# Design and Implementation of C-Band Large-Power Planar Butler Matrix in SRS
## 3 Results  
### Simulation  
The optimally designed coupler, crossover junction, \(45^{\circ}\) phase shifter, and \(0^{\circ}\) phase shifter are applied to the Butler matrix beamforming network, and the entire model is electromagnetically simulated to analyze the performance, e.g., port reflection coefficients, input and output port isolations, transmission coefficients, and output port phase differences. Due to the model's symmetry, the scattering parameters related to input port 1 and input port 4 are identical when the input port is fed. Similarly, this works for input port 2 and input port 3 as well. The phase difference between the output ports is \(45^{\circ}\), \(-135^{\circ}\), \(135^{\circ}\), and \(-45^{\circ}\), respectively.  
Figure 14: The fabricated Butler matrix’s inner conductor.  
Figure 15: The fabricated Butler matrix’s outer conductor.  
When input port 1 and input port 2 are fed separately, the input reflection coefficient, transmission coefficient, and isolation of the Butler matrix beamforming network are shown in Figure 16. In the frequency range of 3.85-4.15 GHz, the input reflection coefficient of input port 1 is less than \(-20\) dB, the input isolation is greater than 20 dB, and the transmission coefficient is \(-6.0\) dB \(\pm\) 0.4 dB. The input reflection coefficient of input port 2 is less than \(-20\) dB. The isolation between input ports is greater than 20 dB, and the transmission coefficient is \(-6.0\) dB \(\pm\) 0.4 dB. The insertion loss of the matrix is small. It shows that the performance of the Butler matrix is close to an ideal matrix.  
The isolations between the output ports are greater than 20 dB in the frequency range of 3.8-4.2 GHz, as shown in Figure 17. The high isolation between output ports guarantees the independence of each output port, which will benefit the phased array for beamforming. Meanwhile, the reflection coefficients of output port 5 and output port 6 are less than \(-20\) dB as well. The Bulter matrix's output port is matched to 50 \(\Omega\), i.e., standard antennas connected to the output port will avoid impedance mismatch and prevent large microwave power being reflected to the Butler matrix.  
Figure 16: Simulation results of Butler matrix input ports’ scattering parameters: (**a**) reflection coefficient of input port 1 and transmission coefficients of input port 1 to other ports; (**b**) reflection coefficient of input port 2 and transmission coefficients of input port 2 to other ports.  
Figure 17: Simulation results of Butler matrix output ports scattering parameters: (**a**) reflection coefficient of output port 5 and isolation of output port 5 to other ports; (**b**) reflection coefficient of output port 6 and isolation of output port 6 to other ports.  
When the output port is fed, the phase difference between the output ports is in the frequency range of 3.9-4.1 GHz, as shown in Figure 18, and the phase difference between neighboring output ports is 45 \(\pm\) 5\({}^{\circ}\) when input port 1 is fed. The phase difference between neighboring output ports is \(-\)135 \(\pm\) 5\({}^{\circ}\) when input port 2 is fed. The stabilized phase frequency range is shifted to the lower frequency when input port 3 is fed, and the phase difference between neighboring output ports is 135 \(\pm\) 10\({}^{\circ}\). The phase difference between neighboring output ports is \(-\)45 \(\pm\) 6\({}^{\circ}\) when input port 4 is fed.