# Analysis of Shielding Effectiveness of a Cavity with Internal Dielectric Plate and Apertures
## 2 Theoretical Analysis of Cavity Shielding Effectiveness  
### Model of Shielding Effectiveness for Single-Hole Cavity  
A metal cavity with a rectangular opening was considered. Figure 1 shows a rectangular cavity with an opening under external plane-wave irradiation. The internal dimensions of the cavity are \(a\times b\times d\), and the wall thickness of the cavity is t. The rectangular opening hole is located at the center of the panel with a size of \(l\times w\). Observation point P is located inside the cavity at a distance of \(d-z_{X}\) from the opening position; the incident plane wave is perpendicular to the panel.  
Figure 2 shows the equivalent circuit of the shielded cavity. In this circuit, the incident plane wave is equivalent to a voltage source with voltage \(V_{0}\) and impedance \(Z_{0}\approx 377\)\(\Omega\). The shielding cavity is equivalent to a rectangular waveguide with a terminal short circuit, with a characteristic impedance of \(Z_{g0}\) and a propagation constant of \(K_{g0}\).  
According to the equivalent circuit method [5], the aperture impedance \(Z_{ap}\) is expressed as  
\[Z_{ap}=\frac{1}{2}\left(\frac{l}{a}\right)jZ_{0s}\tan\frac{k_{0}l}{2} \tag{1}\]  
In the equation, \(k_{0}=2\pi/\lambda\). For the equipment we used, \(Z_{0s}\) was approximated as  
\[Z_{0s}=120\pi^{2}\left[\ln\left(2\frac{1+\sqrt[4]{1-\left(w_{e}/b\right)^{2}}}{ 1-\sqrt[4]{1-\left(w_{e}/b\right)^{2}}}\right)\right]^{-1} \tag{2}\]  
In (2), \(w_{e}=w-\frac{5t}{4\pi}\left(1+\ln\frac{4\pi w}{t}\right)\). The size of the circular opening can be expressed as \(l=w=\sqrt{\pi}\cdot r\) using [PERSON]'s theory and calculated using (2). In the equivalent circuit shown in Figure 2, the equivalent voltage and impedance can be calculated according to [PERSON]'s theorem.  
\[V_{1}=V_{0}\frac{Z_{ap}}{Z_{ap}+Z_{0}} \tag{3}\]  
\[Z_{1}=Z_{0}\frac{Z_{ap}}{Z_{ap}+Z_{0}} \tag{4}\]  
According to the \(TE_{10}\) propagation mode, the characteristic impedance and propagation constant are expressed as  
\[Z_{g0}=\frac{Z_{0}}{\sqrt{1-\left(\frac{\lambda}{2a}\right)^{2}}} \tag{5}\]  
Figure 1: Single-cavity model with rectangular openings.  
Figure 2: Equivalent circuit model of a single cavity with an open hole.  
\[K_{g0}=k_{0}\sqrt{1-\left(\frac{\lambda}{2a}\right)^{2}} \tag{6}\]  
The equivalent voltage and impedance at point \(d-z_{X}\) can be calculated as  
\[V_{2}=\frac{V_{1}}{\cos\bigl{(}K_{g0}(d-Z_{X})\bigr{)}+\frac{jZ_{1}}{Z_{g0}\sin \bigl{(}K_{g0}(d-Z_{X})\bigr{)}}} \tag{7}\]  
\[Z_{2}=Z_{g0}\frac{Z_{1}+jZ_{g0}\tan\bigl{(}K_{g0}(d-Z_{X})\bigr{)}}{Z_{g0}+jZ_{ 1}\tan\bigl{(}K_{g0}(d-Z_{X})\bigr{)}} \tag{8}\]  
\[Z_{3}=jZ_{g0}\tan\bigl{(}K_{g0}(d-Z_{X})\bigr{)} \tag{9}\]  
According to Davinan, the voltage \(V_{p}\) and current \(I_{p}\) at point P are expressed as  
\[V_{p}=V_{2}\frac{Z_{3}}{Z_{2}+Z_{3}} \tag{10}\]  
\[I_{p}=\frac{V_{2}}{Z_{2}+Z_{3}} \tag{11}\]  
According to the above formula, the shielding efficiency of the electric and magnetic fields at point P can be derived as  
\[SE_{E}=-20\log_{10}\left|\frac{V_{p}}{V_{p}^{\prime}}\right|=-20\log_{10} \left|\frac{2V_{p}}{V_{0}}\right| \tag{12}\]  
\[SE_{M}=-20\log_{10}\left|\frac{I_{p}}{I_{p}^{\prime}}\right|=-20\log_{10} \left|\frac{2I_{p}Z_{0}}{V_{0}}\right| \tag{13}\]