## 4 Results and Discussion  
Figure 16a shows a photograph of the fabricated antenna unit and subarray. The antennas bonded on the PCB through BGA are fixed on a metal base through the conductive adhesive. SMA connectors are installed on the side of the metal base for connection to coaxial transmission lines. Figure 16b shows a side view and a partial zoom-in zone of the BGA pattern after bonding. The shapes of the solder balls have a good consistence.  
The antenna was tested in a microwave chamber. Figure 17a,b show the simulated and measured results of the reflection coefficient and boresight gain of the unit. The simulated impedance bandwidth (\(S_{11}\leq-10\) dB) was from 26.5 GHz to 30.7 GHz, while the measured bandwidth was from 26.2 to 30.1 GHz. The measured gain fluctuated to some extent, but the trend of variation versus frequency was consistent with the simulated one. Figure 18 shows the simulated and measured normalized radiation patterns of the antenna unit in the \(xoz\) and \(yoz\) planes at 28, 29, and 30 GHz. Due to the testing conditions, only the frontal radiation was measured. The simulated and measured patterns were in good agreement.  
Figure 16: (a) Fabricated antenna unit and 2 \(\times\) 2 array. (b) Detail photograph of BGA.  
Figure 15: The assembled 2 \(\times\) 2 array and PCB feeding network.  
The simulated and measured results of the array were in rough agreement, as shown in Figure 19. In addition to the frequency shift, note that an unexpected measured gain null occurred near 27 GHz and the reflection coefficient showed a peak. Consequently, the impedance bandwidth decreased compared with the simulated result. This discrepancy between the measured and simulated results of the array antenna was probably due to multiple factors. First, the TSV fabrication had a significant impact on the performance of the devices. Second, there may have been a slight misalignment between the silicon wafer and the PCB. Third, the material properties of silicon and the substrate for the test PCB were different from those used for simulation. All the above-mentioned factors could  
Figure 17: Simulated and measured results. (**a**) S\({}_{11}\); (**b**) boresight gain.  
Figure 18: Simulated and measured normalized radiation patterns of the proposed antenna unit. (**a**) 28 GHz; (**b**) 29 GHz; (**c**) 30 GHz.  
have contributed to the discrepancy, and more samples are needed to confirm the cause. The simulated and measured normalized radiation patterns of the subarray in the xoz and yoz planes at 28.5, 29.5, and 30.5 GHz are shown in Figure 20, which also shows a good agreement.  
Figure 19: Simulated and measured results of the 2 \(\times\) 2 array. (**a**) S\({}_{11}\); (**b**) boresight gain.  
Figure 20: Simulated and measured normalized radiation patterns of the array. (**a**) 28.5 GHz; (**b**) 29.5 GHz; (**c**) 30.5 GHz.  
Table 2 shows a performance comparison between our design and the micromachined antennas in the previously reported articles. Our proposed antennas with wide band and high gain can be integrated in a 3-D manner with other components. The compact size can be used in highly integrated multi-functional systems.