**1. **A thin cylindrical dipole antenna of radius *a* and length 1.65*l* is driven by a time harmonic gap voltage *V*0. Develop a computer program to solve the Pocklington integral equation for the unknown antenna current distribution *I(z)* using the method of moments. Given: *a*=0.0001m , *l=*0.5m, *V*0*=*100V. Use the magnetic frill generator as the source model assuming an input impedance of the ideal 1.65l antenna. Assume the gap is *d*=1mm. Include the following in your answer:

**a.** An investigation of the element density required for adequate coverage of the numerical solution.

**b.** Plot the current distribution along the antenna.

**c.** Calculate the input impedance of the antenna and compare with the assumed impedance.

**d.** Now suppose that we are free to change the thickness of the antenna, keeping all other parameters constant. Show how the current in the antenna changes as* a* is changed from *a*=0.0001m, *to* *a*=0.005m. Compare the current along the antenna by plotting the results for the various thicknesses on a single plot. Calculate the input impedance in each case. Comment on the results.

**e.** Plot the input impedance as a function of antenna thickness for radii from 0.01mm to 5mm

**e.** Assume *a*=0.01mm and the gap is varied. Calculate the current distribution for a gap equal to *d*=0.01mm, *d*=0.1mm, *d*=0.5mm, and *d*=5mm. Compare the current along the antenna by plotting the results for the various gaps on a single plot. Calculate the antenna input impedance in each case.

**f.** Plot the antenna input impedance as a function of gap for gap values from 1mm to 100 mm.

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**2.** The same antenna as in (1) is given. Use the Hallen equation and the delta gap generator and repeat the calculations. Compare the results between the two models.

**3. **In each case defined above, calculate the radiated power of the antenna. Radiated power can be done numerically.

**4. **In each case defined above, calculate the radiation pattern in the E-plane. Plot the patterns and compare.

**5.** Discuss the results in comparison with an ideal equivalent antenna

**A note on computer program:**

1. My first preference is for you to write your own program (Matlab seems to be easiest). This is the best way to understand the intricacies of the method.

2. There are many software sources that you can use for this purpose. The following are a few sources, listed in the order of ease of use.

a. Dr. Sophocles J. Orfanidis from Rutgers University has developed comprehensive software for antenna analysis based on the Matlab toolbox. You can find these and download them at http://www.ece.rutgers.edu/~orfanidi/ewa/

b. Nasa JPL (Jet Propulsion Laboratory) has developed a very large piece of software called NEC (Numerical Electromagnetics Code). This code is in the public domain and you can get a copy of it. But it is written in FORTRAN. NEC has been developed by various people in various forms including conversions to C and has been ported to Windows. Some of these are free of charge, some are commercial. NEC2, NEC3, NEC4, MiniNec and a few others are available. The JPL website lists various versions and their availability

Of the available versions, there is one that is very easy to use and can be downloaded (actually installed) from the following web site. It is called mmona. The only problem with this software is that the manual has been translated from Japanese and is very difficult at times to follow (the guy that ported this version happens to be Japanese).

http://www.smeter.net/antennas/mmana.php

This program is based on MiniNec and is excellent for non-linear antennas.

There are many other programs available and a quick search will show you what they are. You are welcome, and encouraged, to use any of the available programs. If you find a particular program that may be useful to other students let me know.