Electrodynamic modeling of microwave structures and antennas is an important stage in the design of complex radio engineering systems. To solve these problems, developers use powerful and effective CAD tools, which implement a wide range of electromagnetic modeling methods. One of these tools is the FEKO software package from Altair. FEKO is a multifunctional software environment for numerical electromagnetic modeling based on modern computing technologies. Let's look at how FEKO solves the problem of ensuring electromagnetic compatibility of antenna systems installed on aircraft.

The requirements for computing resources of computers used for electromagnetic modeling increase as the complexity and physical size of antenna systems increase. At a certain point in time, the resources available to calculate electrically large objects may not be enough. To solve this problem, the FEKO software package provides the following features:

An efficient solver writes matrix blocks to a hard disk during operation, allowing you to handle complex tasks on computers with less RAM;

parallel processing of the problem being solved on multicore processors is used;

The multi-Level Fast Multipole Method (MLFMM) significantly reduces the need for computing resources compared to the Method of Moments (MoM);

approximate asymptotic methods, such as the method of physical Optics (Physical Optics – PO) and the method of uniform Theory of diffraction (Uniform Theory of Diffraction – UTD), are ideal for solving problems of radiation and scattering of electrically very large objects.

Analyzing the scattering of an electromagnetic field on electrically large objects has always been a difficult task. To achieve high calculation accuracy, FEKO usually uses MoM or MLFMM electrodynamic analysis methods. Asymptotic methods such as the RO method are used for electrically large structures. However, the use of electrodynamic methods on large objects is limited by computer computing resources, while the PO method can use a very dense partition grid, which dramatically increases the calculation time.

To solve these problems, FEKO implemented the Ray–propagated geometric optics (Ray Launching Geometric Optics - RL-GO) method, which allows the use of plane wave excitation. The RL-GO method is based on the modeling of rays incident and reflected from the model of objects, in accordance with the theory of propagation, reflection and refraction of optical rays. The effect of rays on metallic and dielectric structures is modeled using Huygens sources placed at each point of contact of the rays with material boundaries. The ray launching process is easy to control based on the angular (for localized sources) or transverse (for plane wave sources) ray interval and the number of multiple allowed interferences.

The RL-GO method provides a high degree of coincidence of results with the MLFMM method with lower requirements for computer computing resources. An example of modeling the scattering of an electromagnetic field on an aircraft (Fig.1) shows that the RL-GO method requires only 4.6 MB of memory, while the MLFMM method requires 441 MB with a significantly longer calculation time. Such a radical reduction in computing resource requirements is a crucial factor in solving complex problems.

The requirements for computing resources of computers used for electromagnetic modeling increase as the complexity and physical size of antenna systems increase. At a certain point in time, the resources available to calculate electrically large objects may not be enough. To solve this problem, the FEKO software package provides the following features:

An efficient solver writes matrix blocks to a hard disk during operation, allowing you to handle complex tasks on computers with less RAM;

parallel processing of the problem being solved on multicore processors is used;

The multi-Level Fast Multipole Method (MLFMM) significantly reduces the need for computing resources compared to the Method of Moments (MoM);

approximate asymptotic methods, such as the method of physical Optics (Physical Optics – PO) and the method of uniform Theory of diffraction (Uniform Theory of Diffraction – UTD), are ideal for solving problems of radiation and scattering of electrically very large objects.

Analyzing the scattering of an electromagnetic field on electrically large objects has always been a difficult task. To achieve high calculation accuracy, FEKO usually uses MoM or MLFMM electrodynamic analysis methods. Asymptotic methods such as the RO method are used for electrically large structures. However, the use of electrodynamic methods on large objects is limited by computer computing resources, while the PO method can use a very dense partition grid, which dramatically increases the calculation time.

To solve these problems, FEKO implemented the Ray–propagated geometric optics (Ray Launching Geometric Optics - RL-GO) method, which allows the use of plane wave excitation. The RL-GO method is based on the modeling of rays incident and reflected from the model of objects, in accordance with the theory of propagation, reflection and refraction of optical rays. The effect of rays on metallic and dielectric structures is modeled using Huygens sources placed at each point of contact of the rays with material boundaries. The ray launching process is easy to control based on the angular (for localized sources) or transverse (for plane wave sources) ray interval and the number of multiple allowed interferences.

The RL-GO method provides a high degree of coincidence of results with the MLFMM method with lower requirements for computer computing resources. An example of modeling the scattering of an electromagnetic field on an aircraft (Fig.1) shows that the RL-GO method requires only 4.6 MB of memory, while the MLFMM method requires 441 MB with a significantly longer calculation time. Such a radical reduction in computing resource requirements is a crucial factor in solving complex problems.

The advantages of the RL-GO method are also clearly evident in the analysis of mirror antennas and lenses. In this case, the best option is a combination of RL–GO and MoM methods. Radiation antennas illuminating a lens or mirror can be modeled using the MoM method, and when working with a large structure, the RL-GO method using far-field or near-field communication is very effective.

One of the important tasks facing designers of aircraft radio channels is to ensure electromagnetic compatibility (EMC) of radio channels. The need to solve it is due, firstly, to a large number of various electronic means (RES), including those with overlapping frequency ranges, and secondly, to the rapidly changing relative position of aircraft in space and in grouping.

To ensure electromagnetic compatibility (EMC), the operation of the RES as part of the complex (switching on, off, switching modes of operation) should be regulated according to spatial (antenna directional patterns), frequency and time spacing. This can be achieved by creating a control system for the parameters of electromagnetic radiation (frequency, power and time modes, as well as the direction of antenna radiation) of all mutually influencing RES [1].

When solving this problem, it is required to determine the in-system electromagnetic situation in real time, including the calculation of the electromagnetic coupling coefficients in pairs of all antennas of the RES complex (each with each). At the same time, the complexity of the aircraft geometry, which affects the radiation characteristics of antennas, necessitates the use of electrodynamic calculation methods that require significant computing resources [2].

At the preliminary stage, a limited discrete set of scenarios for the relative location of aircraft in space is formed in the MATLAB software environment. With the help of a computer with the necessary computing resources, a series of corresponding tasks are solved at the electrodynamic level. Based on the results of the electrodynamic calculation of the electromagnetic coupling coefficients of all antennas of the RES complex in pairs, a database (DB) is formed for a variety of scenarios. After the necessary compilation, the database is placed in the onboard computers of all aircraft for subsequent use of data in real time.

Within the framework of the concept under consideration, three classes of tasks can be distinguished at the electrodynamic level:

calculation of the coupling coefficients of each pair of antennas on one side (for each aircraft grouping). This class of tasks also includes the tasks of determining the coupling coefficients of the antennas of one side when other aircraft are located nearby, the fuselages of which affect the analyzed connections;

determination of radiation parameters in the far zone for all antennas, taking into account the influence of its own fuselage and neighboring (for example, shading) aircraft. The results of calculating the radiation patterns of all antennas for various scenarios of the relative position of the aircraft in space form an array of data of moderate volume (in the form of approximating functions or their discrete representation);

attenuation of mutual interference and interference from own current-carrying parts The device is designed to increase the signal-to-noise ratio when receiving and processing communication, guidance and tracking signals.

Quarter-wave vibrators on the metal body of the aircraft are implemented as antennas in the aircraft models. The wired ports are located at the bases of the vibrators. The spatial location of each aircraft (Fig.2) is determined by the coordinates of the origin of the associated coordinate system (SC) of each aircraft relative to the earth SK and the orientation of its axes, described by three Euler angles (heading angle, pitch angle and roll angle).

One of the important tasks facing designers of aircraft radio channels is to ensure electromagnetic compatibility (EMC) of radio channels. The need to solve it is due, firstly, to a large number of various electronic means (RES), including those with overlapping frequency ranges, and secondly, to the rapidly changing relative position of aircraft in space and in grouping.

To ensure electromagnetic compatibility (EMC), the operation of the RES as part of the complex (switching on, off, switching modes of operation) should be regulated according to spatial (antenna directional patterns), frequency and time spacing. This can be achieved by creating a control system for the parameters of electromagnetic radiation (frequency, power and time modes, as well as the direction of antenna radiation) of all mutually influencing RES [1].

When solving this problem, it is required to determine the in-system electromagnetic situation in real time, including the calculation of the electromagnetic coupling coefficients in pairs of all antennas of the RES complex (each with each). At the same time, the complexity of the aircraft geometry, which affects the radiation characteristics of antennas, necessitates the use of electrodynamic calculation methods that require significant computing resources [2].

At the preliminary stage, a limited discrete set of scenarios for the relative location of aircraft in space is formed in the MATLAB software environment. With the help of a computer with the necessary computing resources, a series of corresponding tasks are solved at the electrodynamic level. Based on the results of the electrodynamic calculation of the electromagnetic coupling coefficients of all antennas of the RES complex in pairs, a database (DB) is formed for a variety of scenarios. After the necessary compilation, the database is placed in the onboard computers of all aircraft for subsequent use of data in real time.

Within the framework of the concept under consideration, three classes of tasks can be distinguished at the electrodynamic level:

calculation of the coupling coefficients of each pair of antennas on one side (for each aircraft grouping). This class of tasks also includes the tasks of determining the coupling coefficients of the antennas of one side when other aircraft are located nearby, the fuselages of which affect the analyzed connections;

determination of radiation parameters in the far zone for all antennas, taking into account the influence of its own fuselage and neighboring (for example, shading) aircraft. The results of calculating the radiation patterns of all antennas for various scenarios of the relative position of the aircraft in space form an array of data of moderate volume (in the form of approximating functions or their discrete representation);

attenuation of mutual interference and interference from own current-carrying parts The device is designed to increase the signal-to-noise ratio when receiving and processing communication, guidance and tracking signals.

Quarter-wave vibrators on the metal body of the aircraft are implemented as antennas in the aircraft models. The wired ports are located at the bases of the vibrators. The spatial location of each aircraft (Fig.2) is determined by the coordinates of the origin of the associated coordinate system (SC) of each aircraft relative to the earth SK and the orientation of its axes, described by three Euler angles (heading angle, pitch angle and roll angle).

Thus, the instantaneous position of each aircraft is characterized by six generalized coordinates. To describe scenarios of the relative position of aircraft in space, the concept of fuzzy generalized coordinates (NOC) of each aircraft grouping (three Cartesian coordinates of the origin of the associated SK and three Euler angles) [1].

Fuzzy generalized coordinates are a fuzzy subset from the universal (basic) set Q of generalized coordinates q! Q, which has a normal and convex multidimensional membership function µc(q!), that is, such that, firstly, there is a carrier value in which the membership function is equal to one, and secondly, when departing from its maximum in any direction, the membership function does not increase.

For the problem under consideration in [1], it is proposed to use unimodal NOC when the membership function of the fuzzy coordinate C has a maximum value only at a single point (more precisely, it has an infinitesimal tolerance region). On each NOC carrier, to describe a physical quantity, we define an approximating function φc(q!). Each of these functions can be constructed in various ways: using different analytical functions, or by training artificial neural networks (you can get the most accurate approximation). The method of constructing approximating functions for each task is chosen based on two quality indicators: approximation accuracy and minimization of computing resources.

To solve the problem under conditions of a random distribution of the aircraft position and, as a result, the communication and guidance characteristics, the following algorithm is used [3]:

a discrete set of scenarios for the spatial location of the LA grouping in the associated SC of the LA transmitter is formed, in which the LA receiver and other LA affecting the propagation of electromagnetic radiation are located in the modes of the NOC {Cn}. Many scenarios are being built for each pair of antennas;

For each scenario, the electromagnetic coupling coefficient for the considered pair of antennas in the FEKO environment is determined. By calculating the coupling coefficients for arbitrary values A system of approximating (basic) functions φ(q) is formed and the approximating function of the electromagnetic coupling coefficient of the antennas is determined. All these calculations are performed in the "home" mode;

the limited amount of information received ! (the set of cn modes) and the system of approximating (basic) functions φ(q) for each scenario are stored in the onboard computers of the aircraft.;

Relative generalized q coordinates are calculated in real time for each pair of antennas on board the aircraft! and the corresponding coupling coefficient is determined.

Consider a monopole antenna located on a metal plane of finite size in space (Fig.3). Such an antenna has no radiation along the vertical axis. We can say that this is the direction along which signal suppression is observed.

Fuzzy generalized coordinates are a fuzzy subset from the universal (basic) set Q of generalized coordinates q! Q, which has a normal and convex multidimensional membership function µc(q!), that is, such that, firstly, there is a carrier value in which the membership function is equal to one, and secondly, when departing from its maximum in any direction, the membership function does not increase.

For the problem under consideration in [1], it is proposed to use unimodal NOC when the membership function of the fuzzy coordinate C has a maximum value only at a single point (more precisely, it has an infinitesimal tolerance region). On each NOC carrier, to describe a physical quantity, we define an approximating function φc(q!). Each of these functions can be constructed in various ways: using different analytical functions, or by training artificial neural networks (you can get the most accurate approximation). The method of constructing approximating functions for each task is chosen based on two quality indicators: approximation accuracy and minimization of computing resources.

To solve the problem under conditions of a random distribution of the aircraft position and, as a result, the communication and guidance characteristics, the following algorithm is used [3]:

a discrete set of scenarios for the spatial location of the LA grouping in the associated SC of the LA transmitter is formed, in which the LA receiver and other LA affecting the propagation of electromagnetic radiation are located in the modes of the NOC {Cn}. Many scenarios are being built for each pair of antennas;

For each scenario, the electromagnetic coupling coefficient for the considered pair of antennas in the FEKO environment is determined. By calculating the coupling coefficients for arbitrary values A system of approximating (basic) functions φ(q) is formed and the approximating function of the electromagnetic coupling coefficient of the antennas is determined. All these calculations are performed in the "home" mode;

the limited amount of information received ! (the set of cn modes) and the system of approximating (basic) functions φ(q) for each scenario are stored in the onboard computers of the aircraft.;

Relative generalized q coordinates are calculated in real time for each pair of antennas on board the aircraft! and the corresponding coupling coefficient is determined.

Consider a monopole antenna located on a metal plane of finite size in space (Fig.3). Such an antenna has no radiation along the vertical axis. We can say that this is the direction along which signal suppression is observed.

Changing the position of the antenna's directional pattern (DN) allows you to track the direction of interference and suppress it, thus increasing the signal-to-noise ratio at the receiver input. However, when installing such an antenna on the body of a complex aircraft, the type of bottom changes noticeably (Fig.4). To change the position of the receiving antenna on the housing, you can use the DN, calculated as a separate task, as a receiving antenna (receiver antenna) and change the position of only this object to solve the problem of communication and field scattering.

Let's calculate an aircraft with a length of 20 m at a frequency of 200 MHz. The calculation time using the MLFMM method on a computer with 16 GB RAM and a processor clock speed of 1 GHz is 10 minutes per frequency point.

In addition to calculating the DN, this method allows you to determine the connection between the antennas located on the aircraft body in the frequency range, as well as optimize the position of the antennas. A three-dimensional DN recorded in a file can be used both to describe the excitation of such an antenna in the form of a point source, and as a receiving antenna with the same DN. Thus, the task of aircraft interaction, taking into account the NOC, is simplified and reduced to analyzing the characteristics of radio channels. To evaluate the total power received by the antenna, as well as the scattering induced by metal objects, FEKO provides a special option Include Only the Scattered Part of the Field (only the scattered part of the field). This option is used to estimate the total and scattered part of the power received by individual antennas mounted on a complex-shaped aircraft.

Let's calculate the power on individual receiving antennas deployed in space at an angle of 0, 10 and 30°, when irradiated with a plane wave incident at various angles in the range Θ = 0-90° (Fig.5).

In addition to calculating the DN, this method allows you to determine the connection between the antennas located on the aircraft body in the frequency range, as well as optimize the position of the antennas. A three-dimensional DN recorded in a file can be used both to describe the excitation of such an antenna in the form of a point source, and as a receiving antenna with the same DN. Thus, the task of aircraft interaction, taking into account the NOC, is simplified and reduced to analyzing the characteristics of radio channels. To evaluate the total power received by the antenna, as well as the scattering induced by metal objects, FEKO provides a special option Include Only the Scattered Part of the Field (only the scattered part of the field). This option is used to estimate the total and scattered part of the power received by individual antennas mounted on a complex-shaped aircraft.

Let's calculate the power on individual receiving antennas deployed in space at an angle of 0, 10 and 30°, when irradiated with a plane wave incident at various angles in the range Θ = 0-90° (Fig.5).

Then we place the element of the calculated antenna base on the full aircraft model and calculate the dependence of the scattered part of the power on the angle of incidence (Fig.6). Having calculated this parameter in all directions with a given angular pitch, we obtain the necessary information to form a data bank using which the processor will correct the signals received from a given direction.

In the latest versions of FEKO, another method has been implemented – calculation in the time domain. In this case, the incident radio pulse of the electromagnetic field, deployed along the time axis, allows us to isolate the time process of both the incident and reflected pulse that appeared at the antenna input due to reflection from the rear tail and from the metal current-carrying parts of the aircraft body (Fig.7).

The powerful FEKO electrodynamic modeling CAD allows you to calculate the radiation patterns of large antenna systems installed on aircraft in conditions of fuzzy coordinate systems. When the communication between aircraft constantly changing their position relative to each other is random, it is important to ensure high accuracy and speed of calculation. This article shows how using FEKO CAD it is possible to improve communication between radio channels and minimize induced spatial interference.

Literature

- Kurushin A.A., Muhkerya I.V., Podkovyrin S.I. Determination of electromagnetic connections of antennas of radioelectronic means in the grouping of aircraft // International conference "Radioelectronic devices and systems for infocommunication technologies" REDS-2015 RNTORES named after A.S.Popov. Reports. Series: Scientific conferences dedicated to Radio Day (issue LXX). – M., 2015. pp. 262-265.
- Banks S.E., Gribanov A.N., Kurushin A.A. Electrodynamic modeling of antenna and microwave structures using FEKO. – M., OneBook, 2013.
- Vedenkin D.A., Latyshev V.E., Sedelnikov Yu.E. Evaluation of antenna coupling coefficients for the tasks of providing EMC for on-board REO of promising unmanned aerial systems // Journal of Radioelectronics. 2014. No 12.