Greetings, dear friends. In touch Timur Garanin.
Today's video, I decided once again to devote to fractal antennas.
Probably, everyone saw similar images of cross-shaped fractal antennas,
but in few places you will find satisfactory explanations of how they work, how their ranges are calculated and in general what type of antenna it is in terms of application.
Today I will answer all these questions and we ourselves will create a similar antenna and calculate its frequency properties.
But before that, consider the simple conversion of a linear antenna web to a fractal.
The simplest example of a line transformation is the Koch triangle.
The construction algorithm is as follows:
- we break the line into three equal parts
- instead of the middle part, we insert two lines, the length of each of which is exactly the length of the cut section.
This one iteration ends.
At the next iteration, we split already new segments into three parts and replace their middle part with two lines.
It is obvious that with each iteration the total length of the line increases
And it grows 4/3 times for each iteration.
This just means that the use of a fractal allows you to create an antenna with the same length of the canvas, but smaller.
Plus, due to the appearance of segments of shorter lengths in the canvas, the range of received frequencies expands upward.
Please note that you can position two lines in place of the cut-out line at different angles
And the more this angle tends to 90 degrees, the more effectively space is latched.
Now we apply this knowledge in practice and make a fractal dipole.
To do this, from the very beginning you need to know the lower frequency of the received range, and correlate each quarter-wave segment with it.
And after that, we just start to bend the wire to the desired degree of fractal.
The use of a fractal will allow us to reduce the dimensions of the antenna, and most importantly, expand the range of received frequencies up.
The Koch Triangle is far from the only popular fractal.
The use of the Koch square is widespread
The fractal is constructed as follows:
- break the line into three segments
- instead of the middle segment, insert three segments of equal length at an angle of 90%.
We see that the total line length has grown 5/3 times.
At the next iteration, we divide the already newly formed segments into three, and instead of the middle we insert three segments.
Thus, each iteration increases the length of the curve by 5/3 times with the same dimensions.
Or it reduces the dimensions as many times with the same length of the canvas.
Well, now, armed with this knowledge, let's start creating a cross-shaped fractal antenna.
This antenna is essentially a loop antenna, to which the Koch square construction algorithm has been applied several times.
The iterations of the fractal construction you see in the figure.
Note that in a real antenna, the conductors must be isolated from each other so as not to cause a short circuit in any segment.
The lower frequency of the range is calculated by the total length of the entire curve of the canvas
In order to determine it, we must measure the size of the finished antenna and multiply by 5/3 as many times as the number of iterations of the fractal in this particular antenna is applied.
The upper frequency of the range with each iteration increases several times, it is already much more difficult to determine it and it depends on the specific fractal.
So, now we know that the most famous cross-shaped antenna is a loop or loop antenna, to which the algorithm for constructing the Koch square is applied.
But this is far from the only type of cross-shaped antennas
You can also find an antenna formed by the use of the Sierpinski square.
This is also a loop antenna, but due to the complexity of the fractal, it is usually found only on printed circuit boards, but not in the form of wire antennas.
Sierpinski curves, Koch curves, Peano, Hilbert curves and many others can be used to convert the straight line of the antenna web into a fractal.
But apart from fractals that transform lines, there are fractals that transform planes and volumes.
One of these fractals is the Visekka cross, it is sometimes called the Minkowski cross, and even the Koch cross, although Koch has no direct relationship to it.
This fractal is formed by alternately removing the middle parts from the sides of the square, or from the corners of the square.
As a result, cross-shaped figures are formed.
We will get a more rational use of space in cross-shaped antennas formed by the area under the curve of the Koch triangle with a construction angle tending to 90 degrees.
Such antennas, of course, will not work as frame antennas - they represent one of the forms of tree-shaped antennas.
The current induced by an external electric field will be summed up in all branches of the tree, and at the central point where the central core of the cable should be connected, the current will be maximum.
As already mentioned, one of the main advantages of fractal antennas is their small size.
Fractal antennas may well be attributed to EMA (electrically small antennas), i.e. their dimensions can be significantly less than the wavelength.
However, with regard to specifically cross-shaped antennas, it is obvious that this type of antennas, although smaller than their non-fractal counterparts, however, uses space not quite efficiently.
If we want to use space more efficiently, we should use other fractals.
The Hilbert, Peano curves, and in some cases even the usual meander, can reduce the size of the antenna no worse than the Koch square, and it’s more efficient to use space.
Now let's summarize what we learned today:
1. Fractal antennas are created by applying fractal construction algorithms to the antenna sheet
2. The lower frequency of the range of the fractal antenna is determined by the length of the conductor, the upper frequency increases with each iteration of the fractal
3. Cross shaped antennas most often are loop antennas that have passed several iterations of the Koch square
4. There are many fractals that use space much more efficiently than Koch square.
That's all for today, dear friends
As always, share this video, if you find it useful, like, and most importantly, write in the comments what questions and topics you would be interested in.
Good luck!