Changes

Real antenna arrays have finite extents, that is, finite numbers of elements along the X and Y directions. Earlier, you saw how to excite an array of line objects using an array of lumped sources or an array of rectangular waveguides (hollow boxes) using an array of waveguide sources. Setting up array structures of this kind using [[EM.Cube]]'s '''Array Tool '''and exciting the individual elements using individual lumped or waveguide sources results in an accurate full-wave analysis of your antenna array. This type of simulation takes into account all the inter-element coupling effects as well as the finite edge and corner effects of the finite-sized array. At the end of the FDTD simulation of your antenna array, you can plot the radiation patterns and other far field characteristics of the array just like any other FDTD structure. However, depending on the total size of your array, a full-wave simulation like this may easily lead to a very large computational problem. As the number of elements grow very large, the array starts to look like an infinite periodic structure. In that case, it is possible to consider and analyze a periodic unit cell of the array structure and use an "Array Factor" representing the finite-extent topology of the array grid to calculate the radiation pattern of your antenna array. This approach works well for most large arrays. However, it ignores the finite edge and corner effects, which may be important for certain array architectures. In that case we recommend that you use [[EM.Cube]]'s [[Planar Module]]. Also, note that using an array factor for far field calculations, you cannot assign non-uniform amplitude or phase distributions to the array elements. For this purpose, you have to define an array object.

In the previous section, you saw how to excite a periodic unit cell using a lumped source or a waveguide source. You can specify the beam scan angles in the source dialogs. The finite array factor is defined in the radiation pattern dialog. At the end of the periodic FDTD simulation, you can visualize the 3D radiation patterns in the project workspace and plot the 2D Cartesian and polar pattern graphs in EM.Grid. [[EM.Cube]] also calculates the '''Directive Gain (DG)''' as a function of the θ and φ angles. This is defined as:

<math>D(\theta,\phi) = \dfrac{4\pi [S(\theta,\phi)]}{P_{rad}} =

\dfrac{4\pi \big| \mathbf{E}^{ff}(\theta,\phi) \big|^2} {\int\limits_0^{2\pi} \int\limits_0^{\pi} \big| \mathbf{E}^{ff}(\theta,\phi) \big|^2 \sin\theta \, d\theta \, d\phi}</math>

The directivity D₀ is the maximum value of the directive gain. [[EM.Cube]] generates four Cartesian graphs of directive gain in the three principal XY, YZ, ZX planes as well as in the user defined f-plane cut. The radiation patterns of antenna arrays usually have a main beam and several side lobes. Some [[parameters]] of interest in such structures include the '''Half Power Beam Width (HPBW)''', '''Maximum Side Lobe Level (SLL)''' and '''First Null [[Parameters]]''' (i.e. first null level and first null beam width). You can have [[EM.Cube]] calculate all such [[parameters]] if you check the relevant boxes in the "Additional Radiation Characteristics" section of the '''Radiation Pattern Dialog'''. These quantities are saved into ASCII data files of similar names with '''.DAT''' file extensions. You can plot graphs of such data files at the end of a sweep simulation in''' '''EM.Grid. You can also plot the directive gain as a function of the sweep variable at the end of an FDTD sweep simulation. In that case, the directive gain is computed at a fixed pair of &theta; and &phi; angles. These angles are specified in degrees as '''User Defined Azimuth & Elevation''' in the "Output Settings" section of the Radiation Pattern dialog. The default values of the user defined azimuth and elevation are both zero corresponding to the zenith. The results are saved to an ASCII data file called "DGU.DAT". Note that DGU is also one of [[EM.Cube]]'s standard output [[parameters]] and can be used to define custom output or design objectives.