## 6 Simulation and Results
### Inter-Chip Communication  
In this section, we present the transmission characteristics of the inter-chip communication by using the antennas discussed in this paper. The architecture for the inter-chip communication is shown in Figure 15. Here, we use the same antenna mentioned in the paper earlier to characterize the transmission in the inter-chip communication scenarios with the flip-chip packaging model. The distance between the chips is 14 mm by using FR408 (\(\epsilon_{r}\) = 3.66 and tan\(\delta\) = 0.012) PCB. The bottom of the PCB is a perfect electric conductor (PEC).  
The diameters of the solder balls in the grid are 0.1 mm, and their pitch is 0.25 mm, respectively, with a total of 25 solder balls. The \(|S_{11}|\) for both antennas is shown in Figure 16. Here, the slight change in inter-chip \(|S_{11}|\) compared with intra-chip \(|S_{11}|\) is due to the surrounding structure of the inter-chip configuration. In order to reduce the computational complexity, only the antennas on the edges are computed. The transmission between Antenna A and Antenna B is shown in Figure 17. It is evident that the transmission coefficient is approximately \(-60\) dB for the zigzag antenna, while it measures \(-43\) dB for the dipole antenna. These higher losses could pose challenges in practical applications. However, we have provided a calculation detailing the feasibility of communication with high insertion loss in Appendix A.  
Figure 16: \(|S_{11}|\) under inter-chip communication.  
Figure 15: Inter-chip communication configuration.  
Furthermore, Figures 18 and 19 show the E- and H-plane of the dipole and zigzag antenna in the case of inter-chip communication. The dipole antenna's 2D radiation pattern shows that it radiates electromagnetic energy more efficiently into two opposite directions perpendicular to the antenna's axis, but the zigzag antenna's 2D radiation pattern is more distorted and non-symmetrical with respect to the antenna's axis.  
Figure 19: Radiation pattern of the zigzag antenna in the E- and H-plane.  
Figure 17: Transmission coefficients (\(|S_{21}|\)) under inter-chip communication.  
Figure 18: Radiation pattern of the dipole antenna in the E- and H-plane.  
We investigate further to observe the variation in electric field distribution across the inter-chip structure. The top view and side view for both dipole and zigzag antennas are shown in Figures 20 and 21, where only Antenna A is excited. From the side view, we can see that the radiated field is reflected back from the heat sink (used aluminum for simulation) and bounces back from the PCB structure. Under the same identical structure, the maximum electrical field magnitude is greater for the zigzag antenna than for the dipole antenna. The geometry of the inter-chip communication model, the die substrate, and the operating frequency all affect the electric field distribution.  
In addition, Figure 22 shows the simulated magnitude of an electric field along the line connecting Antenna A and Antenna B. We can observe the rise of an electric field at around 4.5 mm (for the zigzag antenna) and 6 mm (for the dipole antenna), which is due to the reflected electric field from the bottom PCB structure.  
Figure 21: Electric field distribution across the inter-chip communication in the case of the zigzag antenna.  
Figure 20: Electric field distribution across the inter-chip communication in the case of the dipole antenna.