Mathematica Examples

## D. Antenna Array Analysis and Design Using JavaTM Enhanced Mathematica Interfaces.

• Example D.1: Point-and-Click Code Generation
• Example D.2: Non-Uniformly Excited Equally Spaced Linear Array Simulation (non-WebMath supported)
• Example D.3: Uniformly Excited Equally Spaces Linear Array Directivity (non-WebMath supported)

### Example D.1: Point-and-Click Code Generation.

The following JavaTM applet replaces the form interface, illustrated in Section B.4, to facilitate the definition of an array structure. The user places marks in the location of isotropic elements, instead of entering element coordinates through the form. A single structure, once entered, can be scaled in terms of wavelengths which allows anaylsis of the same array structure at different frequencies. Once submitted, the code generated for analysis is processed in WebMath noninteractive mode (i.e. through the job submission routines).

#### Verification and Final Submission of Task

The submission window gives the user an opportunity to:

• enter a title and description of the job being subitted.
• (optionally) add his/her e-mail address for notification of the task's completion.
• edit the generated code to add new commands or change the anaylsis method.
• copy the code for future use in a simple form.
• learn how to enter code calling similar Mathematica functions in the future.

#### Posted Results

As mentioned above, the jobs submitted through JavaTM interfaces are processed in the noninteractive mode and the results are stored in a static page on the AWS. The following illustrates the format of the static output after processing the above job.

 -UnixWebMath-

In[1] :=

```<< notebooks/ArrPck.m;
<< notebooks/ArrOpt.m;
geom = {
{-0.6000000000000001,0.5900000000000001,0},
{-0.21000000000000002,0.2,0},
{0.2,-0.19000000000000003,0},
{0.6000000000000001,-0.6000000000000001,0},
{0.19000000000000003,0.6100000000000001,0},
{0.5900000000000001,0.2,0},
{-0.6200000000000001,-0.2,0},
{-0.21000000000000002,-0.6000000000000001,0}
};
array=maxDarrayForQ[geom,0.7853981633974483,0.0,2.0,20];
AF3Ddemo[array,PlotPoints->45];
```
 Mathematica Output
```Condition number for this array problem: 17.820879367577734686

Current values for optimal Directivity with Q = 2.:

0.6264502767177395 - 0.03645915531027452 I
-0.588624835347133 - 0.5785366889814525 I
-0.03158264246083917 - 0.3079834077684028 I
0.4420188841759283 - 0.1572778176768101 I
-0.228570527263726 - 0.06083841512181934 I
0.1907858804043586 - 0.4783748800693714 I
0.861098309783999 + 0.1766758942804685 I
-0.4304027379074689 - 0.2574817653901749 I

```

```Directivity is: 3.80875
```

rendition of:

rendition of:

 Processed by Mathematica version 2.2 running on a UNIX platform. This script was developed at the Center for Computational Electromagnetics (CCEM) - University of Illinois at Urbana with funding from the Sloan Center for Asynchronous Learning Environments(SCALE)

### Example D.2: Non-Uniformly Excited Equally Spaced Linear Array Simulation

This applet displays the radiation field (magnitude of the electric field) of a linear antenna array.

The menu bar at the bottom allows the user to choose between a fixed linear scale and a dB scale with a dynamic range for more accurate viewing of sidelobes. The scrollbars allow the user to:

• (num) select the number of radiating elements,
• (dist) select the distance between the array elements (in units of wavelength/100),
• (phase) select the phase shift between elements (in degrees),
• (AMPLITUDES) select the amplitudes of the current fed into each element,
• (dynamic range,to be used with the dB scale mode) select the -dB level that corresponds to the origin of the pattern plot. The outer ring is 0 dB.
• View the source.

### Example D.3: Uniformly Excited Equally Spaces Linear Array Directivity

#### (3 element types: isotropic, collinear short dipole & parallel short dipoles)

This applet displays the directivity versus operating frequency of a linear antenna array constructed of one of three possible element types. The horizontal axis represents element separation in wavelengths.

The scrollbars allow you to:

• (number of elements) select the number of radiating elements,
• (phase difference) select the progressive phase shift between adjacent elements in degrees,
• (scale factor) set the Directivity scale for a more accurate reading of values for different settings.
• View the source.

### Click on graph to refresh

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