One of the main advantages of array antennas is its beam-forming 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 two-level 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 half-wavelength dipole at 300MHz is modeled 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 72.45+j2.72Ω. 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 of the 9x9 uniform array is shown in Figure 5 along with the input impedance per element (the numbering in Figure 5a is used on the horizontal axis in Figure 5b). The element spacing is 0.6 wavelengths in either direction.

Figure 5: 9x9 uniform array and impedance variation
(a) Array model and element numbering (b) Input impedance per element

A two-level 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 6a according to the element numbering in Figure 6b.  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 two-level 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 xy-plane from the x-axis and theta is measured from the z-axis.

Figure 7: Array gain patterns
(a) Phi = 0 (b) Phi = 90

References