J.J. Biebuma and Akpoilih Onoriode Emmanuel
Electrical/Electronic Engineering Department, University of Port-Harcourt, Port-Harcourt
One of the problems of satellite systems or microwave systems is interference. Interference is the combination of two or more waves having the same or different sources but arriving at a given point through different propagation path. Certain forms of interference can present particular problems for satellite systems which are not encountered in other radio systems, and minimizing these requires special attention to those features of the antenna design which control interference. Although the general principles of aperture antennas may apply to each type, the constraints set by the physical environment lead to quite different designs in each case. The goal of this research work was to model two “Parameters of the Aperture Antenna that controls interference”. The parameters were Gain and Radiation Pattern. An approximate approach was used to provide intuitive insights into the operation of the antennas, with the hope that the results obtained are reasonably accurate, and sufficient for a design in some cases.

Keywords: Aperture, antenna, microwave, transmission


A fundamental principle of antennas, called reciprocity, states that antenna performance is the same whether radiation (transmission) or reception is considered. The implication of this principle is that antenna parameters may be measured by either transmitting or receiving. The principle of reciprocity means that estimates of antenna, gain, beamwidth and polarization are the same for both transmit and receive. A useful abstraction in the study of antennas is the isotropic radiator, which is an ideal antenna that radiates (or receives) equally in all directions, with a spherical pattern, (Seybold, 1995). However in practice, most real antennas radiate better in some directions than others and cannot be isotropic. That is, no real antenna can radiate equally in all directions, and the isotropic radiator is therefore hypothetical. It does, however, provide a very useful theoretical standard against which real antennas can be compared. For a realizable antenna, there will be certain angles of radiation which provide greater power density than others (when measured at the same distance), that is, there will be one direction in which the power density is highest. To give a quantitative value to this maximum, it is compared with some reference, the most common being the power density from an isotropic antenna (Dunlop and Smith, 1994).
Procedure for the gain
The gain is an indicator of the antenna’s effectiveness, (Mithal,1994). It is the push power of the antenna. Two different models were presented for the modeling of the gain. They are
(1)        Approximating an antenna pattern using an elliptical area, and
(2)        Approximating an antenna pattern using a rectangular area.
From Kyes (2009), assuming the antenna pattern is uniform, the gain is equal to the area of the isotropic sphere (4πr2) divided by the sector (cross section) area. That is,


G = Area of sphere / Area of antenna pattern  -----------------------------------1
G = 4π / BWØazBWθel               or         4π / Øθ(radians) ---------------------2
A.        Approximating the antenna pattern as an elliptical area:










Figure 1. An ideal antenna pattern 3D view
where θ = BWθ,  and Ø = BWØ
Area of ellipse = πab ------------------------------------------------------------------------3
            a = (r sin θ) / 2             ;           b = (r sin Ø) / 2
Area = π [(r sin θ) / 2] [(r sin Ø) / 2]
            = (π r2 sin θ sin Ø) / 4 -------------------------------------------------------------4
Equation 4 is the area of antenna pattern. From equation 1
G =            Area of sphere / Area of antenna pattern
            G = (4πr2) / [(π r2 sin θ sin Ø) / 4]
            G = 4πr2 [4 / (π r2 sin θ sin Ø)]
            G = 16 / sin θ sin Ø ---------------------------------------------------------------------------5
For small angles, sin Ø = Ø in radians, so from equation 5,
            G = 16 / sin θ sin Ø = 16 / θ Ø (radians)
            G = (16 / θØ) (180o/π . 180o/π)
Note that: 1 radian = 180/π (degree)
            G = 52525 / θ Ø (degrees) -------------------------------------------------------------------6
or         G = 52525 / BWØ BWθ (degrees) -------------------------------------------------7
The second term in the equation above is very close to equation 2

B.        Approximating the antenna pattern as a rectangular area.









Figure 2. An ideal antenna pattern 3D view
where θ = BWθ, and Ø = BWØ
Area of a rectangle = ab ----------------------------------------------------------------8
a = r sin θ        ;           b = r sin Ø
Area = ab =  r2 sin θ sin Ø--------------------------------------------------------------9
G =      Area of sphere / Area of antenna pattern
    = 4πr2 / (r2 sin θ sin Ø)
    = 4π / sin θ sin Ø ---------------------------------------------------------------------1.0
For small angles, sin Ø = Ø in radians, so
G = 4π / sin θ sin Ø = 4π / θ Ø (radians)
                = (4π / θ Ø) (180o/π . 180o/π)
                = 41253 / Ø θ (degrees)
or             = 41253 / BWØ BWθ -----------------------------------------------------1.1
The second term in equation 1.1 above is identical to equation 2
            Gmax(dB) = 10 log [41253 / BWØ BWθ]-----------------------------------------------1.2

Simulation for the Gain


The graph for the gain above was as a result of entering the values of the beamwidths (phi and theta) and the final values of the beamwidths (phi and theta). These values are flexible and can be altered depending on choice. From the above simulation, it was discovered that:
1. Large angles for Ø and θ can reduce the gain and efficiency of the antenna.
2. As the angles for Ø and θ is reduced, the gain is high.
3. Gain equation is optimized for small angles.
Reduced gain and efficiency result in high interference.
Procedure for the radiation pattern
Before describing some of the practical aspects of the aperture antennas, the radiation pattern of an idealized aperture will be used to illustrate certain features which are important in satellite communications.
The idealized aperture is shown below. It consists of a rectangular aperture of sides a and b cut in an infinite ground plane. A uniform electric field exists across the aperture parallel to the side b, and the aperture is centered on the coordinate system, with the electric field parallel to the y–axis.










Perfect conducting infinite ground plane












Figure 3. An idealized aperture radiator



According to Dennis (1995), radiation from different parts of the aperture adds constructively in some directions and destructively in others, with the result that the radiation pattern exhibits a mainlobe and a number of side lobes. Mathematically, this is shown as follows. At some fixed distance r in the far field region the electric field components are given by

            Eθ(θ,Ø) = C sinØ (sin X/X) (sin Y/Y) -----------------------------------------------------1.3
            EØ(θ,Ø) = C cosθ cosØ (sin X/X) (sin Y/Y) ----------------------------------------------1.4

Here, C is a constant which depends on the distance r, the lengths a and b, the wavelength λ, and on the electric field strength Eo. For present purposes, it can be set equal to unity. X and Y are variables given by,

            X = (πa/λ) . sinθ cosØ------------------------------------------------------------------------1.5
            Y = (πb/λ) . sinθ sinØ-------------------------------------------------------------------------1.6

It will be seen that even for the idealized and hence simplified aperture situation, the electric field equations are quite complicated. The two principal planes of the coordinate system are defined as the H plane, which is the x–z plane, for which Ø=0, and the E plane, which is the x-y plane, for which Ø=90o. It simplifies matters to examine the radiation pattern in these two planes. Consider first the H plane.

With Ø = 0 it is ready shown that Y = 0, Eθ = 0, and
            X = (πa/λ) . sinθ-------------------------------------------------------------------------------1.7

And, with C set equal to unity,
            EØ(θ) = cosθ (sinX/X)------------------------------------------------------------------------1.8
The radiation pattern is given by
            g(θ) = /EØ(θ)/2---------------------------------------------------------------------------------1.9


A similar analysis may be applied to the E plane resulting in X = 0, EØ = 0, and
            Y = (πb/λ) . sinθ----------------------------------------------------------------------------1.1.0
            Eθ(θ) = sinY/Y------------------------------------------------------------------------------1.1.1
            g(θ) = /Eθ/2 ----------------------------------------------------------------------------------1.1.2


For instance if we plot the E–plane and H–plane radiation patterns for the uniformly illuminated aperture for which a = 3λ, b = 2λ.

Since the dimensions are normalized to wavelength this may be set equal to unity: l: = 1m
a: = 3.λ      ;     b: = 2.λ     ;       dB: = 1
Define a range for θ:
                     θ: = -90.deg, -88. deg..  90. deg
For the E–plane, with Ø = 90 deg:
                     Y(θ): = (π.b/λ) . sin (θ)
                     Eθ(θ): =sin(Y(θ)) / Y(θ)
                     gE (θ): = E(θ) (θ)2
                     GE(θ): = 10. Log (gE (θ))
For the H–plane, with Ø = 0 deg:
                     X(θ): = (π.a/λ) . sin (θ)
                     EØ(θ): =cos(θ) . [sin(X(θ)) / X(θ)]
                     gH (θ): = EØ(θ)2
                     GE(θ): = 10. Log (gH (θ))


Simulation for the Radiation Pattern

The result of the example above shows the mainlobe and the sidelobes. These are a general feature of aperture antennas. The pattern is the result of interference phenomena. Mathematically, the lobes result from the (sin X/X) and (sin Y/Y) terms. One of the main concerns in satellite communications is the reduction of interference caused by sidelobes. The graph for the radiation pattern above was as a result of entering values of the aperture widths, a and b.
From the simulation, it was discovered that:
1. For large apertures (a>1 and b>1), the width of the main beam will be narrow.
2. For small apertures (a<1 and b<1), the width of the main beam will be large and sidelobes will be reduced.
3. The number of secondary lobes in the pattern can be determined from the number of nulls in the pattern.
The aperture used in modeling was linearly polarized. This means that the locus of the electric field vector always lies along a straight line as time varies. In communications with satellites and space vehicles, linear polarization has the disadvantage that its direction is affected by a  phenomenon known as Faraday rotation, which occurs in the earth’s ionosphere. Since the electron density of the ionosphere is variable, it is difficult to predict the direction of the electric field of a linearly polarized wave as it arrives at the location of the satellite. If the rotation is such that its direction at the satellite cannot induce a voltage at the terminals of the receiving antenna, no signal will be received. This problem can be overcome if the radiation is circularly polarized instead of linearly polarized, (Kai,1982). It is recommended that the aperture should be circularly polarized.
The use of arrays can reduce interference. Beam shaping can be achieved by using an array of basic elements. The elements are arranged so that their radiation patterns provide mutual reinforcement in certain directions and cancellation in others hence minimizes interference. Most arrays used in satellite communications are two dimensional.

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Dunlop J. and Smith D.G. (1994): Telecommunications Engineering. Cheltenham, Stanley
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Kai F.L. (1982): Antenna Introduction. Hong Kong. Chinese University of Hong Kong

KYES (2009):  Antennas Introduction/Basics (Rules of Thumb).

KYES formulas. Accessed on 27/04/2009.

Mithal G.K. (1994): Radio Engineering (Applied Electronics Vol. II). Delhi. Khanna Publishers.

Seybold J.S. (2005): “Introduction to Antennas”. In SunCam online continuing education course,, 33pp. Accessed on 12/02/2009.