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In this tutorial lesson, you will model a 4 × 4 array of probe-fed patch antennas. At an operating frequency of 1.575GHz, the free-space wavelength is about 190mm. Your patch array will have a uniform spacing of <i>S<sub>x</sub></i> = <i>S<sub>y</sub></i> = λ<sub>0</sub>/2 = 95mm in both X and Y directions.
== Building a Finite-Sized Array ==
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Next, visualize the 3D radiation pattern of the array. The directivity of the 4 × 4 patch array has now reduced to D0 = 34.0708, but the side lobe have disappeared.
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== Steering the Beam of the Finite-Sized Array ==
In the last part of this tutorial lesson, you will steer the beam of your patch antenna array. In order to steer the beam of an antenna array to the spherical angles (<i>θ</i>, <i>φ</i>), a two-dimensional phase progression among the array elements is required along the X and Y directions given by the following equations:
<math>\Psi_x = -\frac{2\pi S_x}{\lambda_0} \sin\theta \cos\phi</math>
<math>\Psi_y = -\frac{2\pi S_y}{\lambda_0} \sin\theta \sin\phi</math>
where <i>S<sub>x</sub></i> and <i>S<sub>y</sub></i> are the element spacing along the X and Y directions, respectively. In this project, S<sub>x</sub> = S<sub>y</sub> = λ<sub>0</sub>/2. The phase progression is therefore given by:
<math>\Psi_x = - \pi \sin\theta \cos\phi</math>
<math>\Psi_y = - \pi \sin\theta \sin\phi</math>
In order to steer the array beam to <i>θ </i> = <i>φ </i> = +45°, you need phase progressions equal to Ψ<sub>x</sub> = Ψ<sub>y</sub> = -90° that is equal phase progression along both X and Y directions.
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Run a new FDTD analysis of your beam-steered antenna array and visualize its 3D far-field radiation pattern. Note that the linear-scale direcitivity directivity of the steered beam has reduced to D0 = 41.4547.
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