Figure 1 demonstrates the use of a wire mesh to replace a solid plate. We located a resonant (≈ λ/2) dipole λ/4 distance over a λ-wide ground plane in the H-plane and offset 3/8λ from one edge. This is repeated in Figure 2-20 using GTD analysis. The rods only run parallel to the dipole because cross wires do not have currents induced on them in the ideal world of analysis. The circumference of the rods equals the spacing between the rods and forms an equivalent solid plate. An actual antenna could use smaller-diameter rods and work as effectively as the solid plate and would reduce weight and wind loading. NEC analysis produces the same pattern as the GTD analysis, except that the E-plane size of the rods alters the backlobe predicted by GTD to some extent, because that analysis assumes infinite-length rods.
FIGURE 1 Use of a wire mesh to replace a solid plate for dipole over a ground plane in a MOM calculation.
Over most of the pattern angles the two analyses produce identical results. The NEC analysis accounts for the mutual impedance between the dipole and its image in the finite ground plane. For impedance calculations a small ground plane gives almost the same reaction to the antenna as an infinite ground plane.
Figure 2 shows a wire frame model of a cell phone. The model contains more wires than necessary for λ/10 spacing, but more wires improve the geometry match. When using crossed wires that shield both polarizations, we reduce the wire circumference in half since the wires approach the squares from four sides. The small wire antenna must be connected to the wire grid of the model to generate proper currents on the box. Either we restrict possible locations of the antenna or we must distort the wire grid locally. You should write an automatic grid generator if you use this analysis often. Consider that you need to specify whether an edge wire should be generated when two plates share the same edge. The hand holding the cell phone and the head nearby have significant effect on the antenna performance. The model given in Figure 2 has limited use. We need either a moment method analysis, such as WIPL-D, which includes volume dielectric structures, or FDTD, which can include complex material structures to model the head and produce good results.
 FIGURE 2 Wire frame MOM model of a cellular telephone handset with an antenna connected to the mesh.
Figure 3 illustrates a wire frame model of an airplane used for low-frequency analysis. Antennas mounted on free-flying models such as airplanes or spacecraft will excite the structure. Electrically, small antennas can excite the entire vehicle as an antenna. For example, a small antenna mounted on a large ground plane that would produce vertical polarization can excite the wings or fuselage and the entire system will radiate horizontal polarization. Models similar to Figure 3 can eliminate surprises. The model restricts antenna mounting locations to the wire positions and may require local distortions of the grid.
FIGURE 3 Wire frame MOM model of an airplane.
Moment methods can include solid plates. Figure 4 shows an open waveguide horn analysis that uses a combination of plates and a single-feed wire monopole. Locating the monopole or a small dipole inside the waveguide produces excitation of the waveguide mode that feeds the horn. Even though the model does not necessarily produce accurate impedance information, the model accurately calculates the pattern generated by the currents excited in the walls. We can either use an aperture method for the horn that replaces the aperture fields or use the currents excited in the walls to calculate the pattern. Either method works for the front lobe. The moment method calculation requires significantly greater calculation time but produces results that better match measurements in all directions. Figure 5 demonstrates how to reduce calculation time by using planes of symmetry in a moment method analysis. In this case the small dipole feed is separated by two equally fed closely spaced dipoles. The right–left symmetry of the antenna allows reduction of the model by half. A vertical PMC wall divides the antenna into two parts, with only one remaining in the analysis. A horizontal PEC conductor divides the remaining model in half because halfway between the dipole feed is a virtual short circuit. Figure 5 contains only one-fourth the size of the original problem. Since matrix inversion requires N3 calculations for an N × N matrix, dividing the analytical model down to one-fourth size reduces this calculation by a 64 : 1 factor. This also reduces the matrix element (fill time) calculations by 16 : 1. Reducing the model by using symmetry planes enables the solution of larger problems and reduces calculation time.
 FIGURE 4 MOM model of a pyramidal horn using flat plates fed by a small dipole.
FIGURE 5 Use of electric and magnetic walls to reduce the model size in MOM analysis of a pyramidal horn: (a) PEC wall divides the horn; (b) PMC wall divides the horn.
Analyses in later chapters use the moment method to predict antenna performance. Wire frame and plate analyses determine vehicle and mounting structure pattern effects. The moment method produces excellent analyses because it determines the approximate current distribution as a sum of simple basis functions and we need not start with an assumed current distribution on the antenna.
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