# An Improved PIN Diode Model Design for a Tunable Frequency Selective Absorber
## 2 Unit Design Process
### Improved Unit Design
Mode 4 (Third-Order Diffraction Mode) Simulation Results: \(dB(\text{S}(FloquetPort1:4,FloquetPort1:1))<-12\) dB Corresponding power reflection coefficient: \(R_{4}=10^{-12/10}=0.063\) Physical Interpretation: The scattered energy in Mode 4 is significantly higher than in Modes 1-3, indicating that approximately 6.3% of the energy is coupled into this higher-order mode. This mode is likely related to the periodic dimensions or design imperfections of the absorber. 5. Mode 5 (Fourth-Order Diffraction Mode) Simulation Results: \(dB(\text{S}(FloquetPort1:5,FloquetPort1:1))<-15\) dB Corresponding power reflection coefficient: \(R_{5}=10^{-15/10}=0.0316\) Physical Interpretation: The scattered energy in Mode 5 is also relatively high, with approximately 3.16% of the energy coupled into this mode. This mode corresponds to larger diffraction angles and may play a significant role in edge diffraction effects. Even when accounting for the scattering contributions of higher-order modes, the absorber still demonstrates excellent overall performance. The reflection coefficient of the fundamental mode (Mode 1) is below \(-20\) dB, indicating that more than 99% of the energy in this mode is absorbed. Modes 2 and 3 exhibit low scattering contributions, with reflection coefficients below \(-18\) dB and a combined scattered energy contribution of less than 3%. However, higher-order modes (Modes 4 and 5) contribute approximately 9.4% of the total scattered energy, primarily due to non-specular diffraction at larger angles. Even  
Figure 5: Simulation results of different modes at \(R=20\)\(\Omega\), \(C=0.25\) pF. considering the scattering effects of higher-order modes, the absorber still achieves excellent absorption performance, with a total absorption rate exceeding 90% across the X-band. The normalized intrinsic impedance of the absorber is key to optimizing its absorption characteristics. As shown in Figure 6, with a resistance (\(R\)) of 20 \(\Omega\) and a capacitance (\(C\)) of 0.25 pF, the real part of the normalized input impedance reaches 1, while the imaginary part approaches 0 at 10.16 GHz. This indicates that at this frequency, the absorber's input impedance perfectly matches the free space impedance, which is ideal for achieving maximum absorption efficiency according to basic impedance matching theory. Moreover, 10.16 GHz falls within the 97% absorption bandwidth (8.7 GHz to 10.7 GHz), as depicted in Figure 4b, confirming that the structure is effectively tuned to absorb electromagnetic waves within this range. The comparison between Figures 6b-d and 4 supports these findings, showing consistent results across different simulations and configurations. These conclusions emphasize the absorber device's capability to adjust its reflectivity response by varying resistors and capacitors within the 8-12 GHz range. This flexibility allows for precise tuning of the absorption properties to meet specific operational requirements, making the device highly adaptable for practical applications. Figure 6: Normalized intrinsic impedance of proposed structure for different combinations: (a) R = 20 \(\Omega\), C = 0.25 pF; (b) R = 60 \(\Omega\), C = 0.01 pF; (c) R = 80 \(\Omega\), C = 0.15 pF; (d) R = 150 \(\Omega\), C = 0.1 pF.