An optimum gain pyramidal horn antenna (see Antenna Theory and Design by W. Stutzman and G. Thiele, John Wiley & Sons, New York, 1981, pgs 413-415) was simulated using XFDTD.

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  Figure 2
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  Figure 3
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  Figure 8

The pyramidal horn aperture dimensions are 18.46 cm by 14.55 cm with a path length of the horn apex of 29.75 cm. The horn is fed by a WR-90 waveguide with an input signal of 9.3 GHz. The theoretical gain for this antenna is 22.1 dB with half-power beamwidths of 12 degrees in the E-plane and 13.6 degrees in the H-plane.

For this simulation the XFDTD Geometric Modeler will be used to draw the horn. First the pyramidal horn will be created from two wedges. The pyramid primitive can be used to create a wedge, and the dialog for the first wedge is shown in Figure 1.

Similarly the second wedge for the other flare angle of the horn is drawn, then rotated to produce the outline of the horn shown in Figure 2.

The two wedges are then combined to form a solid horn using Boolean intersection operation. The result is shown in Figure 3.

Next the waveguide is added as a solid rectangular block attached to the base of the horn. Then to make a hollow horn and waveguide, a copy of the solid horn/waveguide is made, enlarged slightly, then the two objects are subtracted. The result is shown in XFDTD solid view in Figure 4.

Once the geometry is generated it is meshed, the waveguide feed port is added, and the 9.3 GHz excitation is specified. The feed port is the green oblong shown in XFDTD mesh view in Figure 5.

After the calculation is complete the near zone fields and far zone radiation gain patterns are available. The radiation gain pattern is shown in Figure 6. The results match the theoretical gain to within 0.1 dB and the radiation pattern half power beam widths to within a few tenths of a degree in each plane.

The near zone field displays illustrate the physics of the horn. Figure 7 shows the steady state electric field magnitudes in the two principal planes of the horn. The e-plane fields have a relatively high amplitude near the conducting horn walls, while the h-plane fields go to zero.

Figure 8 shows a pair of transient field snapshots which illustrates the diffraction around the horn aperture in the two different planes due to the polarization effects.