home › Navigators › Wire technologies for manufacturing fractal antennas. How to make an antenna for a TV with your own hands from aluminum wire or cable: a simple design for receiving a TV signal. The Minkowski fractal is constructed similarly to the Koch curve and has the same properties

Wire technologies for manufacturing fractal antennas. How to make an antenna for a TV with your own hands from aluminum wire or cable: a simple design for receiving a TV signal. The Minkowski fractal is constructed similarly to the Koch curve and has the same properties

The first thing I would like to write about is a little introduction to the history, theory and use of fractal antennas. Fractal antennas were recently discovered. They were first invented by Nathan Cohen in 1988, then he published his research on how to make a TV antenna from wire and patented it in 1995.

The fractal antenna has several unique characteristics, as written on Wikipedia:

“A fractal antenna is an antenna that uses a fractal, self-repeating design to maximize the length or increase the perimeter (on internal areas or external structure) of a material that can receive or transmit electromagnetic signals within a given total surface area or volume.”

What exactly does this mean? Well, you need to know what a fractal is. Also from Wikipedia:

“A fractal is typically a rough or fragmented geometric shape that can be divided into parts, each part being a smaller copy of the whole—a property called self-similarity.”

Thus, a fractal is a geometric shape that repeats itself over and over again, regardless of the size of the individual parts.

Fractal antennas have been found to be approximately 20% more efficient than conventional antennas. This can be useful especially if you want your TV antenna to receive digital or high definition video, increase cellular range, Wi-Fi range, FM or AM radio reception, etc.

Most cell phones already have fractal antennas. You may have noticed this because cell phones no longer have antennas on the outside. This is because they have fractal antennas inside them etched into the circuit board, allowing them to receive better signal and pick up more frequencies like Bluetooth, Cellular and Wi-Fi from a single antenna.

Wikipedia:

“The fractal antenna's response is noticeably different from traditional antenna designs in that it is capable of operating with good performance at different frequencies simultaneously. The frequency of standard antennas must be cut to be able to receive only that frequency. Therefore, a fractal antenna, unlike a conventional antenna, is an excellent design for wideband and multi-band applications.”

The trick is to design your fractal antenna to resonate at the specific center frequency you want. This means that the antenna will look different depending on what you want to achieve. To do this you need to use mathematics (or an online calculator).

In my example I'm going to do simple antenna, but you can make it more complex. The more complex the better. I'll use a coil of 18-strand solid core wire to make the antenna, but you can customize your own circuit boards to suit your aesthetic, make it smaller or more complex with greater resolution and resonance.

I'm going to make a TV antenna to receive digital TV or TV high resolution. These frequencies are easier to work with and range in length from about 15 cm to 150 cm for half wavelength. For simplicity and low cost of parts, I'm going to place it on a common dipole antenna, it will catch waves in the 136-174 MHz range (VHF).

To receive UHF waves (400-512 MHz), you can add a director or reflector, but this will make the reception more dependent on the direction of the antenna. VHF is also directional, but instead of pointing directly at the TV station in a UHF installation, you will need to mount the VHF ears perpendicular to the TV station. This will require a little more effort. I want to make the design as simple as possible, because this is already quite a complex thing.

Main components:

Mounting surface, such as a plastic housing (20 cm x 15 cm x 8 cm)
6 screws. I used steel sheet metal screws
Transformer with resistance from 300 Ohm to 75 Ohm.
18 AWG (0.8 mm) Mounting Wire
RG-6 coaxial cable with terminators (and with a rubber sheath if installation will be outdoors)
Aluminum when using a reflector. There was one in the attachment above.
Fine marker
Two pairs of small pliers
The ruler is no shorter than 20 cm.
Conveyor for angle measurement
Two drill bits, one slightly smaller in diameter than your screws
Small wire cutter
Screwdriver or screwdriver

Note: The bottom of the aluminum wire antenna is on the right side of the picture where the transformer is sticking out.

Step 1: Adding a Reflector

Assemble the housing with the reflector under the plastic cover

Step 2: Drilling Holes and Installing Mounting Points

Drill small outlet holes on the opposite side of the reflector at these positions and place a conductive screw.

Step 3: Measure, Cut and Strip Wires

Cut four 20cm pieces of wire and place them on the body.

Step 4: Measuring and Marking Wires

Using a marker, mark every 2.5 cm on the wire (there will be bends at these points)

Step 5: Creating Fractals

This step must be repeated for each piece of wire. Each bend should be exactly 60 degrees, since we will be making equilateral triangles for the fractal. I used two pairs of pliers and a protractor. Each bend is made on a mark. Before making folds, visualize the direction of each of them. Please use the attached diagram for this.

Step 6: Creating Dipoles

Cut two more pieces of wire that are at least 6 inches long. Wrap these wires around the top and bottom screws along the long side, and then wrap them around the center screws. Then trim off the excess length.

Step 7: Installation of dipoles and installation of transformer

Secure each of the fractals onto the corner screws.

Attach a transformer of the appropriate impedance to the two center screws and tighten them.

Assembly complete! Check it out and enjoy!

Step 8: More Iterations/Experiments

I made some new elements using a paper template from GIMP. I used a small solid telephone wire. It was small, strong and pliable enough to bend into the complex shapes required for the center frequency (554 MHz). This is the average digital signal UHF for channels terrestrial television in my area.

Photo attached. It may be difficult to see the copper wires in low light against the cardboard and tape on top, but you get the idea.

At this size, the elements are quite fragile, so they need to be handled carefully.

I have also added a template in png format. To print the size you want, you'll need to open it in a photo editor like GIMP. The template is not perfect because I made it by hand using a mouse, but it is comfortable enough for human hands.

The wire fractal antennas studied in this thesis were made by bending the wire according to a printed paper template. Since the wire was bent manually using tweezers, the accuracy of making the antenna “bends” was about 0.5 mm. Therefore, the simplest geometric fractal forms were taken for research: the Koch curve and the Minkowski “bipolar jump”.

It is known that fractals make it possible to reduce the size of antennas, while the dimensions of a fractal antenna are compared with the dimensions of a symmetrical half-wave linear dipole. In further research in the thesis, wire fractal antennas will be compared with a linear dipole with /4-arms equal to 78 mm with a resonant frequency of 900 MHz.

Wire fractal antennas based on the Koch curve

The work provides formulas for calculating fractal antennas based on the Koch curve (Figure 24).

A) n= 0 b) n= 1 c) n = 2

Figure 24 - Koch curve of various iterations n

Dimension D the generalized Koch fractal is calculated by the formula:

If we substitute the standard bending angle of the Koch curve = 60 into formula (35), we obtain D = 1,262.

Dependence of the first resonant frequency of the Koch dipole f K from the fractal dimension D, iteration numbers n and resonant frequency of a straight dipole f D of the same height as the Koch broken line (at the extreme points) is determined by the formula:

For Figure 24, b at n= 1 and D= 1.262 from formula (36) we obtain:

f K= f D 0.816, f K = 900 MHz 0.816 = 734 MHz. (37)

For Figure 24, c with n = 2 and D = 1.262, from formula (36) we obtain:

f K= f D 0.696, f K = 900 MHz 0.696 = 626 MHz. (38)

Formulas (37) and (38) allow us to solve the inverse problem - if we want fractal antennas to operate at a frequency f K = 900 MHz, then straight dipoles must operate at the following frequencies:

for n = 1 f D = f K / 0.816 = 900 MHz / 0.816 = 1102 MHz, (39)

for n = 2 f D = f K / 0.696 = 900 MHz / 0.696 = 1293 MHz. (40)

Using the graph in Figure 22, we determine the lengths of the /4-arms of a straight dipole. They will be equal to 63.5 mm (for 1102 MHz) and 55 mm (for 1293 MHz).

Thus, 4 fractal antennas were made based on the Koch curve: two with 4-arm dimensions of 78 mm, and two with smaller dimensions. Figures 25-28 show images of the RK2-47 screen, from which resonant frequencies can be experimentally determined.

Table 2 summarizes the calculated and experimental data, from which it is clear that the theoretical frequencies f T differ from experimental ones f E no more than 4-9%, and this is a quite good result.

Figure 25 - Screen RK2-47 when measuring an antenna with a Koch curve of iteration n = 1 with /4-arms equal to 78 mm. Resonant frequency 767 MHz

Figure 26 - Screen RK2-47 when measuring an antenna with a Koch curve of iteration n = 1 with /4-arms equal to 63.5 mm. Resonant frequency 945 MHz

Figure 27 - Screen RK2-47 when measuring an antenna with a Koch curve of iteration n = 2 with /4-arms equal to 78 mm. Resonant frequency 658 MHz

Figure 28 - Screen RK2-47 when measuring an antenna with a Koch curve of iteration n = 2 with /4-arms equal to 55 mm. Resonant frequency 980 MHz

Table 2 - Comparison of calculated (theoretical fT) and experimental fE resonant frequencies of fractal antennas based on the Koch curve

Wire fractal antennas based on a “bipolar jump”. Directional pattern

Fractal lines of the “bipolar jump” type are described in the work, however, formulas for calculating the resonant frequency depending on the size of the antenna are not given in the work. Therefore, it was decided to determine the resonant frequencies experimentally. For simple fractal lines of the 1st iteration (Figure 29, b), 4 antennas were made - with a length of /4-arm equal to 78 mm, with half the length and two intermediate lengths. For the difficult-to-manufacture fractal lines of the 2nd iteration (Figure 29, c), 2 antennas with 4-arm lengths of 78 and 39 mm were manufactured.

Figure 30 shows all the manufactured fractal antennas. Figure 31 shows the appearance of the experimental setup with the 2nd iteration “bipolar jump” fractal antenna. Figures 32-37 show the experimental determination of resonant frequencies.

A) n= 0 b) n= 1 c) n = 2

Figure 29 - Minkowski curve “bipolar jump” of various iterations n

Figure 30 - Appearance all manufactured wire fractal antennas (wire diameters 1 and 0.7 mm)

Figure 31 - Experimental setup: panoramic VSWR and attenuation meter RK2-47 with a fractal antenna of the “bipolar jump” type, 2nd iteration

Figure 32 - Screen RK2-47 when measuring a “bipolar jump” antenna of iteration n = 1 with /4-arms equal to 78 mm.

Resonant frequency 553 MHz

Figure 33 - Screen RK2-47 when measuring a “bipolar jump” antenna of iteration n = 1 with /4-arms equal to 58.5 mm.

Resonant frequency 722 MHz

Figure 34 - Screen RK2-47 when measuring a “bipolar jump” antenna of iteration n = 1 with /4-arms equal to 48 mm. Resonant frequency 1012 MHz

Figure 35 - Screen RK2-47 when measuring a “bipolar jump” antenna of iteration n = 1 with /4-arms equal to 39 mm. Resonant frequency 1200 MHz

Figure 36 - Screen RK2-47 when measuring a “bipolar jump” antenna of iteration n = 2 with /4-arms equal to 78 mm.

The first resonant frequency is 445 MHz, the second is 1143 MHz

Figure 37 - Screen RK2-47 when measuring a “bipolar jump” antenna of iteration n = 2 with /4-arms equal to 39 mm.

Resonant frequency 954 MHz

As experimental studies have shown, if we take a symmetrical half-wave linear dipole and a fractal antenna of the same lengths (Figure 38), then fractal antennas of the “bipolar jump” type will operate at a lower frequency (by 50 and 61%), and fractal antennas in the form of a curve Koch operate at frequencies 73 and 85% lower than those of a linear dipole. Therefore, indeed, fractal antennas can be made in smaller sizes. Figure 39 shows the dimensions of fractal antennas for the same resonant frequencies (900-1000 MHz) in comparison with the arm of a conventional half-wave dipole.

Figure 38 - “Conventional” and fractal antennas of the same length

Figure 39 - Antenna sizes for the same resonant frequencies

5. Measuring radiation patterns of fractal antennas

Antenna radiation patterns are usually measured in “anechoic” chambers, the walls of which absorb the radiation incident on them. In this thesis, measurements were carried out in a regular laboratory of the Faculty of Physics and Technology, and the reflected signal from the metal cases of instruments and iron stands introduced some error into the measurements.

The own generator of the panoramic VSWR and attenuation meter RK2-47 was used as a source of the microwave signal. A level meter was used as a radiation receiver from the fractal antenna. electromagnetic field ATT-2592, allowing measurements in the frequency range from 50 MHz to 3.5 GHz.

Preliminary measurements showed that the radiation pattern of a symmetrical half-wave linear dipole significantly distorts the radiation from the outside of the coaxial cable, which was directly (without matching devices) connected to the dipole. One of the ways to suppress transmission line radiation is to use a monopole instead of a dipole together with four mutually perpendicular /4 “counterweights” that play the role of “ground” (Figure 40).

Figure 40 - /4 monopole and fractal antenna with “counterweights”

Figures 41 - 45 show the experimentally measured radiation patterns of the antennas under study with “counterweights” (the resonant frequency of the radiation practically does not change when moving from a dipole to a monopole). Measurements of the microwave radiation power flux density in microwatts per square meter were carried out in the horizontal and vertical planes at intervals of 10. Measurements were carried out in the “far” zone of the antenna at a distance of 2.

The first antenna to be studied was a rectilinear /4-vibrator. From the radiation pattern of this antenna it is clear (Figure 41) that it differs from the theoretical one. This is due to measurement errors.

Measurement errors for all antennas under study can be as follows:

Reflection of radiation from metal objects inside the laboratory;

Lack of strict mutual perpendicularity between the antenna and counterweights;

Not complete suppression of radiation from the outer shell of the coaxial cable;

Inaccurate reading of angular values;

Inaccurate “targeting” of the ATT-2592 meter at the antenna;

Interference from cell phones.

For those who don’t know what it is and where it is used, I can say that watch video films about fractals. And such antennas are used everywhere nowadays, for example, in every cell phone.

So, at the end of 2013, my father-in-law and mother-in-law came to visit us, and then the mother-in-law, on the eve of the New Year holiday, asked us for an antenna for her small TV. My father-in-law watches TV through a satellite dish and usually does something of his own, but my mother-in-law wanted to watch New Year’s programs quietly without bothering my father-in-law.

Ok, we gave her our loop antenna (330x330 mm square), through which my wife sometimes watched TV.

And then the time for the opening of the Winter Olympics in Sochi was approaching and my wife said: Make an antenna.

It’s no problem for me to make another antenna, as long as it has a purpose and meaning. He promised to do it. And now the time has come... but I thought that it was somehow boring to sculpt another loop antenna, after all, the 21st century is in the yard and then I remembered that the most progressive in the construction of antennas are EH-antennas, HZ-antennas and fractal- antennas. Having figured out what was most suitable for my business, I settled on a fractal antenna. Fortunately, I’ve seen all sorts of films about fractals and pulled all sorts of photos from the Internet a long time ago. So I wanted to translate the idea into material reality.

Photos are one thing, a specific implementation of a certain device is another. I didn’t bother for long and decided to build an antenna based on a rectangular fractal.

I took out copper wire with a diameter of about 1 mm, took pliers and began to make things... the first project was full-scale using many fractals. Out of habit, I did it for a long time, on cold winter evenings, I finally did it, glued the entire fractal surface to the fiberboard using liquid polyethylene, soldered the cable directly, about 1 m in length, began to try... Oops! And this antenna received TV channels much more clearly than a frame antenna... I was pleased with this result, which means it was not in vain that I struggled and rubbed calluses while bending the wire into a fractal shape.

About a week passed and I got the idea that the size of the new antenna is almost the same as a frame antenna, there is no particular benefit, unless you take into account a slight improvement in reception. And so I decided to mount a new fractal antenna, using fewer fractals, and therefore smaller in size.

Fractal antenna. First option

On Saturday, 02/08/2014, I took out a small piece of copper wire that was left over from the first fractal antenna and quite quickly, about half an hour, mounted a new antenna...

Fractal antenna. Second option

Then I soldered the cable from the first one and it turned out to be a complete device. Fractal antenna. Second option with cable

I started checking the performance... Wow, damn it! Yes, this one works even better and receives as many as 10 channels in color, which previously could not be achieved using a loop antenna. The gain is significant! If you also pay attention to the fact that my reception conditions are completely unimportant: the second floor, our house is completely blocked from the television center by high-rise buildings, there is no direct visibility, then the gain is impressive both in reception and in size.

On the Internet there are fractal antennas made by etching on foil fiberglass... I think it makes no difference what to do, and the dimensions should not be strictly observed for a television antenna, within the limits of working on the knee.

The world is not without good people:-)
Valery UR3CAH: "Good afternoon, Egor. I think this article (namely the section "Fractal antennas: less is more") corresponds to the theme of your site and will be of interest to you:) 73!"
Yes, of course it’s interesting. We have already touched on this topic to some extent when discussing the geometry of hexabims. There, too, there was a dilemma with “packing” the electrical length into geometric dimensions :-). So thank you, Valery, very much for sending the material.
Fractal antennas: less is more
Over the past half century, life has rapidly begun to change. Most of us accept achievements modern technologies for granted. You get used to everything that makes life more comfortable very quickly. Rarely does anyone ask the questions “Where did this come from?” and “How does it work?” A microwave heats up breakfast - great, a smartphone gives you the opportunity to talk to another person - great. This seems like an obvious possibility to us.
But life could have been completely different if a person had not sought an explanation for the events taking place. Take, for example, Cell Phones. Remember the retractable antennas on the first models? They interfered, increased the size of the device, and in the end, often broke. We believe they have sunk into oblivion forever, and part of the reason for this is... fractals.
Fractal patterns fascinate with their patterns. They definitely resemble images of cosmic objects - nebulae, galaxy clusters, and so on. It is therefore quite natural that when Mandelbrot voiced his theory of fractals, his research aroused increased interest among those who studied astronomy. One of these amateurs named Nathan Cohen, after attending a lecture by Benoit Mandelbrot in Budapest, got the idea practical application acquired knowledge. True, he did this intuitively, and chance played an important role in his discovery. As a radio amateur, Nathan sought to create an antenna with the highest possible sensitivity.
The only way to improve the parameters of the antenna, which was known at that time, consisted of increasing its geometric dimensions. However, the owner of the property in downtown Boston that Nathan rented was categorically against installing large devices on the roof. Then Nathan began experimenting with different antenna shapes, trying to get the maximum result with the minimum size. Inspired by the idea of fractal forms, Cohen, as they say, randomly made one of the most famous fractals from wire - the “Koch snowflake”. Swedish mathematician Helge von Koch came up with this curve back in 1904. It is obtained by dividing a segment into three parts and replacing the middle segment with an equilateral triangle without a side coinciding with this segment. The definition is a little difficult to understand, but in the figure everything is clear and simple.
There are also other variations of the Koch curve, but the approximate shape of the curve remains similar.

When Nathan connected the antenna to the radio receiver, he was very surprised - the sensitivity increased dramatically. After a series of experiments, the future professor at Boston University realized that an antenna made according to a fractal pattern has high efficiency and covers a much wider frequency range compared to classical solutions. In addition, the shape of the antenna in the form of a fractal curve makes it possible to significantly reduce the geometric dimensions. Nathan Cohen even came up with a theorem proving that to create broadband antenna it is enough to give it the shape of a self-similar fractal curve.

The author patented his discovery and founded a company for the development and design of fractal antennas, Fractal Antenna Systems, rightly believing that in the future, thanks to his discovery, cell phones will be able to get rid of bulky antennas and become more compact. In principle, this is what happened. True, to this day Nathan is engaged in a legal battle with large corporations, who illegally use his discovery to produce compact communication devices. Some famous manufacturers mobile devices, such as Motorola, have already reached a peace agreement with the inventor of the fractal antenna. Original source

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Introduction

An antenna is a radio device designed to transmit or receive electromagnetic waves. The antenna is one of the most important elements of any radio engineering system associated with the emission or reception of radio waves. Such systems include: radio communication systems, radio broadcasting, television, radio control, radio relay communications, radar, radio astronomy, radio navigation, etc.

Structurally, the antenna consists of wires, metal surfaces, dielectrics, and magnetodielectrics. The purpose of the antenna is illustrated by a simplified diagram of the radio link. High-frequency electromagnetic oscillations, modulated by the useful signal and created by the generator, are converted by the transmitting antenna into electromagnetic waves and radiated into space. Typically, electromagnetic waves are supplied from the transmitter to the antenna not directly, but using a power line (electromagnetic wave transmission line, feeder).

In this case, electromagnetic waves associated with it propagate along the feeder, which are converted by the antenna into diverging electromagnetic waves of free space.

The receiving antenna picks up free radio waves and converts them into coupled waves, which are fed through a feeder to the receiver. In accordance with the principle of antenna reversibility, the properties of an antenna operating in transmitting mode do not change when this antenna is operating in receiving mode.

Devices similar to antennas are also used for excitation electromagnetic vibrations V various types waveguides and volumetric resonators.

1. Main characteristics of antennas

1.1 Brief information on the main parameters of antennas

When choosing antennas, their main characteristics are compared: operating frequency range (bandwidth), gain, radiation pattern, input impedance, polarization. Quantitatively, the antenna gain Ga shows how many times the signal power received by a given antenna is more power signal received by the simplest antenna - a half-wave vibrator (isotropic emitter) placed at the same point in space. Gain is expressed in decibels dB or dB. A distinction must be made between the gain defined above, denoted dB or dBd (relative to a dipole or half-wave vibrator), and the gain relative to an isotropic radiator, denoted dBi or dB ISO. In any case, it is necessary to compare similar values. It is desirable to have an antenna with high gain, but increasing the gain usually requires increasing the complexity of its design and dimensions. There are no simple small-sized antennas with high gain. The radiation pattern (RP) of an antenna shows how the antenna receives signals from different directions. In this case, it is necessary to consider the antenna pattern in both horizontal and vertical planes. Omnidirectional antennas in any plane have a pattern in the shape of a circle, that is, the antenna can receive signals from all sides equally, for example, the radiation pattern of a vertical rod in a horizontal plane. A directional antenna is characterized by the presence of one or several pattern lobes, the largest of which is called the main one. Usually, in addition to the main lobe, there are back and side lobes, the level of which is significantly lower than the main lobe, which nevertheless worsens the performance of the antenna, which is why they strive to reduce their level as much as possible.

The antenna input impedance is considered to be the ratio of the instantaneous voltage values to the signal current at the antenna feed points. If the voltage and current of the signal are in phase, then the ratio is a real value and the input resistance is purely active. When the phases shift, in addition to the active component, a reactive component appears - inductive or capacitive, depending on whether the phase of the current lags behind the voltage or advances it. The input impedance depends on the frequency of the received signal. In addition to the listed main characteristics, antennas have a number of other important parameters, such as SWR (Standing Wave Ratio), cross-polarization level, operating temperature range, wind loads, etc.

1.2 Antenna classification

Antennas can be classified according to various criteria: according to the broadband principle, according to the nature of the radiating elements (antennas with linear currents, or vibrator antennas, antennas emitting through an aperture - aperture antennas, surface will antennas); by the type of radio engineering system in which the antenna is used (antennas for radio communications, for radio broadcasting, television, etc.). We will adhere to the range classification. Although antennas with the same (type) radiating elements are very often used in different wave ranges, their design is different; The parameters of these antennas and the requirements for them also differ significantly.

Antennas of the following wave ranges are considered (the names of the ranges are given in accordance with the recommendations of the “Radio Regulations”; names that are widely used in the literature on antenna-feeder devices are indicated in brackets): myriameter (ultra-long) waves (); kilometer (long) waves (); hectometer (average) waves (); decameter (short) waves (); meterwaves(); decimeter waves (); centimeterwaves(); millimeter waves (). The last four bands are sometimes combined under the common name “ultra-short waves” (VHF).

1.2.1 Antenna bands

In recent years, a large number of new communication systems for various purposes with different characteristics have appeared on the radio communication and broadcasting market. From the point of view of users, when choosing a radio communication system or broadcasting system, attention is first paid to the quality of communication (broadcasting), as well as the ease of use of this system (user terminal), which is determined by dimensions, weight, ease of operation, and a list of additional functions. All these parameters are significantly determined by the type and design of antenna devices and elements of the antenna-feeder path of the system under consideration, without which radio communication is unthinkable. In turn, the determining factor in the design and efficiency of antennas is their operating frequency range.

In accordance with the accepted classification of frequency ranges, several large classes (groups) of antennas are distinguished, which are fundamentally different from each other: antennas of the ultra-long-wave (VLF) and long-wave (LW) ranges; mid-wave (MF) antennas; shortwave (HF) antennas; ultra-short wave (VHF) antennas; microwave antennas.

The most popular in recent years from the point of view of providing personal communication services, radio and television broadcasting are HF, VHF and microwave radio systems, the antenna devices of which will be discussed below. It should be noted that, despite the seeming impossibility of inventing something new in the antenna business, in recent years, based on new technologies and principles, significant improvements have been made to classic antennas and new antennas have been developed that are fundamentally different from previously existing ones in design, size, basic characteristics, etc. etc., which has led to a significant increase in the number of types of antenna devices used in modern radio systems.

In any radio communication system, there may be antenna devices designed for transmitting only, for transmitting and receiving, or for receiving only.

For each of the frequency ranges, it is also necessary to distinguish between the antenna systems of radio devices with directional and non-directional (omnidirectional) action, which in turn is determined by the purpose of the device (communications, broadcasting, etc.), the tasks solved by the device (notification, communications, broadcasting, etc.). d.). In general, to increase the directivity of antennas (to narrow the radiation pattern), antenna arrays can be used, consisting of elementary radiators (antennas), which, under certain conditions of their phasing, can provide the necessary changes in the direction of the antenna beam in space (provide control of the position of the antenna radiation pattern). Within each range, it is also possible to distinguish antenna devices that operate only at a certain frequency (single-frequency or narrow-band), and antennas that operate in a fairly wide range of frequencies (broadband or wide-band).

1.3 Radiation from antenna arrays

To obtain high directivity of radiation, often required in practice, you can use a system of weakly directional antennas, such as vibrators, slits, open ends of waveguides, and others, located in a certain way in space and excited by currents with the required amplitude and phase ratio. In this case, the overall directionality, especially with a large number of emitters, is determined mainly by the overall dimensions of the entire system and, to a much lesser extent, by the individual directional properties of individual emitters.

Such systems include antenna arrays (AR). Typically, AR is a system of identical radiating elements, identically oriented in space and located according to a certain law. Depending on the arrangement of the elements, linear, surface and volumetric lattices are distinguished, among which the most common are rectilinear and flat ARs. Sometimes the radiating elements are located along a circular arc or on curved surfaces that coincide with the shape of the object on which the AR is located (conformal AR).

The simplest is a linear array, in which the radiating elements are located along a straight line, called the array axis, at equal distances from each other (equidistant array). The distance d between the phase centers of the emitters is called the grating pitch. Linear AR, in addition to its independent significance, is often the basis for the analysis of other types of AR.

2 . Analysis of promising antenna structures

2.1 HF and VHF antennas

Figure 1 - Base station antenna

In HF and VHF bands Currently, a large number of radio systems for various purposes are in operation: communications (radio relay, cellular, trunking, satellite, etc.), radio broadcasting, television broadcasting. According to the design and characteristics, all antenna devices of these systems can be divided into two main groups - antennas of stationary devices and antennas of mobile devices. Stationary antennas include antennas of base communication stations, receiving television antennas, antennas of radio relay communication lines, and mobile antennas include antennas of personal communication user terminals, car antennas, antennas for wearable (portable) radio stations.

Base station antennas are mostly omnidirectional in the horizontal plane, as they provide communication mainly with moving objects. The most widely used vertical polarization whip antennas are the “Ground Plane” (“GP”) type due to the simplicity of their design and sufficient efficiency. Such an antenna is a vertical rod of length L, selected in accordance with the operating wavelength l, with three or more counterweights, usually installed on a mast (Figure 1).

The length of the pins L is l/4, l/2 and 5/8l, and the counterweights range from 0.25l to 0.1l. The input impedance of the antenna depends on the angle between the counterweight and the mast: the smaller this angle (the more the counterweights are pressed against the mast), the greater the resistance. In particular, for an antenna with L = l/4, an input impedance of 50 Ohms is achieved at an angle of 30°...45°. The radiation pattern of such an antenna in the vertical plane has a maximum at an angle of 30° to the horizon. The antenna gain is equal to the gain of a vertical half-wave dipole. In this design, however, there is no connection between the pin and the mast, which requires additional use short-circuited cable cable length l/4 to protect the antenna from thunderstorms and static electricity.

An antenna with a length of L = l/2 does not need counterweights, the role of which is played by a mast, and its pattern in the vertical plane is more pressed to the horizon, which increases its range. In this case, a high-frequency transformer is used to lower the input impedance, and the base of the pin is connected to the grounded mast through a matching transformer, which automatically solves the problem of lightning protection and static electricity. The antenna gain compared to a half-wave dipole is about 4 dB.

The most effective of the “GP” antennas for long-distance communication is the antenna with L = 5/8l. It is slightly longer than the half-wave antenna, and the feeder cable is connected to the matching inductance located at the base of the vibrator. Counterweights (at least 3) are located in a horizontal plane. The gain of such an antenna is 5-6 dB, the maximum DP is located at an angle of 15° to the horizontal, and the pin itself is grounded to the mast through a matching coil. These antennas are narrower than half-wave antennas, and therefore require more careful tuning.

Figure 2 - Half-wave vibrator antenna

Figure 3 - Rhombic antenna of a half-wave vibrator

Most base antennas are installed on rooftops, which can greatly affect their performance, so the following must be considered:

It is advisable to place the antenna base no lower than 3 meters from the roof plane;

There should be no metal objects or structures near the antenna ( television antennas, wires, etc.);

It is advisable to install antennas as high as possible;

The operation of the antenna must not interfere with other base stations.

A significant role in establishing stable radio communication is played by the polarization of the received (emitted) signal; since with long-distance propagation surface wave experiences significantly less attenuation with horizontal polarization, then for long-distance radio communications, as well as for television transmission, antennas with horizontal polarization are used (vibrators are located horizontally).

The simplest of the directional antennas is the half-wave vibrator. For a symmetrical half-wave vibrator, the total length of its two identical arms is approximately equal to l/2 (0.95 l/2), the radiation pattern has the shape of a figure eight in the horizontal plane and a circle in the vertical plane. The gain, as stated above, is taken as the unit of measurement.

If the angle between the vibrators of such an antenna is equal to b<180є, то получают антенну типа V, у которой ДН складывается из ДН составных её частей, причём угол раскрыва зависит от длины вибратора (рисунок 2). Так, например, при L =л получаем б=100є, а при L = 2л, б =70є, а усиление равно 3,5 дБ и 4,5 дБ, входное сопротивление - 100 и 120 Ом соответственно.

When two V-type antennas are connected in such a way that their patterns are summed, a rhombic antenna is obtained, in which the directivity is much more pronounced (Figure 3).

When connecting to the top of the diamond, opposite the power points, a load resistor Rn, dissipating power equal to half the transmitter power, suppression of the back lobe of the pattern by 15...20 dB is achieved. The direction of the main lobe in the horizontal plane coincides with diagonal a. In the vertical plane, the main lobe is oriented horizontally.

One of the best relatively simple directional antennas is a “double square” loop antenna, the gain of which is 8...9 dB, the suppression of the back lobe of the pattern is no less than 20 dB, the polarization is vertical.

Figure 4 - Wave channel antenna

The most widespread, especially in the VHF range, are antennas of the “wave channel” type (in foreign literature - Uda-Yagi antennas), since they are quite compact and provide large Ga values with relatively small dimensions. Antennas of this type are a set of elements: active - vibrator and passive - reflector and several directors installed on one common boom (Figure 4). Such antennas, especially those with a large number of elements, require careful tuning during manufacture. For a three-element antenna (vibrator, reflector and one director), the basic characteristics can be achieved without additional configuration.

The complexity of antennas of this type also lies in the fact that the input impedance of the antenna depends on the number of passive elements and significantly depends on the configuration of the antenna, which is why the literature often does not indicate the exact value of the input impedance of such antennas. In particular, when using a Pistolkors loop vibrator, which has an input impedance of about 300 Ohms, as a vibrator, with an increase in the number of passive elements, the input impedance of the antenna decreases and reaches values of 30-50 Ohms, which leads to mismatch with the feeder and requires additional matching. With an increase in the number of passive elements, the antenna pattern narrows and the gain increases, for example, for a three-element and five-element antennas, the gains are 5...6 dB and 8...9 dB with the width of the main beam of the pattern 70º and 50º, respectively.

More broadband compared to “wave channel” type antennas and not requiring tuning are traveling wave antennas (AWA), in which all vibrators, located at the same distance from one another, are active and connected to the collecting line (Figure 5). The signal energy they receive is added up in the collecting line almost in phase and enters the feeder. The gain of such antennas is determined by the length of the collecting line, is proportional to the ratio of this length to the wavelength of the received signal, and depends on the directional properties of the vibrators. In particular, for ABC with six vibrators of different lengths corresponding to the required frequency range and located at an angle of 60° to the collecting line, the gain ranges from 4 dB to 9 dB within the operating range, and the level of back radiation is 14 dB lower.

Figure 5 - Traveling wave antenna

Figure 6 - Antenna with logarithmic periodicity structure or log periodic antenna

The directional properties of the antennas considered vary depending on the wavelength of the received signal. One of the most common types of antennas with a constant shape of the pattern in a wide frequency range are antennas with logarithmic periodicity of the structure or log-periodic antennas (LPA). They have a wide range: the maximum wavelength of the received signal exceeds the minimum by more than 10 times. At the same time, good matching of the antenna with the feeder is ensured throughout the entire operating range, and the gain remains practically unchanged. The collecting line of the LPA is usually formed by two conductors located one above the other, to which the arms of the vibrators are attached horizontally, one at a time (Figure 6, top view).

The LPA vibrators turn out to be inscribed in an isosceles triangle with an angle at the vertex b and a base equal to the largest vibrator. The operating bandwidth of the antenna is determined by the dimensions of the longest and shortest vibrators. For a logarithmic antenna structure, a certain relationship must be satisfied between the lengths of adjacent vibrators, as well as between the distances from them to the top of the structure. This relationship is called the structure period f:

B2? B1=B3? B2=A2? A1=A3? A2=...=f

Thus, the size of the vibrators and the distance to them from the vertex of the triangle are reduced exponentially. The characteristics of the antenna are determined by the values of f and b. The smaller the angle b and the larger b (b is always less than 1), the greater the antenna gain and the lower the level of the back and side lobes of the radiation pattern. However, at the same time, the number of vibrators increases, and the dimensions and weight of the antenna increase. The optimal values for angle b are chosen within 3є…60є, and φ - 0.7…0.9.

Depending on the wavelength of the received signal, several vibrators are excited in the antenna structure, the sizes of which are closest to half the wavelength of the signal, therefore the LPA is similar in principle to several “wave channel” antennas connected together, each of which contains a vibrator, a reflector and a director . At a certain wavelength of the signal, only one trio of vibrators is excited, and the rest are so detuned that they do not affect the operation of the antenna. Therefore, the gain of the LPA turns out to be less than the gain of a “wave channel” antenna with the same number of elements, but the bandwidth of the LPA turns out to be much wider. Thus, for an LPA consisting of ten vibrators and values b = 45є, f = 0.84, the calculated gain is 6 dB, which practically does not change over the entire range of operating frequencies.

For radio relay communication lines, it is very important to have a narrow radiation pattern so as not to interfere with other radio-electronic equipment and ensure high-quality communication. To narrow the pattern, antenna arrays (AR) are widely used, narrowing the pattern in different planes and providing different values of the width of the main lobe. It is quite clear that the geometric dimensions of the antenna array and the characteristics of the radiation pattern significantly depend on the range of operating frequencies - the higher the frequency, the more compact the array will be and the narrower the radiation pattern, and, consequently, the greater the gain. For the same frequencies, with increasing AR sizes (the number of elementary emitters), the pattern will narrow.

For the VHF band, arrays are often used consisting of vibrator antennas (loop vibrators), the number of which can reach several tens, the gain increases to 15 dB and higher, and the width of the pattern in any plane can be narrowed to 10º, for example for 16 vertically located loop vibrators in the frequency range 395...535 MHz, the pattern narrows in the vertical plane to 10º.

The main type of antennas used in user terminals are vertically polarized whip antennas, which have a circular pattern in the horizontal plane. The efficiency of these antennas is quite low due to low gain values, as well as due to the influence of surrounding objects on the radiation pattern, as well as the lack of proper grounding and limitations on the geometric dimensions of the antennas. The latter requires high-quality matching of the antenna with the input circuits of the radio device. Typical design matching options are inductance distributed along the length and inductance at the base of the antenna. To increase the radio communication range, special extended antennas several meters long are used, which achieves a significant increase in the level of the received signal.

Currently, there are many types of car antennas, varying in appearance, design, and price. These antennas are subject to strict requirements for mechanical, electrical, operational and aesthetic parameters. The best results in terms of communication range are achieved by a full-size antenna with a length of l/4, however, large geometric dimensions are not always convenient, therefore various methods of shortening antennas are used without significantly deteriorating their characteristics. To provide cellular communications In cars, microstrip resonant antennas (single-, dual- and tri-band) can be used, which do not require installation of external parts, since they are attached to the inside of the car glass. Such antennas provide reception and transmission of vertically polarized signals in the frequency range 450...1900 MHz, and have a gain of up to 2 dB.

2.1.1 General characteristics of microwave antennas

In the microwave range in recent years there has also been an increase in the number of communication and broadcasting systems, both previously existing and newly developed. For terrestrial systems - these are radio relay communication systems, radio and television broadcasting, cellular television systems, etc., for satellite systems - direct television broadcasting, telephone, fax, paging communications, video conferencing, Internet access, etc. The frequency ranges used for these types of communications and broadcasting correspond to the sections of the frequency spectrum allocated for these purposes, the main ones being: 3.4...4.2 GHz; 5.6...6.5 GHz; 10.7…11.7 GHz; 13.7…14.5 GHz; 17.7…19.7 GHz; 21.2…23.6 GHz; 24.5…26.5 GHz; 27.5…28.5 GHz; 36…40 GHz. Sometimes in technical literature the microwave range includes systems operating at frequencies above 1 GHz, although this range strictly starts from 3 GHz.

For terrestrial microwave systems, antenna devices are small-sized mirror, horn, horn-lens antennas, installed on masts and protected from harmful atmospheric influences. Directional antennas, depending on their purpose, design and frequency range, have a wide range of characteristics, namely: in gain - from 12 to 50 dB, in beam width (level - 3 dB) - from 3.5 to 120º. In addition, cellular television systems use biconical omnidirectional (in the horizontal plane) antennas, consisting of two metal cones with their vertices pointing towards each other, a dielectric lens installed between the cones, and an excitation device. Such antennas have a gain of 7...10 dB, the width of the main lobe in the vertical plane is 8...15є, and the level of the side lobes is no worse than minus 14 dB.

3. Analysis of possible methods for synthesizing antenna fractal structures

3.1 Fractal antennas

Fractal antennas are a relatively new class of electrically small antennas (EMA), which are fundamentally different in their geometry from known solutions. In fact, the traditional evolution of antennas was based on Euclidean geometry, operating with objects of integer dimension (line, circle, ellipse, paraboloid, etc.). The main difference between fractal geometric forms is their fractional dimension, which is externally manifested in the recursive repetition of the original deterministic or random patterns on an increasing or decreasing scale. Fractal technologies have become widespread in the development of signal filtering tools, the synthesis of three-dimensional computer models of natural landscapes, and image compression. It is quite natural that the fractal “fashion” did not bypass the theory of antennas. Moreover, the prototype of modern fractal technologies in antenna technology was the log-periodic and spiral designs proposed in the mid-60s of the last century. True, in a strict mathematical sense, such structures at the time of development had no relation to fractal geometry, being, in fact, only fractals of the first kind. Currently, researchers, mainly through trial and error, are trying to use known fractals in geometry in antenna solutions. As a result of simulation modeling and experiments, it was found that fractal antennas make it possible to obtain almost the same gain as conventional ones, but with smaller dimensions, which is important for mobile applications. Let us consider the results obtained in the field of creating fractal antennas of various types.

The results of studies of the characteristics of the new antenna design published by Cohen attracted the attention of specialists. Thanks to the efforts of many researchers, today the theory of fractal antennas has turned into an independent, fairly developed apparatus for the synthesis and analysis of EMA.

3.2 Propertiesfractal antennas

SFCs can be used as templates for making monopoles and dipole arms, forming the topology of printed antennas, Frequency Selection Surfaces (FSS) or reflector shells, constructing the contours of loop antennas and horn aperture profiles, as well as milling slots in slot antennas .

Experimental data obtained by Cushcraft specialists for the Koch curve, four iterations of a square wave and a helical antenna allow us to compare the electrical properties of the Koch antenna with other emitters with a periodic structure. All compared emitters had multi-frequency properties, which was manifested in the presence of periodic resonances in the impedance graphs. However, for multi-band applications, the Koch fractal is most suitable, for which, with increasing frequency, the peak values of reactive and active resistances decrease, while for the meander and spiral they increase.

In general, it should be noted that it is difficult to theoretically imagine the mechanism of interaction between a fractal receiving antenna and electromagnetic waves incident on it due to the lack of an analytical description of wave processes in a conductor with a complex topology. In such a situation, it is advisable to determine the main parameters of fractal antennas by mathematical modeling.

An example of constructing the first self-similar fractal curve was demonstrated in 1890 by the Italian mathematician Giuseppe Peano. In the limit, the line he proposed completely fills the square, running around all its points (Figure 9). Subsequently, other similar objects were found, which received the general name “Peano curves” after the discoverer of their family. True, due to the purely analytical description of the curve proposed by Peano, some confusion arose in the classification of SFC lines. In fact, the name “Peano curves” should only be given to original curves, the construction of which corresponds to the analytics published by Peano (Figure 10).

Figure 9 - Iterations of the Peano curve: a) initial line, b) first, c) second and d) third iterations

Figure 10 - Iterations of the polyline proposed by Hilbert in 1891

Often interpreted as a recursive Peano curve

Therefore, in order to specify the objects of antenna technology under consideration, when describing one or another form of a fractal antenna, one should, if possible, mention the names of the authors who proposed the corresponding modification of the SFC. This is all the more important since, according to estimates, the number of known varieties of SFC is approaching three hundred, and this figure is not a limit.

It should be noted that the Peano curve (Figure 9) in its original form is quite suitable for making slits in the walls of a waveguide, printed and other aperture fractal antennas, but is not acceptable for constructing a wire antenna, since it has touching sections. Therefore, Fractus specialists proposed its modification, called “Peanodec” (Figure 11).

Figure 11 - Variant of modification of the Peano curve (“Peanodec”): a) first, b) second c) third iteration

A promising application of antennas with Koch topology is MIMO communication systems (communication systems with many inputs and outputs). To miniaturize the antenna arrays of user terminals in such communications, specialists from the Electromagnetism Laboratory of the University of Patras (Greece) proposed a fractal similarity to an inverted L-antenna (ILA). The essence of the idea comes down to bending the Koch vibrator by 90° at a point dividing it into segments with a length ratio of 2:1. For mobile communications with a carrier frequency of ~2.4 Hz, the dimensions of such a printed antenna are 12.33×10.16 mm (~L/10ChL/12), the bandwidth is ~20% and the efficiency is 93%.

Figure 12 - Example of a dual-band (2.45 and 5.25 GHz) antenna array

The azimuth radiation pattern is almost uniform, the gain in terms of the feeder input is ~3.4 dB. True, as noted in the article, the operation of such printed elements as part of a lattice (Figure 12) is accompanied by a decrease in their efficiency compared to a single element. Thus, at a frequency of 2.4 GHz, the efficiency of a Koch monopole bent by 90° decreases from 93 to 72%, and at a frequency of 5.2 GHz - from 90 to 80%. The situation is somewhat better with the mutual influence of high-frequency band antennas: at a frequency of 5.25 GHz, the isolation between the elements forming the central pair of antennas is 10 dB. As for the mutual influence in a pair of adjacent elements of different ranges, depending on the signal frequency, the isolation varies from 11 dB (at 2.45 GHz) to 15 dB (at a frequency of 5.25 GHz). The reason for the deterioration in antenna performance is the mutual influence of printed elements.

Thus, the ability to select many different parameters of an antenna system based on a Koch broken line allows the design to satisfy various requirements for the value of internal resistance and the distribution of resonant frequencies. However, since the interdependence of the recursive dimension and antenna characteristics can be obtained only for a certain geometry, the validity of the considered properties for other recursive configurations requires additional research.

3.3 Characteristics of fractal antennas

The Koch fractal antenna shown in Figure 13 or 20 is just one of the options that can be implemented using an equilateral initiating recursion triangle, i.e. the angle and at its base (indentation angle or “indentation angle”) is 60°. This version of the Koch fractal is usually called standard. It is quite natural to wonder whether it is possible to use modifications of the fractal with other values of this angle. Vinoy proposed to consider the angle at the base of the initiating triangle as a parameter characterizing the antenna design. By changing this angle, you can obtain similar recursive curves of different dimensions (Figure 13). The curves retain the property of self-similarity, but the resulting line length can be different, which affects the characteristics of the antenna. Vinoy was the first to study the correlation between the properties of the antenna and the dimension of the generalized Koch fractal D, determined in the general case by the dependence

(1)

It was shown that as the angle increases, the dimension of the fractal also increases, and at u>90° it approaches 2. It should be noted that the concept of dimension used in the theory of fractal antennas somewhat contradicts the concepts accepted in geometry, where this measure is applicable only to infinitely recursive objects.

Figure 13 - Construction of the Koch curve with an angle of a) 30° and b) 70° at the base of the triangle in the fractal generator

As the dimension increases, the total length of the broken line increases nonlinearly, determined by the relation:

(2)

where L0 is the length of the linear dipole, the distance between the ends of which is the same as that of the Koch broken line, n is the iteration number. The transition from u = 60° to u = 80° at the sixth iteration allows the total length of the prefractal to be increased by more than four times. As you would expect, there is a direct relationship between the recursive dimension and such antenna properties as the primary resonant frequency, internal resistance at resonance and multi-band characteristics. Based on computer calculations, Vinoy obtained the dependence of the first resonant frequency of the Koch dipole fk on the dimension of the prefractal D, the iteration number n and the resonant frequency of the rectilinear dipole fD of the same height as the Koch broken line (at the extreme points):

(3)

Figure 14 - Electromagnetic wave leakage effect

In the general case, for the internal resistance of the Koch dipole at the first resonant frequency, the following approximate relation is valid:

(4)

where R0 is the internal resistance of the linear dipole (D=1), which in the case under consideration is equal to 72 Ohms. Expressions (3) and (4) can be used to determine the geometric parameters of the antenna with the required values of the resonant frequency and internal resistance. The multiband properties of the Koch dipole are also very sensitive to the value of the angle u. With an increase, the nominal values of the resonant frequencies become closer, and, consequently, their number in a given spectral range increases (Figure 15). Moreover, the higher the iteration number, the stronger this convergence.

Figure 15 - Effect of narrowing the interval between resonant frequencies

At the University of Pennsylvania, another important aspect of the Koch dipole was studied - the effect of the asymmetry of its power supply on the degree to which the internal resistance of the antenna approaches 50 Ohms. In linear dipoles, the feed point is often located asymmetrically. The same approach can be used for a fractal antenna in the form of a Koch curve, the internal resistance of which is less than the standard values. Thus, in the third iteration, the internal resistance of the standard Koch dipole (u = 60°), without taking into account losses when connecting the feeder in the center, is 28 Ohms. By moving the feeder to one end of the antenna, a resistance of 50 ohms can be obtained.

All configurations of the Koch broken line considered so far were synthesized recursively. However, according to Vina, if you break this rule, in particular by specifying different angles and? With each new iteration, the antenna properties can be changed with greater flexibility. To preserve the similarity, it is advisable to choose a regular scheme for changing the angle and. For example, change it according to the linear law иn = иn-1 - Di·n, where n is the iteration number, Di? - increment of the angle at the base of the triangle. A variant of this principle of constructing a broken line is the following sequence of angles: u1 = 20° for the first iteration, u2 = 10° for the second, etc. The configuration of the vibrator in this case will not be strictly recursive, however, all its segments synthesized in one iteration will have the same size and shape. Therefore, the geometry of such a hybrid broken line is perceived as self-similar. With a small number of iterations, along with a negative increment Di, a quadratic or other nonlinear change in the angle un can be used.

The considered approach allows you to set the distribution of the resonant frequencies of the antenna and the values of its internal resistance. However, rearranging the order of changing angle values in iterations does not give an equivalent result. For the same height of a broken line, various combinations of identical angles, for example u1 = 20°, u2 = 60° and u1 = 60°, u2 = 20° (Figure 16), give the same expanded length of prefractals. But, contrary to expectation, complete coincidence of parameters does not ensure the identity of the resonant frequencies and the identity of the multiband properties of the antennas. The reason is a change in the internal resistance of the segments of the broken line, i.e. The key role is played by the configuration of the conductor, not its size.

Figure 16 - Generalized Koch prefractals of the second iteration with a negative increment Dq (a), positive increment Dq (b) and the third iteration with a negative increment Dq = 40°, 30°, 20° (c)

4. Examples of fractal antennas

4.1 Antenna overview

Antenna topics are one of the most promising and of significant interest in the modern theory of information transmission. This desire to develop precisely this area of scientific development is associated with the continuously increasing requirements for speed and methods of information transfer in the modern technological world. Every day, communicating with each other, we transmit information in such a natural way for us - through the air. In exactly the same way, scientists came up with the idea to teach numerous computer networks to communicate.

The result was the emergence of new developments in this area, their approval in the computer equipment market, and later the adoption of standards wireless transmission information. Today, transmission technologies such as BlueTooth and WiFi are already approved and generally accepted. But development does not stop there, and cannot stop; new requirements and new wishes of the market appear.

Transmission speeds, so amazingly fast at the time the technologies were developed, today no longer meet the requirements and wishes of the users of these developments. Several leading development centers have begun new project WiMAX in order to increase speed, based on expanding the channel in the already existing WiFi standard. What place does the antenna topic have in all this?

The problem of expanding the transmission channel can be partially solved by introducing even greater compression than the existing one. The use of fractal antennas will solve this problem better and more efficiently. The reason for this is that fractal antennas and frequency-selective surfaces and volumes based on them have unique electrodynamic characteristics, namely: broadband, repeatability of bandwidths in the frequency range, etc.

4.1.1 Construction of the Cayley tree

The Cayley tree is one of the classic examples of fractal sets. Its zero iteration is just a straight line segment of a given length l. The first and each subsequent odd iteration consists of two segments of exactly the same length l as the previous iteration, located perpendicular to the segment of the previous iteration so that its ends are connected to the middle of the segments.

The second and each subsequent even iteration of the fractal are two segments l/2 half the length of the previous iteration, located, as before, perpendicular to the previous iteration.

The results of constructing the Cayley tree are shown in Figure 17. The total height of the antenna is 15/8l, and the width is 7/4l.

Figure 17 - Construction of the Cayley tree

Calculations and analysis of the “Cayley Tree” antenna Theoretical calculations of a fractal antenna in the form of a 6th order Cayley Tree were performed. To solve this practical problem, a fairly powerful tool was used for the rigorous calculation of electrodynamic properties of conductive elements - the EDEM program. The powerful tools and user-friendly interface of this program make it indispensable for this level of calculations.

The authors were faced with the task of designing an antenna, estimating the theoretical values of the resonant frequencies of signal reception and transmission, and presenting the problem in the EDEM program language interface. The designed fractal antenna based on the “Cayley Tree” is shown in Figure 18.

Then, a plane electromagnetic wave was sent to the designed fractal antenna, and the program calculated the field propagation before and after the antenna, and calculated the electrodynamic characteristics of the fractal antenna.

The results of calculations of the fractal antenna “Cayley Tree” carried out by the authors allowed us to draw the following conclusions. It is shown that a series of resonant frequencies repeats at approximately twice the previous frequency. The current distributions on the antenna surface were determined. Areas of both total transmission and total reflection of the electromagnetic field were studied.

Figure 18 - Cayley tree of the 6th order

4 .1.2 Multimedia antenna

Miniaturization is advancing across the planet by leaps and bounds. The advent of computers the size of a bean grain is just around the corner, but in the meantime, the Fractus company brings to our attention an antenna whose dimensions are smaller than a grain of rice (Figure 19).

Figure 19 - Fractal antenna

The new product, called Micro Reach Xtend, operates at a frequency of 2.4 GHz and supports wireless technologies Wi-Fi and Bluetooth, as well as some other less popular standards. The device is based on patented fractal antenna technologies, and its area is only 3.7 x 2 mm. According to the developers, the tiny antenna will make it possible to reduce the size of multimedia products in which it will find its use in the near future, or to cram more capabilities into one device.

Television stations transmit signals in the range of 50-900 MHz, which are reliably received at a distance of many kilometers from the transmitting antenna. It is known that vibrations of higher frequencies pass through buildings and various obstacles worse than low-frequency ones, which simply bend around them. Therefore, the Wi-Fi technology used in conventional systems wireless communication and operating at frequencies above 2.4 GHz, provides signal reception only at a distance of no more than 100 m. Such injustice towards advanced Wi-Fi technology will soon be ended, of course, without harm to TV consumers. In the future, devices created on the basis of Wi-Fi technology will operate at frequencies between operating TV channels, thus increasing the range of reliable reception. In order not to interfere with the operation of television, each of the Wi-Fi systems (transmitter and receiver) will constantly scan nearby frequencies, preventing collisions on the air. When moving to a wider frequency range, it becomes necessary to have an antenna that can equally well receive signals from both high and high frequencies. low frequencies. Conventional whip antennas do not meet these requirements, because They, in accordance with their length, selectively accept frequencies of a certain wavelength. An antenna suitable for receiving signals in a wide frequency range is the so-called fractal antenna, which has the shape of a fractal - a structure that looks the same no matter what magnification we view it with. A fractal antenna behaves as a structure consisting of many pin antennas of different lengths twisted together would behave.

4.1.3 “Broken” antenna

American engineer Nathan Cohen about ten years ago decided to assemble an amateur radio station at home, but encountered an unexpected difficulty. His apartment was located in the center of Boston, and the city authorities strictly prohibited placing an antenna outside the building. A solution was found unexpectedly, turning the entire subsequent life of the radio amateur upside down.

Instead of making a traditionally shaped antenna, Cohen took a piece of aluminum foil and cut it into the shape of a mathematical object known as a Koch curve. This curve, discovered in 1904 by the German mathematician Helga von Koch, is a fractal, a broken line that looks like a series of infinitely decreasing triangles growing out of one another like the roof of a multi-stage Chinese pagoda. Like all fractals, this curve is “self-similar,” that is, on any smallest segment it has the same appearance, repeating itself. Such curves are constructed by endlessly repeating a simple operation. The line is divided into equal segments, and on each segment a bend is made in the form of a triangle (von Koch method) or a square (Herman Minkowski method). Then, on all sides of the resulting figure, similar squares or triangles, but of a smaller size, are in turn bent. Continuing the construction ad infinitum, you can get a curve that is “broken” at each point (Figure 20).

Figure 20 - Construction of the Koch and Minkowski curve

Construction of the Koch curve - one of the very first fractal objects. On an infinite straight line, segments of length l are distinguished. Each segment is divided into three equal parts, and an equilateral triangle with side l/3 is constructed on the middle one. Then the process is repeated: triangles with sides l/9 are built on segments l/3, triangles with sides l/27 are built on them, and so on. This curve has self-similarity, or scale invariance: each of its elements in a reduced form repeats the curve itself.

The Minkowski fractal is constructed similarly to the Koch curve and has the same properties. When constructing it, instead of a system of triangles, meanders are built on a straight line - “rectangular waves” of infinitely decreasing sizes.

When constructing the Koch curve, Cohen limited himself to only two or three steps. He then glued the figure onto a small piece of paper, attached it to the receiver, and was surprised to find that it worked no worse than conventional antennas. As it turned out later, his invention became the founder of a fundamentally new type of antennas, now mass-produced.

These antennas are very compact: the fractal antenna for a mobile phone built into the case has the size of a regular slide (24 x 36 mm). In addition, they operate over a wide frequency range. All this was discovered experimentally; The theory of fractal antennas does not yet exist.

The parameters of a fractal antenna made by a series of successive steps using the Minkowski algorithm change in a very interesting way. If a straight antenna is bent in the shape of a “square wave” - a meander, its gain will increase. All subsequent meanders of the antenna gain do not change, but the range of frequencies it receives expands, and the antenna itself becomes much more compact. True, only the first five or six steps are effective: in order to bend the conductor further, you will have to reduce its diameter, and this will increase the antenna resistance and lead to loss of gain.

While some are racking their brains over theoretical problems, others are actively implementing the invention into practice. According to Nathan Cohen, now a professor at the University of Boston and chief technical inspector of Fractal Antenna Systems, “in a few years, fractal antennas will become an integral part of cellular and radio telephones and many other wireless communications devices.”

antenna array fractal

4.2 Application of fractal antennas

Among the many antenna designs used today in communications, the type of antenna mentioned in the title of the article is relatively new and fundamentally different from known solutions. The first publications examining the electrodynamics of fractal structures appeared back in the 80s of the 20th century. It's the beginning practical use The fractal direction in antenna technology was started more than 10 years ago by the American engineer Nathan Cohen, now a professor at Boaon University and the chief technical inspector of the company Fractal Antenna Systems. Living in downtown Boston, in order to get around the city government's ban on installing outdoor antennas, he decided to disguise the antenna of a amateur radio station as a decorative figure made of aluminum foil. As a basis, he took the Koch curve known in geometry (Figure 20), the description of which was proposed in 1904 by the Swedish mathematician Niels Fabian Helge von Koch (1870-1924).