Mathematica Examples

## C. Mathematica as a "front-end" to External Programs.

### Example C.1: The Method of Moments and Analysis of a V-Dipole.

The method of moments can be applied to solve very general three-dimensional radiation and scattering problems. A typical problem may involve surface and wire structures that are excited by multiple voltage sources and/or plane-waves. However, increasing the complexity of the problem corresponds to a proportional increase in the computational expense. The next example shows the use of the method of moments in performing the full-wave analysis of a V-dipole antenna. The following also demonstrates the use of the job submission feature of WebMath that allows method of moments programs (or any code) to run unattended.

#### Submission

 -UnixWebMath-

Input Block:

#### Adjacent images can be compiled into a movie and 3D graphics can be converted to a VRML format: Note:VRML images require a VRML viewer and Movies require a MPEG viewer.

Select a display mode

#### Enter values in this section only if you are submitting a job for later retrieval:

Title for job:
Brief description of the job:

 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)

#### Submission Verification

WinWebMath --
Your job has been sucessfully submitted and is underway. When it is completed it will be added to the completed jobs list:
Completed Jobs
This script was developed at the Center for ComputationalElectromagnetics (CCEM) - University of Illinois at Urbana with fundingfrom the Sloan Center for Asynchronous Learning Environments (SCALE)

#### Posted Results

 -UnixWebMath-

In[1] :=

```  frequency=300.;
lgth=.80;
angle=80.5;
<< notebooks/vdipole/fort.m;
<< notebooks/PatPlot.m;
Print["Input Impedance (Re, Im): ",zin];
Print["Directivity: ", dir];
PatPlot2DAll[vdipole];
PatPlot3D[vdipole, PlotPoints -> 60];```
 Mathematica Output
`Input Impedance (Re, Im): {148.2734, 272.5063}`
`Directivity: 3.12395`

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 C.2: The Method of Moments Analysis of a LPMA.

The method of moments is one of the most widely used techniques for analyzing radiation problems. The following series of examples show how Mathematica and WebMath can be effectively used as an interface for codes based on that method.

The following simulation is done by a wire antenna MoM code running in conjuction with a simple transmission line code. Together these programs can perform the full-wave analysis of log-periodic dipole and monopole arrays operating in free-space. The ouput is then interpreted by Mathematica and displayed in a illustrative format.

 -UnixWebMath-

Input Block:

#### Adjacent images can be compiled into a movie and 3D graphics can be converted to a VRML format: Note:VRML images require a VRML viewer and Movies require a MPEG viewer.

Select a display mode

#### Enter values in this section only if you are submitting a job for later retrieval:

Title for job:
Brief description of the job:

 Mathematica Output

`Magnitude bar for relative admittance matrix contours:`

```Contour Plot of Admittance matrix for the Radiating elements(without feeder):
```

```Elemental Impedances (real part, smallest element to largest element):
Element   1    ->   2.94364 - 1657.64 I    Ohms
Element   2    ->   3.91626 - 1375.27 I    Ohms
Element   3    ->   5.59608 - 1131.71 I    Ohms
Element   4    ->   7.89697 - 917.689 I    Ohms
Element   5    ->   11.1576 - 723.907 I    Ohms
Element   6    ->   16.0757 - 551.064 I    Ohms
Element   7    ->   23.534 - 388.474 I     Ohms
Element   8    ->   36.1247 - 231.888 I    Ohms
Element   9    ->   59.1635 - 68.954 I     Ohms
Element   10   ->   100.904 + 121.111 I    Ohms
VSWR = 1.5398  For provided Zs.
Real[Zin]  = 42.71687 - 18.7385 I
```
 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)

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