Modeling of installed antennas using a hybrid EFIECFIE formulation
This example shows how hybrid EFIECFIE integral equation formulation introduced in Efield 5.2
can be used to speed up the solution of antenna installation problems when using the Efield
MLFMM solver. Typical problems where MLFMM is an excellent choice are the analysis of installed
antenna performance or antenna to antenna coupling on large platforms. However, often the antenna
can not be modelled as a closed body and as a consequence CFIE can not be used with the result of
poor convergence in MLFMM. In Efield 5.2 a hybrid hybrid EFIECFIE integral equation formulation
was introduced where the antenna can be modelled with EFIE and the rest of the platform with CFIE.
This results in a formulation with much better convergence properties than pure EFIE.
When using EFIE for the antenna part point voltage sources on thin wires, edge voltage sources and
wave guide ports can be used. For antenna modelled with CFIE only wave guide ports are supported.
Three different cases are considered:
The monopole antennas are mounted on a rectangular box with dimensions 6.4m x 2m x 0.4m,
see Figure 1 and Figure 2. A coupling analysis between the antennas located 5m apart in frequency range
500 MHz to 1.5 GHz is done.
The monopole antenna is modelled as a thin strip of length 75mm and width 4mm. The EFIE is
used for the monopole antenna and CFIE for the rectangular body. A voltage edge excitation is
used on the middle of the strip. Two different meshes was created, a fine mesh consisting of
156834 unknowns (104582 elements) and a course mesh consisting of 121377 unknowns (80944 elements).
The problem was solved using the Efield MLFMM solver.
In Figure 3 and Figure 4 the scattering parameters are shown. The agreement between EFIE and EFIECFIE is
very good for S
_{11} but for S
_{12} there are larger differences at the resonant region. Figure 5
shows the convergence for different frequencies both for the EFIE as well as the EFIECFIE case.
The reduction of number of iterations when using the EFIECFIE formulation is drastic.
Figure 1: Monopole antennas mounted on a rectangular body

Figure 2: Monopole antennas mounted on a rectangular body (closeup of antenna)

Figure 3: Coupling of two monopole antennas mounted on
rectangular box. S_{11}.

Figure 4: Coupling of two monopole antennas mounted on
rectangular box. S_{12}.

Figure 5: Convergence in MLFMM for different frequencies for
monopole antennas mounted on rectangular box

In this case two uslot antennas are mounted on the rectangular box with dimensions 6.4m x 2m x 0.4m,
see Figure 6 and Figure 7. A coupling analysis between the antennas located 5 m apart in frequency range 500 MHz
to 1.5 GHz is done.
The uslot antenna is modelled using thin PEC surfaces and the excitation used is a voltage edge excitation
at the middle of the strip, see Figure 8.
The EFIE is used for the uslot antenna, shown in blue colour in Figure 8, and CFIE for the rectangular body.
A mesh with 157177 unknowns (104858 elements) was created. The problem is solved using the Efield MLFMM solver.
In Figure 10 and Figure 11 the scattering parameters are shown. The agreement between EFIE and EFIECFIE is very good for
S
_{11} but for S
_{12} there are larger differences at the resonant region. Figure 12 shows
the convergence for different frequencies both for the EFIE as well as the EFIECFIE case. The reduction of
number of iterations when using the EFIECFIE formulation is drastic.
Figure 6: Uslot antennas mounted on a rectangular body

Figure 7: Uslot antennas mounted on a rectangular body (close up of antenna)

Figure 8: Uslot antennas. Blue parts modelled with EFIE.

Figure 9: Geometry of microstrip antenna

Figure 10: Coupling of two uslot antennas mounted on
rectangular box. S_{11}.

Figure 11: Coupling of two uslot antennas mounted on
rectangular box. S_{12}.

Figure 12: Convergence in MLFMM for different frequencies for uslot
antennas mounted on rectangular box

The monopole antenna is mounted on a rectangular box with dimensions 0.4m x 0.4m x 0.01m, see Figure 13.
The gain at 2GHz and the input impedance for the frequency range 1500 MHz to 2500 MHz was computed.
The monopole antenna is modelled as a thin wire of length 75 mm and radius 1 mm, see Figure 13. The
EFIE is used for the monopole antenna and CFIE for the rectangular body. A voltage node excitation is
used on the middle of the wire. The mesh created consisted of 688 elements and 1037 unknowns. The problem
was solved using the Efield MoM solver with a GMRES iterative solver. In Figure 14 the gain for the antenna
is shown at 2GHz. The agreement between EFIE and EFIECFIE is very good. Figure 15 shows the convergence for
EFIE as well as EFIECFIE with different alpha parameters. The reduction of number of iterations when using
the EFIECFIE formulation is very large. Figure 16 and Figure 17 shows the input impedance for the monopole
antenna. Very good agreement between EFIE and EFIECFIE is achieved. Finally Figure 18 shows the number of
iterations used to reach convergence for different frequencies with EFIE and EFIECFIE.
Figure 13: Monopole mounted on ground plane

Figure 14: Gain for monopole mounted on ground plane. EFIE
compared with EFIECFIE with different amount of CFIE.

Figure 15: Convergence history for monopole mounted on
ground plane. EFIE compared with EFIECFIE with different amount of CFIE.

Figure 16: Real part of input impedance for monopole mounted on ground
plane.

Figure 17: Imaginary part of input impedance for monopole mounted on ground
plane.

Figure 18: Number of iterations used to reach convergence
for different frequencies for monopole mounted on ground plane. EFIE (black) compared with
EFIECFIE (red).
