# Electromagnetic Interference Shielding Anisotropy of Unidirectional CFRP Composites
## 3 Results
### EMI Shielding Theory of CFRP Composite  
According to the circuit theory [42] for calculating the EM wave attenuation by shielding, the displacement current in the wave would be coupled to the CFRP when the EM wave encounters the CFRP composite, as shown in Figure 5. Then, the surface current density onto the CFRP will generate a magnetic field (H) perpendicular to it, and the magnetic field would create an opposite electromotive force, which can attenuate the current to penetrate the CFRP. This phenomenon leads to the attenuation of EM waves. The shielding attenuation _S(dB)_ for the electric field (E) can be obtained as follows:  
\[S(dB)=20\log\frac{E_{I}}{E_{T}}\ \ =20\log\frac{J_{I}Z_{W}}{J_{T}Z_{C}} \tag{5}\]  
where \(E_{I}\) and \(\mathrm{E_{T}}\) are the electric field at the incident side and transmitted side, respectively; \(J_{I}\) is the surface current density at the incident side of the CFRP, and the current value at the transmitted side \(J_{T}\) is expressed as:  
\[J_{T}=J_{I}e^{-d/\delta} \tag{6}\]  
where \(d\) is the thickness of CFRP, and \(\delta\) is the skin depth.  
\(Z_{W}\) and \(Z_{C}\) are the impedance of the incident wave and CFRP composites, respectively, which is equal to:  
\[Z_{W}=-\frac{j377\lambda}{2\pi L}\ \left(L<\frac{\lambda}{2\pi}\right)\ =377\ \left(L\geq\frac{\lambda}{2\pi}\right) \tag{7}\]  
Figure 4: Skin depth of CFRP as a function of testing angles.  
\[Z_{C}=\frac{1+j}{\sigma\delta\big{(}1-e^{-d/\delta}\big{)}} \tag{8}\]  
where \(\sigma\) is the electrical conductivity of the CFRP composite. Then, the shielding attenuation \(SE\) (\(dB\)) of the CFRP composite can be expressed as:  
\[SE(dB)=20\log\frac{Z_{W}}{e^{-d/\delta}\cdot Z_{C}}. \tag{9}\]  
According to Equation (9), the thickness and skin depth of the material plays a decisive role in the EM shielding performance. The formula's applicability in the frequency range of 5-15 GHz was verified by taking the test angles of 45\({}^{\circ}\) and 90\({}^{\circ}\) as examples. The skin depth, electrical conductivity, and related parameters were substituted into Equation (9). The comparison between the calculated prediction and the experimental results by the free space measurement is shown in Figure 6. It was observed that the experimental and predicted result were in good agreement. The maximum difference at fiber orientation of 45\({}^{\circ}\) is only about 1.9 dB. It can be concluded that Equation (9) can be applied to predict the EMI SE of unidirectional CFRP at the frequency range of 5 to 15 GHz.  
Figure 5: Schematic of EMI shielding mechanism of unidirectional CFRP.  
Figure 6: Comparison of experimental value and formula calculation value of EMI SE.  
By combining Equations (3) and (9), the EMI SE of unidirectional CFRP could be predicted at any carbon fiber orientation angles. Figure 7 shows that the predicted results are highly consistent with the experimental results in the various fiber directions at 10 GHz. When only using Equation (9) to calculate the shielding performance of CFRP at different orientation angles, it is necessary to test the material's EM parameters (skin depth, electrical conductivity, etc.) in each direction. Here, Equations (3) and (9) are used in combination, and it is only necessary to calculate or measure the electromagnetic parameters of CFRP in the 0\({}^{\circ}\) and 90\({}^{\circ}\) directions and substituting the results into the Equation (9) to obtain the EMI SE at any carbon fiber orientation angles. The predicted results were highly in good agreement with the experimental values. There was a difference between the experimental and calculated results in the fiber direction (0\({}^{\circ}\)). That might be due to the device limitation; that is, the EMI SE of the CFRP materials might have exceeded the measuring range of the device in the fiber direction.