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Abstract

Contents

Introduction

The general theory of lens antennas is quite common in the works of both foreign and domestic experts, however, the practical use of lens antennas (based on the Luneberg and Maxwell lenses) is extremely rare. The reason for this is fairly obvious. The emergence of relatively simple methods for implementing models of dielectric antennas occurred, to a greater extent, in the 21st century.

The modern era of antenna systems with a wide viewing angle, such as radars, direction finders, requires a special kind of antenna systems that allow you to change the spatial position of the antenna focus with the highest speed and lowest energy consumption. One way to solve this problem is to use lens antennas.

The use of lens antennas allows you to use several irradiators at the same time, as well as implement a rotary mechanism, rotating the irradiators on the surface of the lens. Lens antennas constructed using a spherical structure (for a Luneberg lens) and a hemispherical (for a Maxwell lens) can be produced in different ways. The main method that has been used for several decades is the use of polymeric materials with different dielectric constants. The following materials suitable for the manufacture of lenses with variable dielectric constant are considered: expanded polystyrene chloride, expanded polystyrene, expanded polyurethane. This group of foams is excellent for manufacturing lenses for several reasons (lightness, strength), but the main reasons are the dielectric constant of the material, which depends on the density, and the relative stability of the dielectric constant, depending on the frequency of irradiation.

1. Theme urgency

The main property of the lenses under consideration is the alignment of the front of a spherical wave, i.e., the transformation of a plane wave into a spherical one. If considering an electromagnetic wave that has traveled a considerable distance (tens and hundreds of thousands of λ), we get a plane front as well. Then, that the direction of energy distribution can be controlled by the lens and the total signal power in the direction of the main lobe of the radiation pattern can be increased by a simple refinement of the antenna system. We can say the same thing about the inverse transformation. Consider the system using the example of a receiving horn antenna – a plane wave passing through the horn opens a current in the antenna-feeder path of a certain power, but if the dielectric lens is in front of the horn, then more power will come into the antenna opening than was received in the absence of the lens, due to the passage of more energy through the lens and its concentration in the focus of the lens, where the horn antenna is located. This property is used in communication systems with a high frequency of the emitted signal (tens of gigahertz), such as inter-satellite communications, as well as in the organization of terrestrial communications – mobile communications and radio relay communications.

It is worth noting that for a long time the following principle was developed for the design of dielectric lenses with a variable dielectric constant: the creation of a prototype based on theory and its further testing in practice. This leads to inappropriate costs. Since it is extremely difficult to produce a substance with variable dielectric constant, we decided to resort to the method of forming a lens from many layers of different dielectric constants. But it was not possible to achieve the desired characteristics from the lens the first time, which affected the final cost of the prototype. Often, the manufactured lens not only required further refinement, but also a complete processing – an increase in the number of layers, the use of polymers of a different type.

Prospects for the use of lens antennas are the possibility of applying technology for different frequency ranges. In the modern world, robotic technology and artificial intelligence are increasingly being used, and automotive industry is currently experiencing particularly strong development in this area. Large concerns Mercedes, BMW, Honda and Hyundai already have their own concepts and prototypes of unmanned vehicles, not to mention such a giant of industrial technology as Tesla. But all these artificial intellects have one thing in common – they need to “see” the road.

The method of radar using a dielectric lens is not new, but this approach to solving the problem is more adaptable. The aim of the study was to create models in the HFSS software product, allowing to reveal the pattern of designing the same type of antenna for different wavelengths. Creating a universal algorithm in the design and development would greatly reduce the time and cost of many technical projects. The main parameter in the modern engineering industry is speed. This is not only the speed of development of a project, but the speed of implementation in production with the use of minimum time for reconstruction of such production.

2. Goal and tasks of the research

The ultimate goal of the study is a simple way of modeling complex structures of variable dielectric constant forming a lens antenna with the possibility of rapid implementation in production.

The main objectives of the study:

  1. Analysis of existing dielectric lens manufacturing technologies.
  2. Analysis of the scope of application of dielectric antennas in practical applications.
  3. Search for alternative methods for manufacturing lens antennas.
  4. Formation of a single algorithm for modeling, analysis and theoretical production, corresponding to different frequency ranges.

3. Overview of research and development in the field of materials used and approaches

Polyfoam – a class of materials, which is a gas-filled plastics – ultralight plastic materials obtained on the basis of various synthetic polymers. Remind the structure of the frozen foam. The filler for such materials is gas [1]

Expanded polystyrene is a fairly common material, in view of the fact that when using a cheap manufacturing method (pressed and non-pressed) it is used as a packaging and transportation material for household appliances. But we are interested in a more complex method of its manufacture – extrusion [2].

Extrusion – the technology of obtaining products by forcing a viscous melt of material or thick paste through a forming hole. Extruders of various shapes allow you to create materials of different densities.

Extruded polystyrene foam does not allow moisture to pass through, so it does not get damaged over time due to exposure to high humidity[3].

Polyvinyl chloride – has high elasticity, there are no highly toxic substances in the composition, it is a self-extinguishing substance. However, in the event of a complete flame environment, suffocating smoke begins to emit. Slightly absorbs moisture, which when frozen can destroy the structure of the material[4].

Polyurethane foam – in everyday life is called foam rubber – has extremely high elasticity and the presence of many pores, allows moisture and air to pass through, is very short-lived, quickly turns yellow and loses its properties when exposed to sunlight and heat. It is characterized by high flammability, emits toxic substances during combustion due to the presence of a large amount of hydrocyanic acid[5].

For this group of foams, there is a graph of the dependence of physical properties on bulk density, in particular a graph of the dependence of the dielectric constant on the density of the substance[6].

From the information on the properties of foamed polymers[7], a clear dependence of the increase in temperature stability with a decrease in the density of the substance is traced. When recalculating the dielectric constant depending on the mass fraction of a substance per unit volume, the most important conclusion can be made: when designing dielectric lenses from polymer materials, one must take into account the coefficient of temperature change in the dielectric constant of the material depending on the density of the layer according to the temperature regime of the end device.

More detailed information on the materials and formulas used in the production of foams of different densities and, accordingly, dielectric constant can be obtained by studying research materials from ASTM International (American Society for Testing and Materials) [8]. For several decades, the properties of materials and their behavior in various environments and under various influences have been studied. As for polymers, I have compiled a list of standards describing the materials needed in the work[9]:

– ASTM D149–09(2013) Standard Test Method for Dielectric Breakdown Voltage and Dielectric Strength of Solid Electrical Insulating Materials at Commercial Power Frequencies – Breakdown voltage and electric strength of electrical insulating materials at industrial frequencies;

– ASTM D150–11 Standard Test Methods for AC Loss Characteristics and Permittivity (Dielectric Constant) of Solid Electrical Insulation – Capacitance at alternating current, dielectric constant and dielectric loss for insulating materials;

– ASTM D1673–94(1998) Standard Test Methods for Relative Permittivity And Dissipation Factor of Expanded Cellular Polymers Used For Electrical Insulation – Dielectric constant and dielectric loss tangent for foams used as electrical insulation;

– ASTM D1531–06 Standard Test Methods for Relative Permittivity (Dielectric Constant) and Dissipation Factor by Fluid Displacement Procedures1 – The dielectric constant and the tangent of the dielectric loss angle of polyethylene;

– ASTM D229–13 Standard Test Methods for Rigid Sheet and Plate Materials Used for Electrical Insulation – Testing of plastic sheets used as insulating materials;

– ASTM D4549–15 Standard Classification System and Basis for Specification for Polystyrene and Rubber-Modified Polystyrene Molding and Extrusion Materials – Injection and extrusion plastics based on polystyrene;

– ASTM D4000–16 Standard Classification System for Specifying Plastic Materials – Polyurethane-based extrusion plastics;

– ASTM D1248–16 Standard Specification for Polyethylene Plastics Extrusion Materials for Wire and Cable – Injection and extrusion plastics based on polyethylene;

– ASTM D2287–12 Standard Specification for Nonrigid Vinyl Chloride Polymer and Copolymer Molding and Extrusion Compounds – Plasticized polyvinyl chloride and vinyl chloride copolymers.

4. Optimization and generalization of methods for developing models of dielectric lenses

The key task at the preparation stage was to find a way to create large and accurate geometric models without losing time resources. The search for ways to automate this process led to the creation of an algorithm using the VBS programming language, which would make it possible to change the geometric dimensions of the model under study, in other words, to model the antenna for a different frequency range. Automation of the process of transferring the model from the field of “thought” to the programming environment of the simulation allowed us to devote more time to quantitative tests during modeling, which in the future will have a beneficial effect on the quality of the models under study. In our case, this means creating a universal model of a dielectric lens antenna. In parallel with the process of increasing the simulation speed, several methods of manufacturing a real model of a lens antenna are also being considered, allowing to determine the best for use in industry. The criteria for determining the best method are, to a greater extent, in obtaining the optimal ratio between the parameters -price, -speed, -quality. The first method involves the use of foamed polymers, allowing, depending on the density, to change the dielectric constant. These polymers will form the lens antenna. The second method involves the use of 3D printing, has its advantages and disadvantages in relation to the first method and is based on the heterogeneous filling of a volume unit with printing material.

An important aspect is not only the dielectric constant, but also the dielectric loss tangent. This parameter is of great importance in antenna systems, which are a load for high-frequency amplifiers of high power, since large losses in the material will lead to the destruction of the dielectric lens.

The main task in computer modeling is the transformation of an idea into a virtual model that would repeat the behavior of a real object with a given accuracy. To determine how exactly the virtual model can correspond to the real one, a simplified comparison method is applied – a very simple model is taken that has basic initial characteristics and a virtual model is created from it, and if the parameters of the virtual and real models coincide, then it makes sense to continue software modeling in the selected environment.

The actual effect on wave propagation is presented in the animation. It should be understood that the more precisely the lens is manufactured (the more the lens structure corresponds to the nonuniformity of the dielectric constant, and, accordingly, the more transition layers are in it), the more qualitative is the transformation of the wave front.

Near field electromagnetic field using a lens

Figure 1 – Near field electromagnetic field using a lens
(animation: 3 frame, 3 loops of repeating, 210 KB)

Conclusion

Currently, dielectric lens antennas are not widely used, however, the developed algorithm is able to open up new possibilities for use in antenna systems, due to the simplicity of preliminary calculation and the ease of physical implementation of virtual models. The prospects for such modeling can most likely appear in the field of using low-power locators to determine the environment when driving cars using artificial intelligence.

References

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  3. Гармонов, И.В. Синтетический каучук / И.В. Гармонов. – Л.: Химия, 1976. – 752 с.
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  5. Глухов, Е.Е. Основные понятия о конструкционных и технологических свойствах пластмасс / Е.Е. Глухов. – М.: Химия, 1970. – 124 с.
  6. Шнейдерович, Р.М. Конструкционные свойства пластмасс / Р.М. Шнейдерович, И.В. Крагельский. – М.: Машиностроение, 1968. – 212с.
  7. Гарбара, М.И. Справочник по пластическим массам / М.И Гарбара, М.С. Акутина, Н.М. Егорова. – М.: Химия, 1967. – 462 с.
  8. Стандарты материалов используемых в производстве диэлектрических материалов [Электронный ресурс]. – Режим доступа: www.astm.org.
  9. Стандарты материалов используемых в производстве пенопласта [Электронный ресурс]. – Режим доступа: www.polyma.ir.