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This paper provides a solution for the design optimization of two-dimensional impedance structures for a given elec-tromagnetic field distribution. These structures must provide electromagnetic compatibility between antennas located on a plane. The optimization problem is solved for a given attenuation of the complete field. Since the design optimiza-tion gives a complex law of impedance distribution with a large real part, we employ the method of pointwise synthesis for the optimization of the structure. We also consider the design optimization case where the structure has zero im-pedance on its leading and trailing edges. The method of moments is used to solve the integral equations and the nu-merical solution is presented. The calculated impedance distribution provides the required level of antenna decoupling. The designs are based on the concept of soft and hard surfaces in electromagnetics.

In recent years, there has been growing interest in artificial electromagnetic materials, such as electromagnetic band-gap (EBG) structures. An EBG material is a periodic structure in which electromagnetic states are not allowed at certain frequency bands (bandgaps) [

In practice, it is often required to provide significant decoupling between the receiving and transmitting antennas located on a common surface at a small distance from each other. One of the most widespread ways of reducing coupling between antennas is the use of a periodic structure [10-17]. The main point of this method consists in the fact that under certain conditions such a structure “pushes away” the field from its surface, in this way reducing the amount of energy which enters the receiving antenna.

Well-known papers from different journals [10-17] are usually devoted to the research of decoupling efficiency between antennas located on different surfaces, by using different electrodynamic structures (interference coverings and corrugated structures). In these papers, the influence on the level of antenna decoupling of different combinations of structural parameters is considered; i.e., only the task of analysis is solved. However, effective design of decoupling structures requires the solution of the design optimization problem. Probably the only example of known research where an effort is made to solve the design optimization problem of decoupling devices is in Reference [

In this paper, we propose a solution to the design optimization problem of impedance surfaces with the goal of creating effective decoupling structures. In particular, we investigate the degree of electromagnetic field (EMF) attenuation along the structure, the degree of reduction of the complete field level across the impedance part of the structure, and the decoupling level between the antennas. In addition, we determine the degree of influence of the resistive part of the impedance on the rate of the field attenuation along the impedance structure and the influence of the initial and final parts of the impedance structure on the level of the complete field.

The paper is organized as follows: In Section 2, we consider a solution to the design optimization problem of complex passive surface impedance using the law of electromagnetic field distribution. A solution to the problem using the pointwise synthesis method is given in Section 3, and numerical results are discussed in Section 4.

In this section, we consider a solution to the design optimization of a complex passive surface impedance for a given EMF distribution, and we study the achieved spatial decoupling of antenna devices located on the same plane. In practice, the problem of design optimization is solved in the absence of the second antenna, meaning the electromagnetic field decreases as a function of increasing distance from the source [

To begin the process of design optimization, we first consider a solution to the two-dimensional design problem for the arrangement shown in

where is the wave number; is the wavelength; is the zeroth-order Hankel function of the 2^{nd} kind; is the current amplitude; and is the characteristic resistance of free space. On the surface, the boundary impedance conditions of Shukin-Leontovich are fulfilled:

It is necessary to determine the dependence of the passive impedance for a given variation of the magnetic field, on the surface. Once is obtained, the complete field in the upper space is found, and then the degree of decoupling between antennas can be obtained.

To solve the problem, we use the Lorentz lemma for the upper space in

where and

is the field of an antenna radiation.

Now, we consider the complete magnetic field on the section for the entire upper space. From Equation. (3), relative to the complete field, , we obtain a Fredholm integral equation of the first kind:

(4)

The solution of Equation (4), a complete magnetic field, , on the final interval relative to, can be obtained numerically. For example, through the method of Krylov-Bogolyubov [

The problem of the optimization of the design of the complex passive surface impedance is solved in the previous section. The resulting structure gives the complex dependence of the impedance, where its real part is large and positive. The realization of such an impedance with a large real (resistive) part is a complicated task on a planar surface. However, there is another way of achieving a large value of impedance: this can in practice be realized by a corrugated structure with the depth of corrugations divisible approximately by, , even though such a structure is narrowbanded.

In this section, we consider the variation of antenna decoupling with the help of a purely reactive structure, for which the real part of the synthesized dependence of the complex impedance is simply taken as equal to zero. We assume a weak dependence of tangential components and on the impedance in Equation (1) and express the boundary impedance conditions, Equation (2), in a complex form:

(5)

Then, the solution of the system of equations

can be obtained with the help of the method of linear programming [20-23]. Here, if the real part of the impedance in Equation (6) is set to equal zero (i.e., the resistive impedance, we obtain the minimum deviation of the solution of the system of equations in Equation (6) at each point of the surface of the decoupling structure (such a synthesis is called “pointwise” [

In order to look at the behavior of the overall impedance, which is the essence of the exchange method, the relationship between the imaginary and real parts of the impedance is explicitly plotted in

· We state the complete magnetic field on the impedance part, specifying the shape of the field as:

where is the coefficient of attenuation.

The synthesized impedance must provide sharper EMF attenuation along the structure, as compared with an ideal conducting plane. The attenuation factor is defined by the value of the coefficient. As an example,

[and] for two different coefficients of attenuation, where the length of the impedance structure is. It is seen that the real parts of the impedance are positive [for (solid) and (dashed)] and two imaginary parts are negative (capacitive) [for (dotted) and (dash-dotted)]. We note here that the impedance has a monotonic increase and the magnitude of the impedance is larger when.

Next, we study the degree of the influence of this impedance on the coupling of antennas.

pendence of for the synthesized impedance (), normalized relative to the field above an ideal conducting plane, with the active component, (solid curve) and without it, , (dashed curve). The calculations show that the presence of the resistive part of the impedance not only doesn’t worsen the level of decoupling between antennas, as stated in Ref. [