Once this new radiating object is created, there is no need to know the details of the DUT to model its operation and integrate it into a more complex environment. The new equivalent source can be imported in an EM simulator. Additional conditions can be introduced, with more quantities computed to simulate the influence of nearby scattering objects on the radiation pattern, the link budget with another antenna, the exposure of a person standing in the near-field and so on (see Figure 3).

Figure 4. Anechoic chamber with spherical scanner, measurement probe supported by the elevation arm, and DUT positioned at the azimuth pole.

Although the three steps of Figure 3 may be implemented in multiple ways,⁶ we detail one as an example. In this example, the measurement data are acquired (step 1) with a system comprising an anechoic mobile antenna measurement chamber and a vector network analyzer (VNA). The Rohde & Schwarz anechoic chamber shown in Figure 4 has tip-to-tip dimensions of 0.64 x 1.25 x 0.93 m between the absorbers and contains a distributed-axis positioner with a 360-degree rotating azimuth table to support the DUT. A gantry arm carries the measurement probe and provides elevation from 0 to 165 degrees. The mechanical precision of this spherical scanner is better than 0.03 degrees in both dimensions. The probe is a dual-polarized Vivaldi antenna, suitable for direct far-field and spherical near-field measurements from 12 to 90 GHz. The probe tip retains a separation of 50 cm from the center of the coordinate system, with the center accurately located using built-in lasers. The center of the DUT can be accurately positioned at this point using a crank, which enables fine DUT height adjustment.

In this test setup, three ports of the VNA are used: Port 1 feeds the RF signal to the DUT via a cable through the azimuth pole. Ports 2 and 3 collect the received signals simultaneously, connecting to a feedthrough at the chamber side and two cables running to the two polarization ports of the probe. To avoid cable movement, rotary joints for both azimuth and elevation are integrated into the chamber. A full measurement obtains S21 and S31 (i.e., magnitude and phase) for all desired angular positions.

Step 2 is performed using the Fast Irregular Antenna Field Transformation Algorithm (FIAFTA).² The FIAFTA, which was developed at the Technical University of Munich, implements a generalized minimal residual equation solver for reconstructing the equivalent currents over a triangular mesh covering Σ_s from the measured S-parameters. The reference complex far-field of the test probe is injected in the algorithm to include a full probe correction. The resolution of the inverse problem is dependent on the applied domain boundary conditions. This study applies the “Huygens radiator” option, which assumes a fixed free-space impedance boundary condition at Σ_s. This approach is computationally efficient at delivering solutions for the emissions, predominantly radiating toward the outside of Σ_s. Subsequently, Σ_s was chosen to be a rectangular box closely encompassing the DUT.

In step 3, the box of equivalent currents is used as an EM source in the finite difference time domain (FDTD) software EMPIRE XPU by IMST GmbH.⁷ To correctly import the data, equivalent currents are interpolated so the triangular mesh is converted into a cube. The original triangulation must be fine enough to ensure the stability conditions of the FDTD are fulfilled. A sampling of λ/15, where λ is the free-space wavelength, meets this requirement.

FULL-VEHICLE APPLICATION

Considering the full-vehicle OTA case, the measurement system shown in Figure 1 can be used to evaluate the performance of a 5G mmWave module integrated into a car; however, it is costly and time-consuming. First, the cost of a large positioning system with a mechanical accuracy meeting the requirements of near-field testing at this frequency range are exorbitant. Second, the car is unlikely to be positioned on the turntable with the antenna module at the center of the coordinate system. With an offset and the small wavelength, the probe would have to scan the upper hemisphere -- at least a large portion of it -- with angular resolution of less than 1 degree. The test time would be extremely long, as distributed-axis positioners of this size have typical speeds of 6 to 12 degrees/s in azimuth and 1 to 2 degrees/s in elevation, respectively. On the other hand, only performing a full-wave simulation of the antenna integrated within the car is not completely suitable, as the simplifying assumptions would not guarantee a suitable model of the real-world installation.

Figure 5. mmWave antenna array integrated in the rear-view mirror.

To show the utility of combining measurement and simulation, we study a 5G mmWave transceiver integrated in the rear-view mirror behind the windshield of a car (see Figure 5). Measurements of the antenna module are used as an input to a full-wave computation, where the module is virtually integrated into a numerical model of the car. The approach uses the Rohde & Schwarz anechoic chamber measurement system with FIAFTA and EMPIRE XPU processing, previously described.

The DUT is an 8 x 8 antenna array with a mmWave front-end module operating at Ka-Band (see Figure 6).⁸ The array uses a 1:8 divider to distribute the signal from one waveguide interface to 16 beamforming ICs. Each IC feeds four, dual-port circular patch antennas, providing individual phase and amplitude control of every antenna element. Both physical and full numerical versions of the array were used. The numerical model, including all accessible knowledge of its architecture and key parameters, was used to design the array.

Figure 6 Antenna side of the 8 x 8 phased array (a). Simulation of the IC side of the array, showing the E-fields at the IC and antenna feeds (b).

Figure 7. 29 GHz azimuth patterns comparing the near-field to far-field processed results (red) with the pattern reconstructed using the combination technique (blue). φ = 0° plane (a); φ = 90° plane (b).

During the measurement step, the complete sphere around the DUT was scanned with 2 degree angular steps in both azimuth and elevation. To verify the results, two methods were used to compute directivity. With the first method, the acquired near-field data was processed using FIAFTA. The algorithm created the equivalent current box, which was then imported into EMPIRE XPU, where the fields were propagated via FDTD through the complete computational domain. With the second method, a far-field multi-level, fast multipole method translation, also supported in FIAFTA, was used to directly compute the far-field radiation pattern from the measurement data.⁹ The results of the two methods, compared in Figure 7, agree across the complete angular region. Observations of additional near-field distributions at various locations show complete consistency between the fields for Σ_s obtained only with FIAFTA and the combination with EMPIRE XPU.

In the next stage, the FDTD software was used to simulate the antenna integrated in the windshield of the car, shown in Figure 5. The computations were performed using two approaches: 100 percent numerical, where both the antenna and the vehicle were modeled, and hybrid, where the combination technique was employed, with the array represented in the EM simulation by its measurement-based equivalent source. Figure 8 compares the two, showing the near-field E-field magnitudes in a defined plane at 29 GHz. The field distributions agree with some differences, especially in the region between the array and the windshield. Figure 9 compares the far-field directivity patterns, showing reasonably consistent results when φ = 0 degrees and more deviations, especially in the sides lobes, when φ = 90 degrees.

These differences are expected. The FDTD model of the array does not account for production tolerances or tolerances in the operation of the electronics. Other error contributors include DUT modeling errors (e.g., imperfect knowledge of dielectric properties), measurement uncertainty and boundary conditions applied at Σ_s for deducing the radiating currents. A more systematic uncertainty evaluation is required, which will be the subject of future investigation.

At this point, neither of the two computational approaches delivers better results, i.e., closer to the real-world implementation. The hybrid or combined approach yields much higher computational efficiency than the 100 percent numerical analysis. Simulating the full EM model of the array is challenging due to the fine details in the multi-layer structure of the 5G module and the computational complexity of the scenario. Simulating the full model with 3600 million FDTD cells requires a computational time of 180 minutes and RAM usage of 108 GB. As these fine details disappear in the hybrid model, the simulation complexity drops to 320 million FDTD cells for the same calculation volume, requiring a calculation time of only 15 minutes and 10 GB of memory.

Figure 8. Near E-fields at 29 GHz using a 40 dB scale: cut-plane orientation with respect to computed model (a), FDTD-only calculations (b) and combination technique (c).

CONCLUSION

Figure 9. 29 GHz azimuth patterns comparing full-wave computation only (blue) with measurement–simulation (red). φ = 0° plane (a); φ = 90° plane (b).

As the need to improve antenna design and performance in real-world applications is constantly growing, as is the complexity of the scenarios, converging measurements with the power of numerical computation seems an unavoidable way forward. This article presented an augmented measurement or augmented simulation technique, exploring this approach and revealing multiple advantages. Numerical computation can be made more realistic, as no a priori and in-depth knowledge of the DUT, including manufacturing tolerances, is required. Calculations are also more efficient - by 12x in speed and 10x in memory in the example described - as much of the complexity in modeling the radiating source is removed. Measurements can be more cost and time effective. In the example, an expensive, full-vehicle OTA facility can be replaced by a 1.3 m² spherical scanning anechoic chamber, used just to measure the array module. Integration of the module in the car is obtained by processing. Future articles will demonstrate such techniques for other applications, involving measurements of active devices transmitting modulated signals and including more systematic evaluation of uncertainty contributors.

References:

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