One of the main advantages of array antennas is its beamforming capabilities and one of the difficulties in designing an array is the feeding network. Coupling between elements in an array adds to variation in the input impedance of the elements which complicates impedance matching, especially for edge elements. In [1] the input impedance variations for a 9x9 uniform dipole array and that for a twolevel Sierpinski Carpet dipole array (64 elements) are compared. Here the input impedance for the elements in these arrays are determined by simulation in FEKO and mutual coupling between dipoles in different configurations are investigated.
First a halfwavelength dipole at 300MHz is modelled to determine the input impedance. The length is then slightly reduced until the imaginary input impedance is nearly zero at 300MHz. Figure 1 shows the input impedance of the reduced length dipole.
Figure 1: Input impedance of dipole antenna 


At 300MHz the dipole has an input impedance of 69.8531  j 0.1586Ω. Next the mutual impedance between two dipole antennas are determined for two configurations as shown in Figure 2. The separation distance for collinear dipoles, s and for parallel dipoles, d are also shown. The mutual impedance is determined by subtracting the input impedance of the single dipole from the input impedance of the dipole with the other dipole present and active.
Figure 2: Two dipoles in collinear (left) and parallel (right) configurations 


Figure 3 and Figure 4 show the mutual impedance for the collinear and parallel case, respectively. In general the coupling between elements is larger for the parallel configuration than for the collinear configuration.
Figure 3: Mutual impedance for two collinear dipoles 


Figure 4: Mutual impedance for two parallel dipoles 


The FEKO model setup of the 9x9 uniform array is shown in Figure 5a. The element spacing is 0.6 wavelengths in either direction. A custom math script is created in POSTFEKO to postprocess the voltage source data from the individual dipole elements in the array. The input impedance of each element is plotted in Figure 5b, using the element numbering from Figure 5a on the horizontal axis.
Figure 5: 9x9 uniform array and impedance variation 

(a) Array model and element numbering  (b) Input impedance per element 




A twolevel Sierpinski Carpet array is simply created by thinning the 9x9 uniform array and 64 elements remain as shown in Figure 6. As before the input impedance per element is shown in Figure 6b according to the element numbering in Figure 6a. As expected a larger variation in input impedance occurs for the Sierpinski Carpet as all the elements in the array are near an edge.
Figure 6: 64 element twolevel Sierpinski Carpet array and impedance variation 

(a) Array model and element numbering  (b) Input impedance per element 




Finally the gain patterns for the two arrays are also calculated and are shown in Figure 7. The angle Phi is measured in the xyplane from the xaxis and Theta is measured from the zaxis.
Figure 7: Array gain patterns 

(a) Phi = 0  (b) Phi = 90 




References
[1] 
R. Martin, R. Haupt, "Element Impedance Variations in Fractal Arrays", Antennas and Propagation Society International Symposium, July 2005, Vol. 2B, pp. 396399.
