The multilevel fast multipole algorithm (MLFMA) has been successfully applied to electromagnetic scattering problems of large complex objects. By adding wire and surface-wire junction basis functions into the existing algorithm, radiation problems of complex surfaces and wire interconnections can be solved within the complexity of O(N log N), where N is the number of unknowns. This extension has several new applications, such as analysis of automobile antennas, aircraft antennas, and electromagnetic compatibility of desktop computers. The comparisons between MLFMA and the method of moments (MoM) show that MLFMA uses less simulation time and memory without losing numerical accuracy. Thus, analysis of antennas within a complex environment can be realized on a small computer. The following results are computed by the combination of the Fast Illinois Solver Code (FISC) and SWJ3D (a general-purposed three dimensional moment method code for surfaces, wires and junctions).

Monopole antenna attached to a metallic plate

These first results test the wire and surface-wire junction basis functions of the new algorithm.

Normalized current distribution

RCS

Monopole antenna attached to a car

The mesh has 2,452 unknowns. The method of moments takes 33 minutes of CPU time and 55MB of memory on a Dec Alpha personal workstation. With two-level fast multipole method, we just need 3.4 minutes of CPU time and 46MB of memory. A delta voltage source is put on the junction between the monopole antenna and the trunk. With isotropic radiation pattern in the horizontal plane, the antenna can receive uniformly from every direction.

Normalized current distribution at 88 MHz (FM radio band)

RCS at 88 MHz (FM radio band)

Monopole array attached to a wing

The mesh has 1,290 unknowns. With the method of moments, we need 332 sec. of CPU time and 128MB of memory on a DEC Alpha personal workstation. With two-level fast multipole method, we only need 54 sec. of CPU time and 21.5MB of memory. A delta voltage source is put at the junction between the shortest wire and the wing. Most of the energy is absorbed by the fourth shortest wire due to the resonance. The rest of the radiation is reflected from the fuselage. Thus the current pattern is like a standing wave at the left side of the source. The radiation pattern has two main beams radiating 30 degress upward and downward from the wing.

Normalized current distribution at 88 MHz (FM radio band)

Normalized current distribution at 90 MHz (VHF band)

EMC analysis of a desktop computer

The following Figures show the triangular-patch mesh used to model the boards and the case of the desktop computer.

Chassis discretization - 3D Front View

Motherboard and daughter cards discretization - 3D Back View

Motherboard discretization - Top View

The internal and external views for two structure with respectively 8 and 16 ground pins between the shielding card and the motherboard are shown on the following four Figures.

External view of the normalized current distribution with 8 ground pins


Internal view of the normalized current distribution with 8 ground pins


Top internal view of the normalized current distribution with 8 ground pins


External view of the normalized current distribution with 16 ground pins


Internal view of the normalized current distribution with 16 ground pins


Top internal view of the normalized current distribution with 16 ground pins

The delta voltage source (2 GHz) is located on a wire which connects the source card and the motherboard. By adding a shielding card with ground pins, we can effectively reduce the electromagnetic emission from the slot on the chassis. The periodic current distribution on the motherboard illustrates the resonance of the chassis.

The following two Figures show the radiation patterns of the desktop computer when the internal voltage source is on.

Radiation patterns with 8 ground pins


Radiation patterns with 16 ground pins

The energy radiated from the 16-pin structure is twice as much as the energy radiated from the 8-pin structure. Thus, it appears that a better shielding effect can be achieved with more ground pins, and more particularly at specific frequency values, as it is shown on the last Figure.

Radiated power for different configurations as a function of frequency.

The above work is a collaboration of Hsueh-yung Chao, Prof. Weng Cho Chew, Prof. Eric Michielssen and Dr. Jiming Song. Please send suggestions, comments, and inquiries to: chao@sunchew.ece.uiuc.edu.