The EIRP is an indication of the power an antenna can radiate in a given direction compared to an isotropic radiator. The result is a plot showing the cumulative distribution function (CDF) of the effective isotropic radiated power (EIRP). However, a macro program in XFdtd is available that allows a full examination of the gain levels at all angles from the array by sweeping the phasing of the individual elements. It is inefficient to simulate all possible phasing combinations to determine the overall performance of the array. In Figure 7 several beam patterns are shown together to illustrate the steering of the beam from normal down to 50 degrees in 10-degree steps. As the phasing is changed to steer the beam toward the horizon, the array reaches a limit due to the patterns of the original patch antennas, and a gain plot with large side lobes forms. Sweeping the beam to a corner of the array at direction (45°, 40°) reduces the peak gain down to 21.7 dBi and broadens the beam a moderate amount (Figure 6). With the phases adjusted to direct a beam toward (20°, 90°) the result is a slight drop in peak gain to 22.9 dBi and a broadening of the beamwidth to about 13.2 degrees, shown in three dimensions in Figure 5. The same pattern is shown over the CAD drawing of the antenna in three dimensions in Figure 4. This resulted in a maximum gain of just over 23 dBi and a 3 dB beamwidth of just over 12 degrees as shown in a line plot through one of the principal planes in Figure 3.

An initial test set all phases equal so all elements are radiating toward the (0°, 0°) direction. Simulations were performed on the array to determine the gain pattern possible for different phasing conditions. In XFdtd, these phases were assigned to each feed element through the use of parameters as shown in Figure 2, where the phase shift is defined by a parameter name. Is the phase shift for the element located at (x

Is W n = expĪre the locations (in meters) of the feeds at each patch referenced to the initial patch in the lower left corner of the array, and w A widely-used formula for determining the phasing of the elements for a beam focused at a direction of θ A 28 GHz sinusoidal waveform is used at each patch with an adjustable phase offset that is determined based on the desired direction of the main beam. The feed point for each antenna is offset from the center of the patch by 0.75 mm in the horizontal direction as this was found to be the location of the best return loss result. A view of the patch layout on the dielectric sheet is visible in Figure 1. Each patch is 3.4025 mm square and is spaced a half-wavelength at 28 GHz (approximately 5.36 mm) apart.

The antenna geometry consists of a 52.5 x 52.5 mm sheet of dielectric material (dielectric constant = 2.2, loss tangent 0.0009, thickness 0.254 mm) that is backed by a conducting ground plane and topped with 64 patch elements in an 8x8 configuration.

Phased array gain calculation