Fig. 1 Cassegrain reflector with conical horn feed.
In many reflector antenna applications, it is convenient to simulate the reflector system fed by a point source whose far field radiation pattern is same as that of the actual feed used in the application. Point sources with the user specified far zone E-field radiation patterns can be input as excitation source in SINGULA . The E-field radiation pattern of the point source can be specified in any one of the three ways provided in the program.
The first way is by selecting from the list of the standard far zone patterns available in the program. This list contains “Isotropic Source”, “Z-Directed Electric Hertzian Dipole”, “Z-Directed Elementary Magnetic Dipole”, “Gaussian Beam”, etc..
The second way is by specifying the far zone radiation pattern in a functional form given by
where the function F(θ , φ) is the pattern of the Eθ component and the function G(θ , φ) is the pattern of the Eφ component. As an example, a scalar feed can be defined in a simulation by specifying F(θ , φ) and G(θ , φ) as
F(θ , φ) = exp(-θ^2) * cos(p) ; G(θ , φ) = exp( – θ^2) * sin(p)
The list of valid operators and different functions allowed to use in the functional form of the point source along with their syntax are given in the manual.
The third way of defining the far zone radiation pattern of the point source is by specifying it in a tabular form in the format given below.
Φ(deg.) , θ(deg.) , | Eθ | (V/m) , Angle Eθ (deg.) , | Eφ | (V/m) , Angle Eφ (deg.)
The data file containing the E-filed data recorded in the above specified format can be read in SINGULA for defining the far zone radiation pattern of the point source in a simulation. The E-field of the point source in any arbitrary θ , φ direction is calculated by a linear interpolation of the E-field values specified in the table.
The third way of defining point source in Singula is useful only if the far zone E-field values in the required φ , θ range are already recorded in a data file in the above specified format. Measured 3D-radiation pattern of the feed antenna recorded in a data file in the above specified format can be read directly in SINGULA for defining the point source. Also, the 3D far zone E-field pattern of a feed antenna simulated in SINGULA can be output to a file which can be read as a far zone E-field pattern of an equivalent point source for the subsequent simulations. This feature is very useful for analyzing the large reflector antennas and/or the large conducting scatterers. However, two simulations are required in SINGULA to handle this type of problems. First the feed antenna alone, centered at the origin of the global XYZ-coordinate system, is modeled and solved. The 3D far zone E-field radiation pattern of the feed antenna thus obtained is output to a file which may arbitrarily be named as ‘Feed Pattern’. Then the reflector antenna system alone is modeled as a separate simulation in which the reflector system is illuminated by a point source whose 3D far zone E-field radiation pattern is read from the file ‘Feed Pattern’.
Large reflector antennas are difficult to simulate using Boundary Element Method (BEM) / Method of Moments (MoM). However, incorporation of the Fast Fourier Transfer (FFT) technique into the BEM makes the simulation of large reflector antennas practical. Here, a large Cassegrain parabolic reflector antenna fed by a conical horn radiating a circularly polarized radiation pattern is considered to illustrate the validity of the use of an equivalent point source as a feed. Simulated radiation patterns of a Cassegrain reflector antenna, fed by the conical horn radiating circularly polarized wave, are compared to that of the same Cassegrain reflector fed by the equivalent point source having the radiation pattern of the same conical horn feed under consideration.
The geometry of the Cassegrain system, employing a concave paraboloid as the main reflector and a convex hyperboloid as the subreflector is shown in Fig. 1. The focal length and the aperture diameter of the main reflector (paraboloid) are 1.221m and 3.8m, respectively. The parameters , distance between the foci and the aperture of the hyperbolic subreflector are 1.221 m and 0.3042 m, respectively. These specifications imply the semi-major axis a and the semi-minor axis b of the hyperbola, whose surface revolution yields the subreflector, are 0.5m and 0.3503m, respectively. The main and the subreflectors are positioned such that the real focus of the hyperbolic subreflector is aligned with the vertex of the main reflector and the virtual focus of the subreflector with the focus of the main reflector. The phase centre of the conical horn feed is aligned with the vertex of the main reflector for illuminating the subreflector. The dimensions of the conical feed horn are shown in Fig. 2.
Fig. 2 The circular horn fed by two orthogonal TE11 waveguide modes.
In the first phase of the simulation, the conical horn is fed by two orthogonal TE11 circular waveguide modes at the beginning of the cylindrical section of the feed horn to generate a circularly polarized radiation from it. After solving the model in SINGULA the phase centre of the feed horn and the 3D E-field radiation pattern at a resolution of 0.2° in the θ-direction and 2° in the φ- direction are obtained. In the program, the angular range for the 3D E-field radiation pattern is set 0°-50° for θ and 0°-360° for φ . The data calculated by the program to draw the 3D pattern can be recorded in a file simply by clicking on the “Export” button designated for this purpose in the user interface of the program. Simulations were carried out at frequencies of 3GHz, 6GHz, and 10GHz. The 2D polar patterns of the directive gain of the conical feed horn in the principal planes at these three frequencies are shown in Figs. 3-5.
Fig. 3 The directive gain pattern of horn at 3GHz Fig. 4 The directive gain pattern of horn at 6GHz
Fig. 5 The directive gain pattern of the conical feed horn at 10GHz
In the second phase of the simulation, the Cassegrain reflector system fed by the conical feed is modeled and solved. In the third phase of the simulation, the Cassegrain reflector is illuminated by an equivalent point source whose radiation pattern is defined by the data files of the feed 3D E-field patterns obtained in the first phase of the simulation. The far zone radiation patterns thus obtained in the second and third phases of the simulation are compared in Figs. 6-11.
In Figs. 6-11, simulated results obtained by different methods for different models are compared. The short legends appear in these figures are explained below.
“LU, single precision” —– Cassegrain reflector fed by the conical horn solved by single precision LU decomposition method.
“FFT” ——– Cassegrain reflector fed by the conical horn solved by iterative method with FFT technique.
“PS-FFT” —— Cassegrain reflector fed by the equivalent point source by iterative method with FFT technique.
Fig. 6 The directive gain pattern in φ=0° plane at 3GHz
Fig. 7 Left Hand Circular Polarization (LHCP)-component pattern of far-zone E-field in φ=0° plane at 3GHz.
Fig. 8 The directive gain pattern in φ=0° plane at 6GHz
Fig. 9 Left Hand Circular Polarization (LHCP)-component pattern of far-zone E-field in φ=0° plane at 6GHz.
From these illustrations, we can observe close agreement between the radiation patterns of the Cassegrain reflector with the conical horn as feed and with the equivalent point source as feed. Fig. 10 and 11 are the radiation patterns of the Cassegrain reflector illuminated by the equivalent point source obtained using iterative method with FFT technique.
Fig. 10 The directive gain pattern at 10GHz
Fig. 11 The LHCP-component pattern of far-zone E-field at 10GHz