7.3 Comparison of the analytical model results to HFSS^® simulations and measurement results

For the validation of the analytical models of Section 7.1 and Section 7.2, results for the electric far field density from an enclosure with dimensions depicted in Figure 7.4 are obtained with the analytical models, with three-dimensional full wave simulation, and with measurements.

$0\,\Omega$

Figure 7.4: Enclosure dimensions and source position for the validation of the analytical model results for the electric far field.

The geometric dimensions are practically relevant, because they are similar to those of the parallel plane cavity between the PCB ground plane and the enclosure bottom of a typical automotive control device depicted in Figure 1.1(a). However, there are geometrical deviations between the shape of an automotive control device enclosure and a rectangular enclosure. Therefore, the validation of the analytical model is carried out on a rectangular test enclosure. The test enclosure in Figure 7.5 is manufactured from copper sheets which are soldered together at the edges. Thus, the geometry dimensions of the test enclosure match the simulation models. The comparison is carried out for 0 W, 50 W, and 1e9 W (open in the measurement). A removable SMA connector with a short copper trace soldered to the rigid SMA wire was used to enable the change of the trace loads. Figure 7.5(a) depicts the test enclosure with mounted SMA connector.

(a) Enclosure with removable SMA connector.

(b) SMA connector with test trace removed.

Figure 7.5: Copper test enclosure for the validation with measurements.

To obtain a reasonably good contact of the SMA connector ground to the enclosure, a conducting silver painting and conducting copper tapes were used to mount the connector. Before mounting the connector, the copper plane surface was cleaned accurately and the surface oxide was removed. Figure 7.5(b) shows the test enclosure with removed SMA connector. The measurements have been carried out with a horn antenna (Amplifier Research [107] AT4002A in Figure 7.6(d)) and a vector network analyzer (Rhode & Schwarz ZVB4) inside a semi-anechoic chamber. Pyramid absorbers have been added on the bottom of the chamber, between the measurement antenna and the test device to obtain similar conditions to those in a fully anechoic chamber. These absorbers can be seen in Figure 7.6(a). The electric field was calculated and measured 1m in front of the enclosure slot. This position has been selected as the main lob of the electric field distribution is oriented in this direction for some of the resonance frequencies within the evaluated frequency range of 800 MHz to 4 GHz. The position is consistent with CISPR 25 Edition 3 [56] for automotive component emission measurements above 1 GHz. A measurement setup overview is depicted in Figure 7.6(c) and the connection of the network analyzer cable to the enclosure SMA connector is depicted in Figure 7.6(b).

(a) Bottom absorbers for anechoic conditions.

(b) Connection of the enclosure.

(c) Measurement setup overview.

(d) Antenna (Amplifier Research AT4002A).

Figure 7.6: Setup for the validation measurement with a horn antenna from 800MHz to 4GHz.

Table 7.2 contains a summary of the measurement equipment.

Table 7.2: Measurement equipment.

Equipment	Designation	Supplier
Horn antenna	AT4002A	Amplifier Research	[107]
Network analyzer	ZVB4	Rhode & Schwarz	[108]
Calibration set	R&S®ZV-Z21	Rhode & Schwarz	[108]
Ferrite Sleeve	7427114	Würth Elektronik	[109]
Ferrite Sleeve	7427733	Würth Elektronik	[109]

Ferrite sleeves have been arranged on the coaxial cables, close to the connectors, to suppress currents on the cable shield. The ferrite sleeve, 7427114 from Würth Elektronik [109], applied close to the SMA connector of the enclosure provides an impedance of about 200 W at about 1 GHz. A second sleeve 7427733 was applied on the antenna cable. The network analyzer was calibrated with a two port TOSM calibration using the calibration set R&S®ZV-Z21 from Rhode & Schwarz [108]. The measurement bandwidth was 10Hz for maximum noise suppression. The comparison of the cavity model results, the HFSS^® simulation results, and the measurement results depicted in Figure 7.8 shows a reasonably good agreement. This confirms the analytical models of Section 7.1 and Section 7.2. The utilized equation (7.32) for the electric far field considers only the radiation from the enclosure slot and neglects the metallic enclosure walls that have some influence on the radiation diagram above the first resonance frequency. However, this is a reasonable simplification, also applied to obtain basic radiation characteristics of horn antennas [104]. Therefore, (7.32) can be used to obtain a good first order information about the radiated field. Figure 7.8 shows not only slight deviations between the measurement results and the cavity model results. It also shows some deviations of the measurement results from the results of the three-dimensional full wave simulation with HFSS^®, which considers the influence of the enclosure walls. Thus, the comparison deviations in Figure 7.8 can be explained mainly from the test enclosure tolerances and test site uncertainties. However, there are maximal 3dB magnitude deviations between the maxima of the cavity model results and the measurements.

The consideration of the radiation loss for the calculation of the slot voltages is crucial to obtain the correct voltage distribution inside the enclosure and the correct radiated far field. Figure 7.7 shows a comparison between the electric far-field obtained from a cavity field model which considers the radiation loss and a cavity model which neglects the radiation loss. For practical simulation investigations an EMC engineer needs quantitative information about the electric far field magnitude, especially at the resonances at which the radiation is at its maximum. A model that neglects the radiation loss with deviations at the resonances of more than 30dB is not sufficient for EMC simulation purposes.

Figure 7.7: Electric far field, one meter in front of the enclosure slot. Comparison of the cavity model results, which includes the radiation loss by introducing the admittance matrix $\textbf {Y}_{a}$, into the results obtained from a cavity field which does not consider the radiation loss.

(a) Load: 0 W.

(a) Load: 1e9 W.

(c) Load: 50 W.

Figure 7.8: Electric far-field 1m in front of the enclosure slot. Comparison of the cavity model results with the HFSS^® simulation results and measurement results.

C. Poschalko: The Simulation of Emission from Printed Circuit Boards under a Metallic Cover