# An Improved PIN Diode Model Design for a Tunable Frequency Selective Absorber
## 2 Unit Design Process
### Improved Unit Design  
In practice, parasitic parameters--the junction capacitance inherent to the encapsulated PIN diode--have a significant impact on the performance over the entire frequency range discussed in this paper, which varies with the applied bias voltage. Therefore, based on the original design, by introducing bias-dependent variable capacitors, as shown in Figure 4a, aiming to optimize the resonant frequency control and absorption characteristics, the overall performance in frequency selective applications can be improved. The simulated reflection coefficient curve shown in Figure 4b reveals significant variations when different capacitors are paralleled with the structure. In comparison to Figure 3, where resonance points shift from 9.4 GHz to 10 GHz after adding a 0.25 pF capacitor, the bandwidth achieving a reflection coefficient below \(-15\) dB expands to 2 GHz (from 8.7 GHz to 10.7 GHz), with an absorption rate reaching 97%. It is important to note that the bandwidth here specifically refers to the frequency range where the absorption rate exceeds 97%. Further analysis shows that with a resistance of 60 \(\Omega\), adding a 0.01 pF capacitor shifts the resonance from 9.1 GHz to 8.7 GHz, broadening the bandwidth to 1.4 GHz (7.9 GHz to 9.3 GHz). When the resistance is increased to 80 \(\Omega\) and a 0.15 pF capacitor is added, the resonance shifts from 8.7 GHz to 10.9 GHz, expanding the bandwidth  
Figure 3: (**a**) Geometric of the basic tunable frequency selective absorber; (**b**) simulation results. to 0.9 GHz (10.4 GHz to 11.3 GHz). Lastly, with a resistance of 150 \(\Omega\) and a 0.1 pF capacitor in parallel, a single resonance peak at 6.2 GHz splits into two peaks, with the higher one at 11.6 GHz, and the bandwidth broadens to 0.8 GHz (11.2 GHz to 12 GHz). These findings highlight the significant enhancement in absorption performance provided by the shunt capacitor, which enables continuous tuning of the absorption rate to exceed 97% across the entire X-band. Additionally, a 10 k\(\Omega\) resistor is used to simulate the off state of the PIN diode, represented by the black line in Figure 4b. This line maintains a high reflection coefficient, exceeding \(-0.3\) dB (indicating that 93.3% of the electromagnetic wave energy is reflected) across the 7-13 GHz range. This characteristic confirms the tunable absorber's capability to function effectively as a total reflector in practical applications. Based on the simulation results, we analyzed the performance of five Floquet modes at \(R=20\)\(\Omega\), \(C=0.25\) pF, and we provided a detailed interpretation of the reflection coefficients for each mode to evaluate the overall performance of the absorber, as shown in Figure 5. Below is the detailed analysis:  
1. Mode 1 (Fundamental Mode, Zeroth-Order Specular Reflection) Simulation Results: \(dB(\)S(FloquetPort1:1, FloquetPort1:1)) <-20\(\) dB Corresponding power reflection coefficient: \(R_{1}=10^{-20/10}=0.01\) Physical Interpretation: The reflection coefficient of Mode 1 is extremely low, indicating that about 99% of the incident energy is either absorbed or scattered in other modes. 2. Mode 2 (First-order diffraction Mode) Simulation Results: \(dB(\)S(FloquetPort1:2, FloquetPort1:1)) <-40\(\) dB Corresponding power reflection coefficient: \(R_{2}=10^{-40/10}=0.0001\) Physical Interpretation: The reflected energy in Mode 2 is very low, showing that only 0.01% of the incident energy couples into Mode 2. This mode likely corresponds to small-angle diffraction directions. Figure 4: (a) Geometric of the improved tunable frequency selective absorber; (b) simulation results. 3. Mode 3 (Second-Order Diffraction Mode) Simulation Results: \(dB(\text{S}(FloquetPort1:3,FloquetPort1:1))<-20\) dB Corresponding power reflection coefficient: \(R_{3}=10^{-20/10}=0.01\) Physical Interpretation: The scattered energy of Mode 3 is similar to that of Mode 1, with a very low reflection coefficient, indicating that this mode's scattering contribution is negligible. 4.