# Applying 2D Axisymmetric Boundary Conditions in Antenna Design

October 14, 2021

### Key Takeaways

• If a body has an axis of symmetry and the boundary conditions are symmetric with respect to the axis, then the problems associated with such bodies are axisymmetric problems.

• Axisymmetric antennas are a set of antennas that exhibit rotational symmetry in geometry and material properties.

• In the finite element analysis of antenna radiation patterns, 2D axisymmetric boundary conditions are used for easy mesh truncation.

High gain antennas are often used in high-speed communications, military, and defense systems to send signals over long distances while maintaining a good signal-to-noise ratio. Often, enlarging the physical dimensions of an antenna is necessary to achieve better directional properties as well as gain.

In antenna design, computational techniques are used to model electromagnetic wave transmission. Adopting 2D axisymmetric boundary conditions in the electromagnetic modeling of antennas saves a designer’s time and computer memory.

In this article, we will discuss how 2D axisymmetric boundary conditions are used in antenna designs, but first, let’s explore axisymmetric antennas.

## Axisymmetric Antennas

Axisymmetric antennas exhibit rotational symmetry in geometry and material properties. They are a body of revolution (BOR) in antenna modeling. Conical horn antennas and corrugated horn antennas are some examples of axisymmetric antennas. These antennas are 3D structures and can be analyzed using 3D models. However, the presence of rotational symmetry allows the elimination of one coordinate axis, thus reducing the analysis into 2D axisymmetric models.

Now that we’ve discussed axisymmetric antennas, let’s take a look at solving axisymmetric problems.

## 2D Axisymmetric Boundary Conditions in Antenna Design

If a body has an axis of symmetry and the boundary conditions are symmetric with respect to the axis, then the problems associated with such bodies are axisymmetric problems. Usually, a cylindrical coordinate system (r, θ, z) is used to represent or analyze problems in 3D objects. By introducing axisymmetric boundary conditions, the system becomes independent of θ and reduces to the r-z plane.

Commonly, there are variations in the electromagnetic field distribution around the azimuth of the axis that is considered for antenna symmetry. Even with these azimuthal field variations, it is possible to obtain solutions for antenna problems by considering the 2D axisymmetric models of them. The investigation of cross-polarization, the calculation of current distribution, and antenna impedance have all become simplified with the inclusion of 2D axisymmetric boundary conditions in antenna modeling.

### Analyzing Electromagnetic Wave Transmission

In antenna design, 3D models can be set up to analyze electromagnetic wave transmission. However, 3D models of antennas take up a large amount of computer memory to analyze and solve the problems associated with electromagnetic propagation. Instead, designers can use 2D axisymmetric boundary conditions to solve these problems while using up less computer memory.

### How Using 2D Axisymmetric Boundary Conditions Saves Computer Memory

The introduction of 2D axisymmetric boundary conditions to antenna modeling helps solve electromagnetic problems with minimal computation time. When converting three-dimensional problems into 2D axisymmetric problems, some of the primary and secondary variables defining the problem become zero. The absence of primary and secondary variables reduces the size of the problem, which makes it easier for computers to solve axisymmetric problems.

### 2D Axisymmetric Boundary Conditions in Finite Element Analysis

In the finite element analysis of antenna radiation patterns, 2D axisymmetric boundary conditions are employed for easy mesh truncation. Compared to other methods, such as the method of moments or ray optical techniques, using 2D axisymmetric modeling is easier for determining the modifications in near-field and far-field antenna radiation patterns.

2D axisymmetric boundary conditions will continue to have an increasing role in antenna design, particularly in finite element analysis. Cadence software offers 2D simulation tools with the option to choose model geometry types.

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