# A Phased Array Antenna with New Elements Designed Using Source Transformations

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## Abstract

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## Featured Application

**The proposed array will have future applications in structurally integrated and conformal phased array antennas for wireless communications, radars, and sensing where antenna performance is a function of structural and mechanical restraints.**

## Abstract

## 1. Introduction

^{®}are used to numerically analyze and demonstrate the performance of the proposed TO-based antenna array for phased array scanning. The proposed “pinwheel” antenna array has potential applications in structurally integrated and conformal phased array antennas where the antenna performance is a function of structural and mechanical restraints. The “pinwheel” transformation shows that with the approach of the transformation electromagnetics/optics, it is possible to design electromagnetic structures and devices of many different complex and arbitrary geometries. Antennas designed in this way have many advantages compared to standard dipole antennas. A “pinwheel”-shaped antenna can be embedded into transformed regions to avoid interference, such as the cloak. The “pinwheel”-shaped antenna may also make use of the inherent properties of metamaterials to meet unique design parameters. For instance, a transformation designed antenna such as a “pinwheel”-shaped antenna may have less overall metal than a standard dipole antenna. The natural dispersion of metamaterials may then result in an antenna that interferes only very weakly at frequencies away from its frequency of operation. Under certain circumstances, the overall weight of the antenna may also be reduced compared to standard dipole antennas.

## 2. Theoretical Model of “Pinwheel” Antenna Array

**Figure 1.**Proposed material-embedded antenna array using TO technique: (

**a**) “pinwheel” transformation of a single dipole antenna element with TO-embedded media; (

**b**) transformation of linear dipole array (reference array) (left) into a linear array of “pinwheel” antenna elements (right).

## 3. Full-Wave Simulation Results and Discussion

^{®}. The transformation electromagnetics/optics (TE/TO) approach often results in anisotropic, non-homogeneous, and complex material parameters in matrix form. COMSOL Multiphysics has the capability to validate works related to transformation electromagnetics/optics, as it allows the specification of material anisotropy and continuous inhomogeneity, as found in [13,14,15,16,17,18]. The work presented here adopts the validation process presented in [13,14,15,16,17,18] by comparing theory with COMSOL results. In the “pinwheel” transformation, along with the transformed current source from Equation (6) and transformed material parameters from Equation (7), the “pinwheel” shaped antenna geometry is also a function of the proposed transformation. COMSOL Multiphysics has a unique functionality, which allows the definition of the complex “pinwheel” shaped geometry and material, as opposed to other commercially available full-wave tools. First, the single element, as shown in Figure 1a, was simulated to verify the transformed current from (6) and the transformed media from (7). Simulation results from a half-wave ($\lambda /2)$ dipole antenna in free-space are shown in Figure 3a. A frequency of 10 GHz was chosen. If the dipole is twisted by an angle of 180° without proper material compensation from (7), the field pattern changes significantly, which is demonstrated in Figure 3b. The field pattern is recovered outside the transformation media once the correct material is used from (7), which is illustrated in Figure 3c. The fields from the dipole in Figure 3a and the transformed “pinwheel” antenna in Figure 3c outside the material shell are the same. This is emphasized in Figure 3d, which shows almost no field distribution outside the transformation media when the difference between the two fields is taken. This also confirms that the current distribution in (1) is conserved under the “pinwheel” coordinate transformation in (6).

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Spatial variation of material parameters inside the shell (

**a**) ${\mathsf{\epsilon}}_{\mathrm{xx}}={\mu}_{xx}$, (

**b**) ${\epsilon}_{xy}={\mu}_{xy}={\epsilon}_{yx}={\mu}_{yx},$ (

**c**)${\epsilon}_{yy}={\mu}_{yy.}$ The material parameters ${\epsilon}_{xy}$, ${\mu}_{xy},$ ${\epsilon}_{yx},$ and ${\mu}_{yx}$ are equal.

**Figure 3.**The z-component of the magnetic field of single antenna element from: (

**a**) dipole antenna of length L = $\lambda /2$ in free-space; (

**b**) dipole that has undergone a “pinwheel” rotation of $\u2206\theta =$ 180° without any material compensation from Equation (7); (

**c**) dipole that has undergone a “pinwheel” rotation of $\u2206\theta =$ 180° with proper material compensation from Equation (7); and (

**d**) the difference between the fields (

**a**,

**c**).

**Figure 4.**Total electric field distributions for three different array configurations for a scan angle of ${\theta}_{s}=$22.5° for (

**a**) reference/original dipole antenna linear array, (

**b**) “pinwheel” antenna array without any material compensation, (

**c**) material-embedded “pinwheel” shaped antenna linear array, and (

**d**) difference between the electric fields in (

**a**,

**c**).

**Figure 5.**Far-field radiation patterns for three different array configurations at scan angles of (

**a**) ${\theta}_{s}=$22.5° and (

**b**) ${\theta}_{s}=$ 11.25°.

**Figure 6.**The electric fields for the proposed TO-based “pinwheel” array for different values of loss factor ($tan\delta $) (

**a**)$tan\delta =0.01$; (

**b**)$tan\delta =0.1$; (

**c**)$tan\delta =0.3$; (

**d**)$tan\delta =0.5$.

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**MDPI and ACS Style**

Mitra, D.; Dev, S.; Lewis, J.; Cleveland, J.; Allen, M.S.; Allen, J.W.; Braaten, B.D. A Phased Array Antenna with New Elements Designed Using Source Transformations. *Appl. Sci.* **2021**, *11*, 3162.
https://doi.org/10.3390/app11073162

**AMA Style**

Mitra D, Dev S, Lewis J, Cleveland J, Allen MS, Allen JW, Braaten BD. A Phased Array Antenna with New Elements Designed Using Source Transformations. *Applied Sciences*. 2021; 11(7):3162.
https://doi.org/10.3390/app11073162

**Chicago/Turabian Style**

Mitra, Dipankar, Sukrith Dev, Jacob Lewis, Jerika Cleveland, Monica S. Allen, Jeffery W. Allen, and Benjamin D. Braaten. 2021. "A Phased Array Antenna with New Elements Designed Using Source Transformations" *Applied Sciences* 11, no. 7: 3162.
https://doi.org/10.3390/app11073162