# Analysis of Shielding Effectiveness of a Cavity with Internal Dielectric Plate and Apertures
## 2 Theoretical Analysis of Cavity Shielding Effectiveness
### Models of Shielding Cavities with Different Aperture Arrays  
The previous section considered the electromagnetic characteristics of shielded cavities with a single aperture. To better understand the influence of rectangular and circular aperture arrays on the electromagnetic shielding ability of shielded cavities, we produced schematics of the aperture array plane distributions, as shown in Figures 3 and 4, to analyze and compare the shielding effects with different shapes and numbers of apertures more intuitively.  
The aperture array consists of two apertures of the same shape and size, as shown in Figure 5. According to [PERSON]'s theoretical research, for aperture arrays with the same  
Figure 4: Circular: (**A**) double-hole; (**B**) four-hole; (**C**) six-hole.  
Figure 3: Rectangular: (**A**) double-hole; (**B**) four-hole; (**C**) six-hole.  
shape, small spacing, and axial symmetry, the impedance of the aperture array is equal to the sum of the impedances of each aperture in the array. Thus, the impedance of a [PERSON] aperture array \(Z_{ap2}\) is expressed as  
\[Z_{ap2}=q\left[\ln 2\times\frac{1+\sqrt[4]{1-\left(\frac{w_{c}}{b}\right)^{2}}}{ 1-\sqrt[4]{1-\left(\frac{w_{c}}{b}\right)^{2}}}\right]^{-1}\frac{j120\pi^{2}l \tan\left(k_{0}\frac{l}{2}\right)}{2a} \tag{14}\]  
where q represents the number of openings. The \(Z_{ap2}\) calculation can be incorporated into (14) to obtain the single-cavity shielding effectiveness of the hole array.  
The aperture exhibits different impedances \(Z_{ap}\) at different positions. In the low-frequency range, the electromagnetic field distributions inside the aperture and cavity are similar, which allows the mode indices p and q of the aperture to be approximately equivalent to the mode indices m and n of the cavity. However, as the frequency increases, there is a significant difference in the electromagnetic field distribution between the aperture and the interior of the cavity, resulting in mode indices p and q of the aperture that cannot be approximated by the mode indices m and n of the cavity. To describe the characteristics of the hole gap at high frequencies more accurately, the eccentricity coefficient Cm is introduced to calculate the impedance \(Z_{ap}\) of the eccentric hole gap.  
\[C_{m}=\int_{x_{0}}^{x_{0}+l}\int_{y_{0}}^{y_{0}+w}\alpha\cdot\beta dxdy/XY \tag{15}\]  
\[Z_{ap}=\frac{1}{2}C_{m}jZ_{c}\tan\frac{k_{0}l}{2} \tag{16}\]  
In (15), \(\alpha\) is represented as \(\cos(n\pi y)\cdot\cos(n\pi(y-y_{0}))/bw\), \(\beta\) is represented as \(\sin(m\pi x)\sin(m\pi(x-x_{0}))/al\), X and Y represent the coordinates of the center point of a single hole, \(x_{0}\) and \(y_{0}\) represents the starting coordinate of the bottom left corner of the hole. Using (16) for specific pore positions, we calculated the pore impedance \(Z_{ap}\)[21] at all positions. To obtain the shielding effectiveness of the cavity corresponding to the pores at any position, we substituted specific coordinate values into the corresponding impedance calculation equation. Thus, we can calculate the impedance value of the pores and the shielding effectiveness when the pores deviate from the center, based on their specific locations and characteristics.