In fields like astronomy and radar technology, high-gain antennas are required for long-distance communication. Due to its relatively large gain, the use of parabolic antennas has become very popular over time, because they can easily achieve gains of above 30 dB at microwave and higher frequencies. Today, most systems’ success depends on how well the antennas perform. These antennas are available in different types and sizes. Each antenna’s effective area usually has less than the actual physical area of the antenna surface. This means that the unused area of the antenna is massive, and a waste. The aim of the research is to show that the actual physical aperture of a parabolic antenna can be reduced as much as possible to equal the effective area, as given by the antenna formula, thereby saving manufacturing costs, improve the aesthetics. In other words, the focus of this work is to experimentally show that reflector antenna can be made of smaller sizes but better performance. Measurements were taken from different positions from a parabolic antenna, the signal level measured and compared with signal levels for optimal performance.
Over the years, parabolic antenna usage has become very popular because of its extreme large gain at high frequencies, the gain limited by the physical size of the parabolic reflector. Today, the success of many systems depends on how functional the antennas used for them are. These antennas come in various types and sizes: wired antennas, aperture antennas, array antennas, reflector antennas, lens antennas, micro-strip antennas, etc. Antennas can be classified in terms of their [
Theory of the Parabolic Reflector Antenna
The reflector or antenna has two purposes, first they collect power in terms of electrical signals (scintillations) and second, they provide directionality, for propagation of electromagnetic signal [
The parabolic surface of the antenna in
ρ ′ 2 = 4 F ( F − z f ) , p ′ ≪ a (1)
Here, ρ ′ is the distance from a point A to the focal point O, where A is the projection of the point R on the reflector surface onto the axis-orthogonal plane (the aperture plane) at the focal point [
The position of R can be modeled by a pair of coordinates in either rectangular ( ρ ′ , z f ) or the polar ( r f , θ f ). The distance r f and the focal length F is related by:
r f = 2 F 1 + cos θ f = F cos 2 ( θ f 2 ) (2)
The displacement P ′ from the axis of the reflector is given by:
ρ ′ = r f sin θ f = 2 F sin θ f 1 + cos θ f = 2 F tan θ f 2 (3)
A common parameter used in specifying a parabola is the F/D ratio. When F/D approaches infinity, the reflector becomes flat. Commonly used paraboloidal shapes are shown below in
Though the paraboloidal reflector is asymmetric, it is rotational symmetric.
To determine the angel from the feed-point to the reflector length, we use the relation.
θ 0 = 2 arctan [ 1 4 ( F / D ) ] (4)
For a reflector, the main design concern is matching the antenna feed pattern to the reflector, with a feed pattern of about −10 dB level in the direction of the rim, i.e. F f ( θ = θ 0 ) = − 10 dB .
Given the height of the antenna H0 and the diameter D, the focal distance D is given by
F = D 2 16 H 0 (5)
To solve Equation (5), we substitute the following values into Equation (1): ρ ′ = D / 2 & z f = F − H 0 .
Iterating different values for F/D into Equation (5), we come to the point where,
F / D = 1 / 4 . Hence H 0 = 1 / 4 .
⇒ H 0 = F i.e. the focal point is on the reflector’s rim.
In analyzing the electromagnetic distribution over the aperture, two methods are used [
1) Current distribution method, which makes use of Physical Optic (PO) approximation.
2) Aperture distribution method, which uses Geometric Optic ray tracing.
The current distribution method assumes that the incident field from the feed is known, and that it excites surface currents on the parabolic reflector’s surface as
J S = 2 n × H i (6)
By integrating the surface density over the surface of the dish, the far-field is obtained; it is assumed that the material used in the antenna is a perfectly conducting material. Using the principle of reciprocity of light, the incident rays from the fed horn is taken to be locally plan wave at the far-field [
The degree of functionality of a system depends on the different components, devices, methodologies and procedures that were carried out during the process of execution.
A schematic diagram of the various processes involved in the research is shown in
When the LNB collects radio waves from the dish, it sends out intermediate frequency (IF) to the decoder, the IF is then sent to the two-way splitter [
The measurement of the spectrum analyser is also varied by moving the strut randomly until a clear reception is seen on the television; measurement for which the DSTV service becomes very clear is taken as the threshold value. The range of values for optimal service are noted, collected, and tabulated.
The surface area of the reflector antenna is reduced in stages by covering the dish with a serrated foam which disallows the reflection of signals to the feed, to control the electromagnetic energy received at the feed. This is achieved by moving the strut slowly, then recording the values of the received energy that are close to the threshold value, needed to get a good reception on the television. Different shapes of antenna area were used, as shown in
The results obtained are used to develop mathematical models.
Antenna gain: G = ( P / S ) antenna ( P / S ) isotropic
where ( P / S ) antenna is the ratio of the intensity radiated (i.e. power per unit surface) by the antenna and ( P / S ) isotropic is the ratio of the intensity radiated (power per unit surface) by an isotropic antenna.
Decibel Conversions:
1) 0 dB = 30 dBm = 1 Watt.
2) −30 dB = 0 dBm = 0.001 Watt.
3) 10 dB = 10 dBi = 7.85 dBd.
This work focuses on the parabolic reflector antenna with the DSTV dish used as the case study. From the principle of reciprocity, when a series of radio signals fall on a reflector whose shape is that of a parabola, the signals are reflected to the focal point of the reflector i.e. these signals become concentrated on a point and they all meet at this single point. On the other hand, if another source of energy (point source) is placed at the focal point (i.e. focus) of the parabolic reflector, parallel rays of signals are reflected. These reflected parallel rays are said to be “collimated” [
The parabolic reflector antenna functions similarly to a searchlight or flashlight reflector which directs the signals in a narrow beam or receives signals from one particular direction only.
Measurement Result
Summary Results
From the tables (Tables 1-7), it is observed that:
1) There’s a slightly linear relationship between the signal quality and the surface area of the parabolic antenna, i.e. the signal strength increases with increase in aperture surface area.
2) Kang, J., Wang, W., Zhang, S., Lian, S. and Bao, H. (2021) Thermal Distortion Compensation for Improving Electrical Performance of Reflector Antennas. Open Journal of Applied Sciences, 11, 523-540. doi: 10.4236/ojapps.2021.104037.
3) In order for television viewing to be made possible, the signal strength must be between 52% and 73%.
| HEIGHT (cm) | DIAMETER (cm) | AREA (cm2) | STRENGTH (%) | SCALED AREA (cm2) | NORMALIZED STRENGTH |
|---|---|---|---|---|---|
| 90 | 80.50 | 16156.47 | 73.00 | 4.03 | 0.73 |
| 90 | 79.00 | 15822.32 | 72.00 | 3.95 | 0.72 |
| 90 | 77.50 | 15489.9 | 71.00 | 3.87 | 0.71 |
| 90 | 76.00 | 15159.2 | 71.00 | 3.78 | 0.71 |
| 90 | 74.50 | 14830.19 | 68.00 | 3.70 | 0.68 |
| 90 | 73.00 | 14502.85 | 66.00 | 3.62 | 0.66 |
| 90 | 71.50 | 14177.14 | 67.00 | 3.54 | 0.67 |
| 90 | 70.00 | 13853.06 | 64.00 | 3.46 | 0.64 |
| 90 | 68.50 | 13530.56 | 62.00 | 3.38 | 0.62 |
| 90 | 67.0 | 13209.63 | 60.00 | 3.30 | 0.60 |
| HEIGHT (cm) | DIAMETER (cm) | AREA (cm2) | STRENGTH (%) | SCALED AREA (cm2) | NORMALIZED STRENGTH |
|---|---|---|---|---|---|
| 90.00 | 80.50 | 16156.47 | 72.00 | 4.03 | 0.72 |
| 90.00 | 79.50 | 15822.32 | 71.00 | 3.95 | 0.71 |
| 90.00 | 77.50 | 15489.9 | 70.00 | 3.87 | 0.70 |
| 90.00 | 76.00 | 15159.2 | 70.00 | 3.78 | 0.70 |
| 90.00 | 74.50 | 14830.19 | 69.00 | 3.70 | 0.69 |
| 90.00 | 73.00 | 14502.85 | 67.00 | 3.62 | 0.67 |
| 90.00 | 71.50 | 14177.14 | 66.00 | 3.54 | 0.66 |
| 90.00 | 70.00 | 13853.06 | 65.00 | 3.46 | 0.65 |
| 90.00 | 68.50 | 13530.56 | 64.00 | 3.38 | 0.64 |
| 90.00 | 67.00 | 13209.63 | 60.00 | 3.30 | 0.60 |
| HEIGHT (cm) | DIAMETER (cm) | AREA (cm2) | STRENGTH (%) | SCALED AREA (cm2) | NORMALIZED STRENGTH |
|---|---|---|---|---|---|
| 90.00 | 79.00 | 15822.32 | 62.00 | 3.95 | 0.62 |
| 90.00 | 76.00 | 15159.2 | 62.00 | 3.78 | 0.62 |
| 90.00 | 73.00 | 14502.85 | 62.00 | 3.62 | 0.62 |
| 90.00 | 70.00 | 13853.06 | 61.00 | 3.46 | 0.61 |
| 90.00 | 67.00 | 13209.63 | 61.00 | 3.30 | 0.61 |
| 90.00 | 64.00 | 12572.37 | 61.00 | 3.14 | 0.61 |
| 90.00 | 61.00 | 11941.05 | 61.00 | 2.98 | 0.61 |
| 90.00 | 58.00 | 11315.47 | 60.00 | 2.82 | 0.60 |
| 90.00 | 55.00 | 10695.4 | 60.00 | 2.67 | 0.60 |
| 90.00 | 52.00 | 10080.61 | 60.00 | 2.52 | 0.60 |
| HEIGHT (cm) | DIAMETER (cm) | AREA (cm2) | STRENGTH (%) | SCALED AREA (cm2) | NORMALIZED STRENGTH |
|---|---|---|---|---|---|
| 88.50 | 82.00 | 16249.71 | 72.00 | 4.06 | 0.72 |
| 87.00 | 82.00 | 16007.47 | 72.00 | 4.00 | 0.72 |
| 85.50 | 82.00 | 15765.68 | 70.00 | 3.94 | 0.70 |
| 84.00 | 82.00 | 15524.36 | 70.00 | 3.88 | 0.70 |
| 82.50 | 82.00 | 15283.54 | 68.00 | 3.82 | 0.68 |
| 81.00 | 82.00 | 15043.23 | 64.00 | 3.76 | 0.64 |
| 79.50 | 82.00 | 14803.46 | 64.00 | 3.70 | 0.64 |
| 78.00 | 82.00 | 14564.25 | 61.00 | 3.64 | 0.61 |
| 76.50 | 82.00 | 14325.64 | 61.00 | 3.58 | 0.61 |
| 75.00 | 82.00 | 14087.64 | 60.00 | 3.52 | 0.60 |
| HEIGHT (cm) | DIAMETER (cm) | AREA (cm2) | STRENGTH (%) | SCALED AREA (cm2) | NORMALIZED STRENGTH |
|---|---|---|---|---|---|
| 87.00 | 82.00 | 16007.47 | 72.00 | 4.00 | 0.72 |
| 84.00 | 82.00 | 15524.36 | 72.00 | 3.88 | 0.72 |
| 81.00 | 82.00 | 15043.23 | 72.00 | 3.76 | 0.72 |
| 78.00 | 82.00 | 14564.25 | 71.00 | 3.64 | 0.71 |
| 75.00 | 82.00 | 14087.64 | 71.00 | 3.52 | 0.71 |
| 72.00 | 82.00 | 13613.63 | 70.00 | 3.40 | 0.70 |
| 69.00 | 82.00 | 13142.48 | 68.00 | 3.28 | 0.68 |
| 66.00 | 82.00 | 12674.5 | 65.00 | 3.16 | 0.65 |
| 63.00 | 82.00 | 12210.04 | 64.00 | 3.05 | 0.64 |
| 60.00 | 82.00 | 11749.48 | 61.00 | 2.93 | 0.61 |
| HEIGHT (cm) | DIAMETER (cm) | AREA (cm2) | STRENGTH (%) | SCALED AREA (cm2) | NORMALIZED STRENGTH |
|---|---|---|---|---|---|
| 87.00 | 82.00 | 16007.47 | 63.00 | 4.00 | 0.63 |
| 84.00 | 82.00 | 15524.36 | 63.00 | 3.88 | 0.63 |
| 81.00 | 82.00 | 15043.23 | 62.00 | 3.76 | 0.62 |
| 78.00 | 82.00 | 14564.25 | 62.00 | 3.64 | 0.62 |
| 75.00 | 82.00 | 14087.64 | 61.00 | 3.52 | 0.61 |
| 72.00 | 82.00 | 13613.63 | 61.00 | 3.40 | 0.61 |
| 69.00 | 82.00 | 13142.48 | 61.00 | 3.28 | 0.61 |
| 66.00 | 82.00 | 12674.5 | 60.00 | 3.16 | 0.60 |
| 63.00 | 82.00 | 12210.04 | 60.00 | 3.05 | 0.60 |
| 60.00 | 82.00 | 11749.48 | 60.00 | 2.93 | 0.60 |
| HEIGHT (cm) | DIAMETER (cm) | AREA (cm2) | STRENGTH (%) | SCALED AREA (cm2) | NORMALIZED STRENGTH |
|---|---|---|---|---|---|
| 88.00 | 80.00 | 15728.51 | 59.00 | 3.93 | 0.59 |
| 86.00 | 78.00 | 14982.73 | 58.00 | 3.74 | 0.58 |
| 84.00 | 76.00 | 14255.04 | 58.00 | 3.56 | 0.58 |
| 82.00 | 74.00 | 13545.44 | 58.00 | 3.38 | 0.58 |
| 80.00 | 72.00 | 12853.92 | 57.00 | 3.21 | 0.57 |
| 78.00 | 70.00 | 12180.49 | 57.00 | 3.04 | 0.57 |
| 76.00 | 68.00 | 11525.15 | 56.00 | 2.88 | 0.56 |
| 74.00 | 66.00 | 10887.9 | 56.00 | 2.72 | 0.56 |
| 72.00 | 64.00 | 10268.73 | 54.00 | 2.56 | 0.54 |
| 70.00 | 62.00 | 9667.65 | 52.00 | 2.41 | 0.52 |
4) From the tables, it was also observed that the minimum strength of the received signal must be received is about 52%. For any values below this, the decoder would be switched off.
5) From the tables, it was observed that as long as the aperture area was more than a certain percentage of the full aperture area, the decoder would be receiving sufficient power to enable clear TV viewing.
6) From the tables, it was observed that the range of values of the aperture area for which a sufficient signal was received falls between about 7800 - 16,160 cm2 after a certain area of the antenna had been covered.
7) The surface area of the full-sized parabolic antenna was found to be about 16,492 cm2 . The minimum surface area of the antenna at which a signal was received was 9667 cm2 ; by expressing this as a percentage of the full aperture area, it was found to be about 58% of this value. This means that the size of the dish can be reduced by as much as 40% of the full size yet it will still perform its needed function of making television viewing possible.
8) Theoretically, the effective aperture of an antenna is about 70% of the total aperture. From the readings taken, it was shown that the true effective aperture of the parabolic reflector antenna is much less than this, it is about 58% of the total aperture.
9) The aim of this research work was to see if the actual area of the antenna can be made to be as close as possible to the effective area without affecting the signal reception. It has therefore been shown that the aperture size can definitely be made closer to the effective aperture. It can even be made smaller than the theoretical effective aperture without deterioration in the antenna’s function.
Through the research, the manufacturing cost and purchasing cost of antennas are reduced, the parabolic reflector antenna becomes very small and therefore easy to move about and various designs for the antenna are developed.
The authors are highly indebted to the management of Covenant University, Ota, Nigeria, for the financial support fund.
The authors declare no conflicts of interest regarding the publication of this paper.
Nsikan, N., Ayoola, A., Oladoyin, O., Eberi, A. and Bobmanuel, I. (2024) Optimization of the Physical Aperture of the Parabolic Reflector Antenna. Open Journal of Applied Sciences, 14, 182-192. https://doi.org/10.4236/ojapps.2024.141014