1 PERFORMANCE COMPARISION BETWEEN HIGHER-ORDER AND RWG BASIS FUNCTIONS

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1 1 PERFORMANCE COMPARISION BETWEEN HIGHER-ORDER AND RWG BASIS FUNCTIONS Two monopoles are mounted on a PEC cylinder oriented along the z axis. The length and radius of the cylinder are 5. m and 1. m, respectively. The surface of the cylinder is meshed into bilinear surfaces for higher-order basis functions in TIDES and into the triangular patches for RWG basis functions at 4 MHz. The S parameters of the antenna network are calculated in the frequency band of 2 4 MHz using 21 sampling frequencies. (a) (b) Figure 1. Simulation model: (a) bilinear patch model for TIDES; (b) triangular patch model for RWG basis functions. x z y

2 S parameter magnitude (db) S 11 (TIDES) S 11 (MLFMA) S 21 (TIDES) S 21 (MLFMA) Frequency (MHz) Figure 2. Magnitude of the S parameters. S parameter phase (degree) S 11 (TIDES) S 11 (MLFMA) S 21 (TIDES) S 21 (MLFMA) Frequency (MHz) Figure 3. Phase of the S parameters. Detailed information about this simulation is listed in Table 1. Only the maximum amount of RAM used is listed. The two codes are executed on a PC with a Pentium P4 chip of 3. GHz CPU, 1. GB RAM, and using the Microsoft Windows XP 32-bit operating system.

3 TABLE 1. Performance Comparison for the Coupling Calculations Algorithm /Equation Basis Function NUN Solver (Preconditioner) RAM (MB) Time (seconds) MoM /EFIE Higher-order 3,66 LU decomposition (no preconditioner) MLFMA /EFIE RWG 15,58 BiCGStab (ILU) EMC PREDICTION FOR MULTIPLE ANTENNAS MOUNTED ON AN ELECTRICALLY LARGE PLATFORM The isolations between the four antennas mounted on a full-size aircraft model are calculated. The full-size aircraft model is meshed at 1.5 GHz and is 58 wavelengths long at this frequency. This simulation employed 7,853 unknowns to discretize the structure into quadrilaterals Antenna 2 Antenna 3 Antenna 1 Antenna 4 Figure 4. Four antennas mounted on a full-size airplane model. To assess the accuracy of the numerical results, isolations between three pair of antennas are plotted together in Figure 5. In the legend of Figure 5, the first number in each pair represents the antenna acting as a transmitter, and the second, represents the antenna used as a receiver.

4 8 Isolation (db) Frequency (GHz) Figure 5. Isolation between different pairs of antennas. 3 ANALYSIS OF COMPLEX COMPOSITE ANTENNA ARRAY Modeling a 112-element Vivaldi array at 4.7 GHz requires 63,938 geometric elements. The total number of unknowns for this array is 89,124. All the elements are excited with amplitude of 1. V. Figure 6. A 112-element Vivaldi array.

5 Figure 7. Azimuth pattern of the Vivaldi antenna array ( starts from x axis in the xoy plane). Figure 8. Elevation pattern of the Vivaldi antenna array ( starts from x axis in the xoz plane). 4 ARRAY CALIBRATION FOR DIRECTION-OF-ARRIVAL ESTIMATION In this application, 176 dipole antennas are put on each side of the Global Hawk unmanned aerial vehicle (UAV) for DOA estimation. The structure is analyzed at 1. GHz. There are 11 rows and 16 columns of antennas on each side of the aircraft.

6 .5.5 Figure 9. Layout of the dipole array at one side of the UAV. Figure 1. Two signals incident on the array. The array calibration is performed at 1. GHz, which creates 68,133 unknowns using the MoM procedure. Table 2 shows the exact and estimated directions of arrival along with the amplitudes of the signal.

7 TABLE 2. Estimated Direction of Arrival of the Signal and Their Amplitudes exact est. θ exact θ est. α exact α est. Signal j 1.5+j.4 Signal j 1.+j.33 5 RADAR CROSS SECTION (RCS) CALCULATION OF COMPLEX TARGETS 5.1 RCS Calculation of a Squadron of Tanks The dimensions of the tanks are 8. m 3.7 m 2.75 m. The simulation for the five tanks at 1 MHz leads to 15,673 unknowns. The distances between the tanks are 5. m each along both the length and width of the tank, respectively. Figure 11. A tank illuminated by a plane wave. Figure 12. Formation of five tanks.

8 One tank Five tanks / 2 (db) Figure 13. Bistatic RCS in the xoz plane ( starts from x axis in the xoz plane). 9 One tank Five tanks / 2 (db) Figure 14. Bistatic RCS in the xoy plane ( starts from x axis in the xoy plane).

9 5.2 RCS of the Tanks inside a Forest Environment The model for the four tanks under the tree canopy generates 19,713 unknowns. The monostatic RCS of the forest and tanks inside the forest is calculated at 1 MHz. Note that there is an infinite PEC ground plane for each model in this example. Figure 15. Tree modeled using wires and loaded plates. z o x y Figure 16. Perspective view of four tanks inside a small forest of size 5 m 5 m.

10 5 Forest Tanks inside forest Tanks 4 (db) (degree) Figure 17. Monostatic RCS at cut plane ( starts from x axis in the xoz plane). 4 Forest Tanks inside forest Tanks 3 (db) (degree) Figure 18. Monostatic RCS at θ cut plane ( starts from x axis in the xoy plane).

11 5.3 RCS from an Aircraft and a Formation of Aircraft The distances between any two neighboring aircraft are x = 1. m along the head direction, y = 1. m along the wing direction, and z =. m along the height direction. The RCS is calculated at 1.25 GHz. The number of unknowns for the aircraft formation is 351,71. Figure 19. An aircraft with a plane wave excitation. Figure 2. Aircraft flying in a V formation.

12 Formation Single (db) Figure 21. Bistatic RCS at cut plane ( starts from x axis in the xoz plane) Formation Single (db) Figure 22. Bistatic RCS at θ cut plane ( starts from x axis in the xoy plane).

13 5.4 RCS Simulation with Million Level Unknowns The bistatic RCS of a single aircraft is calculated at 6.15 GHz. The numbers of unknowns in this case is 954,618 (approximately one million unknowns). Figure 23. The meshed airplane model (db) Figure 24. Bistatic RCS at cut plane ( starts from x axis in the xoz plane).

14 5.5 RCS of an Aircraft Carrier The aircraft carrier model is about 265 m long, 66 m wide, and 47 m high. The body of the helicopter is modeled as the material with parameters ε r = 2 and μ r = 2, whereas the rotating blades are modeled as metals. The simulation for this model at 15 MHz requires a total of 559,59 unknowns. Figure 25. An aircraft carrier carrying 61 aircraft and 6 helicopters. Figure 26. A model of a helicopter.

15 (a) (b) (c) Figure 27. Layout of the aircraft carrier with relevant aircraft on deck: (a) top view; (b) side view; (c) front view.

16 / 2 (db) Figure 28. Bistatic RCS at cut plane ( starts from x axis in the xoz plane) / 2 (db) Figure 29. Bistatic RCS at θ cut plane ( starts from x axis in the xoy plane).

17 6 ANALYSIS OF RADIATION PATTERNS OF ANTENNAS OPERATING INSIDE A RADOME ALONG WITH THE PLATFORM ON WHICH IT IS MOUNTED Modern aircraft utilize electromagnetically transparent radome structures to protect antennas from environmental stresses while preserving the aerodynamic integrity of the vehicle s superstructure. feed (a) Figure 3. Layout of the Yagi array: (a) dimensions of a single Yagi antenna; (b) Yagi array and the reflection plate. (b) Figure 31. Yagi array inside the radome.

18 A total of 611,318 unknowns are required to model the antenna array along with the radome, and the aircraft frame at 1 GHz. The aircraft model is 36 m long, 4 m wide, and 1.5 m high. It corresponds to 12λ, 133.3λ, and 35λ. The radiation patterns of the Yagi antenna array directed towards the tail are calculated using the parallel out-of-core solver. Figure 32. Perspective drawing of the antenna, radome, and aircraft. Figure 33. Model of the aircraft with the antenna structure and radome.

19 Airborne antenna Antenna Gain (db) Figure 34. Azimuth radiation pattern ( starts from x axis in the xoy plane) Airborne antenna Antenna Gain (db) Figure 35. Elevation radiation pattern ( starts from x axis in the xoz plane).

20 7 ELECTROMAGNETIC INTERFERENCE (EMI) ANALYSIS OF A COMMUNICATION SYSTEM The IRA is fed with 2, V at 2 GHz. The trucks have identical dimensions of 7. m long, 2.6 m wide and 2.47 m high. The number of unknowns in this project is 541,512. Figure 36. IRA model. (,,) m ( ,,-43.22) Figure 37. Diagram of a communication system.

21 kv/m Figure 38. Field distribution around the IRA antenna and the aircraft. kv/m Figure 39. Field distribution around the aircraft.

22 8 COMPARISON BETWEEN COMPUTATIONS USING TIDES AND MEASUREMENT DATA FOR COMPLEX COMPOSITE STRUCTURES Our goal here is to demonstrate that using the computational electromagnetic code TIDES, one can compute results for the radiation pattern which are within several tenths of a db when compared with measurements for the grating lobe amplitudes. The difference between theory and experiment falls within the resolution of the measurements. Figure 4. L-band antenna array with seven ribs Measurement TIDES Peak SLL relative to mainbeam Measured: db / db TIDES : db (rib: r =1.5, riblet: r =1.55) Location: 21? 2? off mainbeam Normalized radiation (db) Degree Figure 41. Comparison of measured array pattern and TIDES calculation.