# Parabolic Antenna Design

**Objective**

The objective of this experiment is to build and test a cylindrical parabolic reflector for the antenna of a wireless communication device.

Introduction

Parabolic reflectors are used in many applications, including: flashlights, optical telescopes, radio telescopes, solar ovens, and even for picking up on-field sounds from the sidelines at football games. What is so special about the parabaloid shape that makes it useful in so many applications?

A parabola is a two-dimensional curve consisting of the points that are equidistant from a point (called the *focus*) and a line (called the *directrix*). Figure 1, below (Weisstein, 1999), illustrates the essentials. The left half of the figure shows the directrix, the vertex and the focus of the parabola. The vertex is at the origin, (0, 0). The directrix (*L*) is the vertical line with x-coordinate *−a*. The focus, *F* is thus at the point (*a*,0). The right half of the figure shows graphically that the points of the parabolic curve are equidistant from *L* and *F*.

Figure 1: Diagram of a parabola, the points equidistant from the line L and the point F. |

The right half of the figure above also implies a property that makes the parabolic shape so useful in the reflector applications mentioned previously. The property is this: waves from a point source placed at the focus, *F*, are reflected by the parabolic curve as waves traveling parallel to the parabola’s axis of symmetry (the line *y* = 0). So the parabolic curve is useful in flashlights because it directs the light in a strong beam out the front.

Conversely, waves parallel to the parabola’s axis of symmetry are reflected to pass through the point, *F*. In the other applications mentioned above (optical telescopes, radio telescopes, solar ovens, and picking up on-field sounds), the parabolic reflector is acting as a *receiver*, collecting parallel waves over its surface and reflecting them to the point *F*. Both situations are illustrated in Figure 2, below (Weisstein, 1999).

Figure 2: Diagram of a parabola showing rays parallel to axis of symmetry reflected through the focus. |

The objective of this project is to build and test a cylindrical parabolic reflector for the antenna of a wireless network transceiver (either at the network access point, the computer, or both). A cylindrical parabolic curve is the three-dimensional shape swept out by a parabola as it is translated, out of the plane of the screen, along a line perpendicular to the vertex. An example is shown in Figure 3, below (Irish Solar Energy Association, Ltd). This shape is not quite as efficient as the parabolic “dish” (the figure swept out by rotating the parabola about its axis of symmetry), but it has the advantage of being much easier to make at home.

Figure 3: Example of a cylindrical parabolic mirror, from a solar heating system. |

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

- parabola,
- parabolic reflector,
- antenna,
- electromagnetic spectrum,
- wavelength,
- frequency.

Questions:

- The cylindrical parabolic surface simply reflects the radio waves from your wireless network transmitters, therefore it does not add energy to the signal. Yet, the received signal
*is*actually stronger. How can this be? - Can you think of ways that the addition of a reflector could help make your home network more secure?

Bibliography

- M. Erskine has a free template and building tips available on the site: Erskine, M. 2002. “Deep Dish Cylindrical Parabolic Template.”

http://www.freeantennas.com/projects/template/ - University of Toronto, Mathematics Network, Question and Discussion Area: finding the focus of a parabolic dish:

http://www.math.toronto.edu/mathnet/questionCorner/parabolic.html - Here is an article on the mathematics of parabolas (this is the source of the diagrams in the Introduction), Weisstein, E.W. 1999. “Parabola.” From MathWorld–A Wolfram Web Resource.

Eric W. Weisstein. “Parabola.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/Parabola.html - This is a short piece on antennas from
*Scientific American*: Fischetti, M. 2003. “Catch a Wave.”*Scientific American*, 288 (May, 2003): 88–89.

Materials and Equipment

For building the cylindrical parabolic antenna, you will need:

- cardboard square from cereal box or equivalent, 15–20 cm (approx. 6–8 in);
- aluminum foil to cover cardboard;
- white glue;
- styrofoam block, 16.5 × 7.5 × 2.5 cm (l×w×h) (approx. 6.5 × 3 × 1 in).

Note that many other choices of materials are possible. You can easily build this with materials you can find around the house (for many examples, see “Deep Dish Cylindrical Parabolic Template” website in the Bibliography).

For testing the signal strength of your wireless network with and without the antenna, you will need:

- a computer with wireless capability (preferably portable),
- a program to monitor connection quality, for example:
- many wireless cards come with a software utility that measures connection strength on 1–5 scale or something similar;
- “ping”: you can ping your router and measure the round-trip transmission time, % packets dropped.

Experimental Procedure

- Build the antenna, using the template and instructions on the “Deep Dish Cylindrical Parabolic Template” website in the Bibliography (Erskine, 2002).
- Attach the reflector to the antenna of your wireless access point.
- With the axis of symmetry of the parabolic reflector oriented toward the test computer, measure and record the signal strength.
- Rotate the reflector through a full circle, in 15° increments, testing the signal strength at each position.
- Compare with the signal strength measured
*without*the reflector. - Graph your results. A polar plot of signal strength vs. angle would be a good choice.

Variations

- Test the ability of your wireless transmitter to send a signal through obstacles that might be encountered in a typical home situation. You can do this in a couple of different ways. One method would be to move either the test computer or wireless access point (or both) in order to place more walls between them. The other method would be to simulate additional walls with pieces of gypsum wallboard placed between the transmitter and receiver. Try to create a situation with measurably decreased signal strength and see if adding the parabolic reflector improves the signal.
- The methods suggested for measuring signal strength are not particularly sensitive for small changes. You
*may*be able to make better measurements with a program designed for detecting wireless local area networks, such as NetStumbler (requires Windows 2000 or Windows XP), written by Marius Milner: http://www.netstumbler.com/downloads/.

- For more science project ideas in this area of science, see Computer Science Project Ideas

## sisay said

where is design &simulation part