It is critical that simulations and tests take place in the design procedure, even at the earliest stages, when changes to improve immunity against external fields can be adopted without appreciably increasing costs. Early simulation and testing can significantly reduce the time spent testing the final product in the chamber.

Each modeling method available has its merits and limitations. No single method currently provides a perfect solution for any problem. Therefore, in some cases, as in the situation analyzed in this article, general-purpose electromagnetic (EM) computer-aided design tools provide a more flexible approach to solving EMC problems. This flexibility, however, is also their drawback: these EM codes are not dedicated to solving a specific problem, so analytical or numerical preprocessing is required to use them efficiently.

This article presents a simulation method that integrates the analysis of an EMC problem into the design stage of a car using a commercial, general-purpose code that has been matched to the situation by analyzing the field representation. In other words, the efficiency of a purely numerical tool can be greatly improved if the user can apply knowledge of the electromagnetic field behavior and its representation.

The simulation output described here is the evaluation of the electromagnetic field distribution inside the car's bodywork. Knowledge of that distribution allows the designer to locate cables and electronic systems in regions characterized by reduced field intensities. In particular, proper formulation of the problem allowed a realistic situation to be addressed using a commercial code.

Applying commercial codes to reproduce typical test conditions of a car in an anechoic chamber presents some obstacles. The large dimensions of the considered volume, which must include the electromagnetic source (the radiating antenna) and the equipment under test (the whole car or a part of it), was the primary challenge. Unfortunately, such large dimensions require prohibitive computer resources, making it very difficult to directly apply the commercial EM code. This problem was overcome by introducing a plane-wave representation of the field radiated by the antenna (in this case a horn antenna), following these steps:

Figure 1 shows a typical measurement setup for the radiated susceptibility test of an automotive vehicle inside an anechoic chamber: the car is placed over a rotating platform, which also acts as a metallic ground plane, and the car is illuminated by an antenna to achieve the required test field.

Figure 1. Geometry of the problem.

The horn antenna and the equipment under test (EUT) were analyzed separately using a commercial code based on an FEM algorithm. Because the program does not accept a field distribution as a source but rather accepts only plane waves as a distributed source, it was difficult to relate the field radiated by the antenna horn and the field impinging on the EUT. The problem, then, could only be approached as a representation of the radiated field in terms of a plane-wave spectrum. Figure 2 shows the geometry of the antenna used for the radiated test.

Figure 2. Geometry of the adopted antenna.

Consider one radiating aperture, defined as that region of the aperture plane z = 0 over which the tangential E_x field is nonzero. Suppose that the field vanishes from the aperture in the plane z = 0. Construct an angular spectrum of plane waves, which will describe the field radiated from the aperture into the half-space z >= 0, based on the knowledge of the tangential component of the electric field in the aperture plane. Now, define the angular spectrum F_x(a,ß) to be such that the x component of the electric field of the elemental plane wave traveling in the direction (a,ß) is F_x(a,ß)DaDß, so that the contribution of the x component of the electric field at one point P(x, y, z) is⁴

Referring to Figure 1, the distance between the antenna and the car was D = 3 m, and the distance between the bottom of the car and the rotating metallic table was 15 cm. The antenna axis was centered with the center of the front face of the motor box (h = 42.5 cm).

Antenna Field Representation. Tests were performed to estimate the most suitable values for M and N, given by the best compromise between the accuracy requirement of the results and the computational efficiency. The field values achieved were compared using Equation 4 and theoretical values obtained in Balanis. Figure 3 shows the electric field at the point P(0,0,3) as a function of the segmentation values N, M (N = M) for a = 49.5 cm and b = 39.5 cm.

Figure 3. Convergence test: electric field (continuous line) in P (0,0,3) as a function of segmentation points; theoretical value is represented by the dashed line.

A good convergence was observed for N = M >51; this result also validates the assumption to disregard evanescent waves. Further confirmation is provided by the radiation pattern in the H plane at a distance of 3 m from the antenna as shown in Figure 4. These results were obtained with a value of 1 V/m for E₀ in Equation 3.

Figure 4. Convergence test: radiation pattern in the H plane.

A second test was performed in an anechoic chamber, comparing the field radiated by the actual horn antenna and the field obtained using Equation 1; the antenna aperture dimensions are a = 49.5 cm and b = 39.5 cm and the working frequency is f = 1 GHz. Figures 5 and 6 show the electric field on the H plane along the z axis, J = 0°, and along the axis J = 15°, respectively; these figures report the field values calculated and measured by two commercial probes. The field is calculated assuming a value in Equation 3 for E₀ corresponding to an input power of 36.5 dBm, which was used during the measurement. The measurements were performed inside the anechoic chamber (according to the geometry of Figure 1) but the antenna was oriented toward a direction far away from the metallic rotating plane to create a free-space condition. The angular value was chosen because the EUT is seen by the antenna under a geometrical angle 2J = 30°.

Figure 5. Electric field on the H plane along the z axis.

 

Figure 6. Electric field on the H plane along the axis (J=15°).

These results indicate that the measured and simulated fields near the antenna exhibit some differences, which are essentially due to the near-field components neglected in the theoretical model. In addition, the two probes gave different values because they disturbed the near field differently. In the far field, however, z > 2 D²/l @ 2.6 m, indicating that the agreement between measured and simulated field was excellent.

Field Inside the Motor Box. For the final test, a car was placed in front of the antenna, and the electric field in the motor box was evaluated. The results were compared with measured data. Figure 7 shows the geometry considered for the simulated motor box. The bottom face of the box is open.

Figure 7. Motor box geometry (dimensions are in mm).

The high-frequency structure simulator (HFSS) code was used in this step. The program was run for each impinging plane wave used to reconstruct the field radiated by the antenna. The application of the superposition effect allows the calculation of the final field distribution produced inside the box.

Figure 8. Location of field points inside the motor box.

Figure 8 shows the position of the grid inside the motor box geometry that was used to calculate and to measure the field values. Figure 9 shows the electric field distribution over a significant plane of the analyzed space. Figure 10 shows the corresponding measured field values.

Figure 9. Simulated electric field distribution inside motor box (dimensions are in mm).

 

Figure 10. Measured electric field distribution inside motor box (dimensions are in mm).

The two apertures centered at x = –175 mm, and x = 25 mm, respectively, corresponded at a high field level, but other resonant points appear in the internal region. For a better comparison, Figures 11a and 11b report the measured and simulated values along the two main axes of the structure. The differences fall in the range of uncertainty because of the combined uncertainties of the measurement probes and of the software used.

Figure 11. a) Comparison between numerical and experimental electric field values along the z axis at x = 25 mm. b) Comparison between numerical and experimental electric field values along the y axis at z = 50 mm.

Conclusion

Electromagnetic simulation can reduce the time spent on the development of the electrical system of a vehicle. In some critical areas, the E-field is so strong it can interfere with the electric and electronic components. Avoiding placement of the electronic control unit (ECU) in these critical areas to optimize the layout of the system can minimize or eliminate this interference.

The simulation described is applicable to both internal and external sources. In fact, the effects of portable radio transmitters and receivers (i.e., mobile phones, CD players, etc.) could be as dangerous as other, outside sources. In ad-
dition, the E-field distribution could be a starting point for evaluating the induced signal on wires con-nected to the ECU in order to identify possible causes of malfunction.

To simulate a radiated immunity test on a car, the plane-wave expansion was combined with a commercial EM field solver that was based on an FEM algorithm. This method allowed the region between the source, the horn antenna, and the EUT to be evaluated analytically. Because this method reduces the spatial dimension of the region in which the fields must be numerically evaluated, the commercial code can be applied efficiently to the analysis of a car. The accuracy of the simulation results is sufficient for planning the layout of cables and components, as long as the analysis is made during early stages of vehicle design.