# An Ultra-Wideband Frequency Selective Rasorber with Low Infrared Emissivity
## 2 Analysis, Design and Experimental Verification
### Transmission/Absorption Conditions Based on EC Analysis Method
Thus, we can easily find that:  
\[\delta=\frac{2\pi}{\lambda_{a}}tcos\theta=\frac{\pi}{2} \tag{12}\]  
According to Equations (10) and (12), we can thus deduce the optimal absorption conditions. 1. FSS should be in a perfect stop band at \(f_{a}\). 2. The equivalent thickness of the DC layer should be represented by \(t_{0}=tcos\theta=\frac{\lambda_{a}}{4}\). * _Transmission conditions_At the transmission frequency \(f_{t}\), the transmission coefficient \(S_{21}\) and reflection coefficient \(S_{11}\) of the two-port network are interrelated as follows: \(|S_{11}|=0\), \(|S_{21}|=1\). Then, we can obtain the equations below according to Equations (6) and (7). \[(Z_{RS}+Z_{FSS})-j(Z_{RS}-Z_{0}-Z_{FSS})=0 \tag{13}\]  
\[(2+\frac{Z_{0}Z_{RS}+Z_{0}Z_{FSS}}{Z_{RS}Z_{FSS}})cos\theta+j(2+\frac{Z_{0}^{2} +Z_{RS}Z_{0}+Z_{FSS}Z_{0}}{Z_{RS}Z_{FSS}})sin\theta=2 \tag{14}\]  
Equation (14) can evidently illustrate that \(Z_{RS}Z_{FSS}\rightarrow\infty\). In addition, the expression of \(Z_{RS}\) and \(Z_{FSS}\) can be represented in terms of EC, as shown in Equations (15) and (16). \[Z_{RS}=R_{1}+\frac{1-\omega^{2}L_{1}C_{1}}{j\omega C_{1}}+\frac{j\omega L_{2}} {1-\omega^{2}L_{2}C_{2}} \tag{15}\]  
\[Z_{FSS}=\frac{j\omega L_{3}}{1-\omega^{2}L_{3}C_{3}} \tag{16}\]  
\[\frac{1}{w_{t}^{2}}=L_{2}C_{2}=L_{3}C_{3} \tag{17}\]  
Then, substitute Equations (15) and (16) into Equation (13), and under the conditions of \(Z_{RS}Z_{FSS}\rightarrow\infty\), it is clear to see that \(Z_{RS}\rightarrow\infty\), \(Z_{FSS}\rightarrow\infty\), which means both RS and FSS should be transparent at the transmission frequency \(f_{t}\). And \(Z_{RS}\rightarrow\infty\) indicates the absolute value of its imaginary part is also infinite, when \(R_{1}\) is limited by absorption conditions. This means the absolute value of \(L_{2}\) should be as large as possible, while the absolute value of \(C_{2}\) should be extremely small according to Equation (17). Further, it can be observed that the primary factor influencing the change in the transmission coefficient \(S_{21}\) is that the imaginary part of \(Z_{RS}\) mismatches rapidly in the spectral range around \(f_{t}\). The discussion of high inductance and low capacitance above is only aimed at enhancing the transmission coefficient at the single frequency point \(f_{t}\). In order to further broaden the wave transmission bandwidth, the key point is to maintain a high transmission coefficient over a wide spectral range around \(f_{t}\). Thus, it is essential to identify a non-frequency-dependent resonant structure to mitigate the rapid mismatch of the imaginary part of the impedance. Finally, the transmission conditions can be illustrated as follows:  
1. Both RS and FSS should be transparent at the frequency transmission frequency \(f_{t}\). 2. The resonant structure corresponding to \(L_{2}C_{2}\) should maximize inductance and minimize capacitance to reduce insertion loss (IL). 3. The utilization of miniaturized resonant structures with non-frequency-varying characteristics may be a crucial method for broadening the wave transmission bandwidth, an aspect that has been overlooked in previous research.