipedia.org/wiki/Very_Large_Array

has 27 large radio dishes riding on railroad tracks for adjusting and tweaking their separation.

 

[poor mystic]

Hi! and thank you for these replies.

I'd wondered about how you would drive such an array.
Say the aerial is made up of dipoles at some small spacing such as a tenth of a wavelength, how can I find impedance?

 

[vk6kro]

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.

To feed them, you could attach a half wavelength of any feedline to each one and then just put the other ends of the feedlines in parallel. This will give an impedance close to 72 ohms and each dipole would share the available power from a transmitter, in phase.

An excellent antenna simulator is Eznec which is available as a Demo (free) version. (www.eznec.com)
Takes a little bit of getting used to the operation of it, but it is easy to use after that.

 

[sophiecentaur]

Spacing the elements by only 1/10 lambda is not very good 'value'. The beamwidth is inversely related to the total 'aperture' of the array. 'Filling in' with lots of elements in a wide array can give a nice 'smooth' radiation pattern but is an expensive solution.

Input impedance can be very dependent upon the way the elements are driven, for a phased, directional, array. To get an idea of the best solution, it would be necessary to know the wavelength and application as it is a very practical subject, each frequency band having its own quirks and solutions.

 

[poor mystic]

Hi Guys, and thanks for looking at this
I have a set of ideas I'm pretty confident about but want to test anyway. These ideas are about wave superposition.

I noticed that a set of aerials, all in a line, closely spaced and transmitting in the same phase, ought work together to make a very tight beam.
I'd like to test the beam-forming idea, and I'm looking for an affordable experiment.

Radio at 400MHz or so sounds good.

I wondered whether a rectangular planar aerial could be driven from an edge (which might be like very many closely-spaced aerials), and whether a circular plane could be driven from the middle, similarly.

The answers I have received are encouraging! Thank you

 

[sophiecentaur]

Superposition works!
For a uniformly illuminated aperture you will end up with a sinx/x pattern - just what you would get from light through a single slit with no phase tilt across it.

Your idea of feeding a rectangular array will introduce a phase tilt across the aperture so will produce a different pattern. You need to excite every bit of the array in phase and this is not compatible with a simple feed arrangement. The transit times along the feed need to be considered. You would need a weird three dimensional shape of surface to achieve a constant path length from source to feed (a conic section probably). This is basically why a parabolic reflector works so well.
The only problem in realising some of these arrays is splitting the feed, introducing no phase errors and producing a reasonable match to a transmitter. Of course, in a simulation, that needn't worry you.

For good acuity, you can make do with a very sparse array of antennae but the radiation pattern of such an array is full of what can be embarrassing sidelobes. We're talking interferometry here, which is the poor man's version of a huge array.

The basic theory of the pattern of a finite number of point sources approaching the pattern of a uniform aperture is not too hard - you go from a summation to an integral. Loads of antenna theory books will tell you about it. Offhand, I can think of an excellent book by Jordan (published in the 50s, I think).

 

[vk6kro]

One way to achieve this is the cylindrical reflector.

You have a dipole at the focal point of a parabolic reflector. Like a dish, but only in two dimensions.

[PLAIN]http://dl.dropbox.com/u/4222062/cylindrical%20reflector.PNG

The spacing of the dipole from the reflector is such that all the reflected waves are in phase with each other as they leave the reflector.

This gives a very concentrated beam of energy, mostly in the same direction.

Did you get a copy of Eznec?

 

[poor mystic]

Hi and thanks for the interesting replies.
It's easy for me to forget that the wavefront from a parabola is in phase for some reason, and I had forgotten it.

The parabolic trough idea is good, especially since several could be placed along an axis at half-wavelength spacing for super-directivity. I don't think there is any lower limit to the size of the parabolic dish?

Thank you, I did get a copy of EZNEC Demo v. 5.0, which I have started to look at.

 

[vk6kro]

The wave from the dipole to the outer edges of the relector has to leave the reflector at the same time as the wave from the dipole to the inner parts of the reflector has traveled in space and is just passing the plane of the outer edges of the reflector.

That is distances A + B must equal distance C in the diagram below to keep the waves in phase across the transmitted wave.

[PLAIN]http://dl.dropbox.com/u/4222062/Parabolic%20reflector.PNG

Mark, continue on email if you want to get started on Eznec.
It doesn't cope with parabolic reflectors, though, especially the Demo version which is limited to 20 segments.

 

[sophiecentaur]

The parabolic trough idea is good, especially since several could be placed along an axis at half-wavelength spacing for super-directivity. I don't think there is any lower limit to the size of the parabolic dish?

The beamwidth is about λ/width of aperture so there is no actual "limit" - it just depends what response you want

 

[poor mystic]

Though I may well be wrong, I had concluded that, within a broad range of designs, any parabolic dish is equivalent to any other.

I got this idea from noticing that a parabolic dish is not really the ideal solution to the problem of focusing waves by reflection. The ideal solution is an ellipse, if I may use this shorthand for 'the figure obtained by rotating an ellipse about its long axis'.
.
An ellipse is made by drawing an inelastic cord tight between 2 points and drawing a curve. The points are the foci, and the tangent at every point of the curve is such as to reflect an image of each focus onto the other.
The distance between the foci, including the reflected part of the hop, is equal no matter which part of the ellipse the reflection is made from.

In the case of a manufactured parabolic dish, the calculation for the ellipse has been simplified and the curve is a little different, but in that it works at all it is an approximation to the ellipse, and probably quite a good one, designed to be less than a mm or so different from the ellipse.

 

[sophiecentaur]

If you want a parallel beam, a paraboloid is the shape you want (no question about it). If you want to focus from one point onto another point, an ellipse is the right shape. Normally, we beam radio waves many wavelengths away (=∞) so you use a paraboloid - like the above sketch - and you put the drive at the focus. The more you spend on size, the narrower beam you get.
All parabolas are, essentially, the same 'shape' - unlike ellipses and hyberbolas, which have a variable parameter, other than just scale.

 

[Pumblechook]

Splitters are generally made of 1/4 wavelengths of coax cable. A 50 Ohm source can be fed to two 50 Ohm aerials. A 1/4 Wave of 75 Ohm cable with transform the impedance to roughly 100 Ohm.. Two in parallel brings you back to 50 Ohm. 4 x 50 Ohm aerials are combined using 1/4 Wave of 50 Ohm cable. Paralell two 50 Ohms gives you 25 Ohms. A 1/4 Wave 50 ohm cable will transform this to 100 Ohms.. Parallel to get beck to 50 Ohm.


Combining/Splitter two aerails. The resistor is not required if both aerials are always connected.



http://www.rfengineer.net/wp-content/uploads/2009/02/clip-image0023.gif



http://www.radio-electronics.com/in...itter/wilkinson-splitter-combiner-divider.php

 

[poor mystic]

If you want a parallel beam, a paraboloid is the shape you want (no question about it). If you want to focus from one point onto another point, an ellipse is the right shape. Normally, we beam radio waves many wavelengths away (=∞) so you use a paraboloid - like the above sketch - and you put the drive at the focus. The more you spend on size, the narrower beam you get.
All parabolas are, essentially, the same 'shape' - unlike ellipses and hyberbolas, which have a variable parameter, other than just scale.

Thanks very much for that insight.
Now I see a little more clearly that S:N is actually a function of the area of the collecting dish or trough.
Is there any advantage in splitting the signal between several small parabolic troughs rather than 1 large trough?

 

[sophiecentaur]

Cheaper, because you are basically paying for area. As I said earlier, you can get good acuity this way (basis of interferometers) but the SNR and purity of pattern will suffer.

 

[sophiecentaur]

You need to bear in mind that it's the two dimensional aperture of the system that governs the received signal power (the vertical and horizontal radiation patterns). Is your beamwidth dictated by directivity (i.e. eliminating interference) or signal gathering power? To get an optimum solution you really need to specify a lot of things.

I haven't come across multiple paraboloids, used side by side. Usually the simplest arrangement will be a single dish as big as you can afford or fit on the support. The problem with big dishes can be windage and many big arrays (again it depends on the frequency used) use stacks of Yagi arrays. Even then, the mutual impedance between elements can result in strange frequency responses and radiation patterns and spacing can be critical. I do remember some simple 'trough' antennae, used for low power UHF TV transmission where a good front-to-back performance was needed. They weren't paraboloids - just 'bathtub' shaped troughs, made of aluminium sheet, pop rivetted together. Complicated home-made arrays are not really to be recommended as the elements can end up 'talking to each other' and you wouldn't know it if you couldn't actually measure the radiation pattern. It's a bit (a lot, actually) like loudspeaker design. Many home made speakers can sound impressive but they may have awful phase / frequency responses which may show up on critical programme material. Simple 'squeaking' in a living room doesn't tell the whole story and no more would waving your antenna about, whilst observing the received signal level. Best to go for a simple system which is less likely to behave oddly. There are a lot of books and articles that discuss antenna arrays but not to much information of how to make the damned things work properly. Even trying to make a good simple bottom-loaded whip antenna ends up with 'suck it and see' with pliers and a VSWR meter (unless you use an already published design.

 

[poor mystic]

You need to bear in mind that it's the two dimensional aperture of the system that governs the received signal power (the vertical and horizontal radiation patterns). Is your beamwidth dictated by directivity (i.e. eliminating interference) or signal gathering power? To get an optimum solution you really need to specify a lot of things.

I think I've been given some very good, practical advice, which I think I would follow very closely if a good, practical system were my goal. However the particular thing I have been playing with, and have done some experiments with in audio, is an array.

It looks to me as though an linear array at half-wavelengths, with all signals summed in correct phase, both gathers by constructive interference and rejects by destructive interference at a S:N determined by the number of aerials in the line. (The arithmetic suggests that the wavelength is immaterial for long arrays, except that the aerials are still tuned devices.)
I'd like to try making up a link and measuring its performance, just to see how good a link I can make with not much technology.

.

 

[berkeman]

I think I've been given some very good, practical advice, which I think I would follow very closely if a good, practical system were my goal. However the particular thing I have been playing with, and have done some experiments with in audio, is an array.

It looks to me as though an linear array at half-wavelengths, with all signals summed in correct phase, both gathers by constructive interference and rejects by destructive interference at a S:N determined by the number of aerials in the line. (The arithmetic suggests that the wavelength is immaterial for long arrays, except that the aerials are still tuned devices.)
I'd like to try making up a link and measuring its performance, just to see how good a link I can make with not much technology.

.

You are pursuing some good math there. I'd suggest calculating the efficiency of multiple dipoles in a linear array, versus a single parabolic receive antenna structure, with the size of the parabola approximately equal to the length of the array. Would be a pretty interesting result!

 

[sophiecentaur]

One good idea is to cast your eyes upwards whenever you go past a comms mast. I have only seen large linear arrays of dipoles used for 'main station' broadcast transmitting antennae (VHF and UHF) and the arrays have been vertically stacked to get a narrow vertical beam - to get the kW where you want them. You mostly get dishes (or cheaper reflectors) and Yagis for anything other than very up-marker systems.

There's little wonder that the Yagi array (and two or three stacked) is such a popular solution because it is cheap to engineer, low windage. But the Yagi is no 'fun' to design and the calculations for the parasitics involve 'trusting' in some harder theory. I did design a very impressive looking (though I say it myself) 2X3 element transmitting array using monopoles rather than dipoles, operated at mf. It was pretty massive (you can still see it on Google Earth aamof) and it laid down the predicted field strength at the target distance, no appreciable interference where it wasn't wanted and also matched to the feeder as expected.
A point that hasn't been made yet, of course, is that a linear array with no reflector will have as big a backwards beam as its forward beam. This could be an embarrassment and an 'end-fire' arrangement is one way of dealing with this.

 

[poor mystic]

One good idea is to cast your eyes upwards whenever you go past a comms mast. I have only seen large linear arrays of dipoles used for 'main station' broadcast transmitting antennae (VHF and UHF) and the arrays have been vertically stacked to get a narrow vertical beam - to get the kW where you want them...
A point that hasn't been made yet, of course, is that a linear array with no reflector will have as big a backwards beam as its forward beam. This could be an embarrassment and an 'end-fire' arrangement is one way of dealing with this.

Some time into this "interference canceling" project, which I undertook on the excuse to myself that I might find a way to minimise the harmful effects of all-night dance "raves", I remembered having seen an aerial stack like the one you describe.
The aerial stack I saw was not quite the same thing I'd was working on, I decided, because if it were, the radiation would be normal to the flat planes of the rectangular array.

I also excused my continued research on the grounds that the explanations I found offered for arrays were couched in difficult terms I was not used to dealing with, and I wanted a "Grandmother" level explanation without compromise on accuracy.
Such understandings are valuable to us I thought, they can enter into the demotic and become well-known unlike the double-integrated frequency transforms beloved of the professional engineers.

I sometimes teach kids maths, and the confidence that this kind of work gives me rubs off and helps my pupils develop their own confident interpretation of numerical results in the real world.
Useful analysis of new phenomena is easier for those who have broken ground in analysis already, this is as much true for me as it is for my pupils, who benefit from appreciating that I do understand and am not merely reciting from a book.
Some of them go on to find new things out for themselves!

 

[poor mystic]

In the matter of aerial 'efficiency' an early result from Wikipedia's formula is that a dish of 1 wavelength aperture has an insertion loss and not a gain. I'd be better off with a ground plane at a half wavelength behind the array.

 

[berkeman]

In the matter of aerial 'efficiency' an early result from Wikipedia's formula is that a dish of 1 wavelength aperture has an insertion loss and not a gain. I'd be better off with a ground plane at a half wavelength behind the array.

That's a mighty small dish. The suggestion in this thread was not a dish, it was a reflective trough (sp?) with a dipole at the focus. That's different from a microwave dish...

 

[berkeman]

That's a mighty small dish. The suggestion in this thread was not a dish, it was a reflective trough (sp?) with a dipole at the focus. That's different from a microwave dish...

Well, maybe not fundamentally different. But yes, you would want the gathering area of the reflector to be several wavelengths if possible for best gain.

 

[sophiecentaur]

In the matter of aerial 'efficiency' an early result from Wikipedia's formula is that a dish of 1 wavelength aperture has an insertion loss and not a gain. I'd be better off with a ground plane at a half wavelength behind the array.

It wouldn't be surprising that an 'infinite' ground plane would do better than a tiny dish, would it? You need an aperture in the order of λ/(required beam width). The dish is, more of a diffractor than a reflector for small sizes - it's not geometric optics under these conditions.

@poor mystic
All of this simple antenna array theory starts with the calculations for the 'two slit' experiment. The first minimum occurs in a direction where the path from one half of the array is a half wavelength differs from the path from the other half by a half wavelength. It's 'just' a matter of adding the contributions of each element vectorially, taking into account the different distances when off axis.
The Fourier relationship between spatial distribution and radiation pattern is nothing to be overwhelmed about; it's only a Mathematician's show-off trick to get an answer (well - errr.. there is a useful fundamental principle involved too). But you can calculate the radiation pattern of an array of a few elements easily with a simple spreadsheet. Simply calculate the geometry and path length differences for signals from each element - then add them all (phase-wise) together. Do it over a range of angles and you can plot a radiation pattern without going near an integral, transformation or convolution!
Just add the cos(θ) for each element, where the θ = path difference / λ (in radians, or your angles may come out wrong!)

Once the spreadsheet works, you can change numbers and spacings (and even weight the elements differently) by just 'turning the handle. It borders on the 'good fun' region.

 

[poor mystic]

Sorry, guys
Other matters have intruded and I haven't been able give this the time it deserves, as a consequence.
I have, months ago, done as suggested and produced a series of polar plots, and full-field plots, whose characteristics include better than 20 dB rejection at 5 degrees off-axis and no sidelobes.

What I most strongly suspect is that this theory must already have been well-investigated for use in radio-telescopy, since if I am right a stack of wide-band antennas could be employed in a 2-D grid to that effect. Mechanical phase adjustments or mechanical displacement of the array could steer it.

Another consequence of the idea is that if an increasing phase lag were to progressively delay the aerials across a grid, a swept frequency would provide a geometric scan usable in radar. A sweep in the perpendicular might with ingenuity be possible on the same array.

I'll get back to the forum in a week or so with newly calculated plots pertaining to this thread.

 

[berkeman]

Sorry, guys
Other matters have intruded and I haven't been able give this the time it deserves, as a consequence.
I have, months ago, done as suggested and produced a series of polar plots, and full-field plots, whose characteristics include better than 20 dB rejection at 5 degrees off-axis and no sidelobes.

What I most strongly suspect is that this theory must already have been well-investigated for use in radio-telescopy, since if I am right a stack of wide-band antennas could be employed in a 2-D grid to that effect. Mechanical phase adjustments or mechanical displacement of the array could steer it.

Another consequence of the idea is that if an increasing phase lag were to progressively delay the aerials across a grid, a swept frequency would provide a geometric scan usable in radar. A sweep in the perpendicular might with ingenuity be possible on the same array.

I'll get back to the forum in a week or so with newly calculated plots pertaining to this thread.

Absolutely a well-developed field. Search on phased array radar, and you'll see lots of fun geometries and techniques. Heck, we even had a phased array HAM antenna setup a year ago at Field Day, with 4 antennas with variable phase delay feeds to focus the pattern in different directions. I think it was a 20m array, but I could be wrong about that. Didn't matter much anyway, because the skip sucked last year. Much better skip this year though!

 

[poor mystic]

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?

 

[vk6kro]

Maybe you could draw what you have in mind.

You can split a flat sheet of metal into two halves and feed the halves with RF, but it will act pretty much like a dipole.
Flat planes of metal generally form omnidirectional or donut shaped radiation patterns. It is a bit like getting magnification from a plane mirror. You really can't do it.

An example is the slot antenna.
Believe it or not, a slot cut into the surface of a flat piece of metal can radiate. This is done at microwave frequencies ie 2 GHz up.

See this site and the links in it:
http://www.antenna-theory.com/antennas/main.php