# Analysis of Shielding Effectiveness of a Cavity with Internal Dielectric Plate and Apertures
## 2 Theoretical Analysis of Cavity Shielding Effectiveness
### Model of a Perforated Single Cavity with Built-In Dielectric Plate  
Next, we considered a single-cavity metal shielding model with a built-in dielectric plate. Figure 6 shows rectangular and circular cavities with holes in the mining dielectric plate located at the center of the plane. The internal structure of the cavity is \(a\times b\times d\), and there is a rectangular hole with a size of \(l\times w\). Observation point P is located inside  
Figure 5: Hole-array cavity models with different shapes. the rectangular cavity. A built-in mining dielectric plate was placed on the right side of the cavity. An equivalent circuit diagram of a single cavity with a built-in mining dielectric plate is shown in Figure 7. The incident electromagnetic wave is equivalent to a voltage source \(V_{0}\) with a wave impedance of \(Z_{0}\approx 377\)\(\Omega\), an equivalent impedance of \(Z_{ap}\) with an opening, a characteristic impedance of \(Z_{g0}\), an equivalent impedance of \(Z_{PCB}\), and a dielectric plate propagation constant of \(K_{g0}\). The electromagnetic topological structure [22] of the single-layer shielded cavity model with a built-in dielectric plate is shown in Figure 8. Node J represents the observation point of the shielded cavity; node \(J_{1}\) represents the external observation point of the cavity; \(J_{2}\) represents the aperture; \(J_{3}\) represents the internal observation point of the cavity; \(J_{4}\) and \(J_{5}\) represent the left and right ends of the dielectric plate; \(J_{6}\) represents the rear end of the cavity; T represents the electromagnetic wave propagation channel in free space; \(T_{1}\) represents the free space transmission channel; \(T_{3}\) represents the dielectric plate transmission channel; \(T_{2}\), \(T_{4}\), and \(T_{5}\) represent the internal transmission channel of the cavity; \(W_{s}\) represents the voltage source in the equivalent circuit of the box; the voltage is represented by \(V_{0}\), \(V_{0}=1V\). The corresponding BLT equation is established according to Figure 8:  
\[V=(\rho+E)(\Gamma-\rho)^{-1}S \tag{17}\]  
where E represents the identity matrix; S represents the node voltage \(S=(V_{0}\ 0\ 0\ 0\ 0\ 0\ 0\ 0\ 0)^{T}\); \(\Gamma\) is the composition of the electromagnetic transmission coefficients in the transmission channel, \(\Gamma=\text{diag}[T_{1}\ T_{2}\ T_{3}\ T_{4}\ T_{5}]\); \(\rho\) is the node scattering matrix \(\rho=\text{diag}[\rho_{1}\rho_{2}\rho_{3}\rho_{4}\rho_{5}\rho_{6}]\); and \(\rho_{i}\) represents the node \(J_{i}\) scattering coefficient, where \(\rho_{1}=0\) and \(\rho_{6}=-1\). The scattering matrix of node \(J_{i}(i=1,2,\dots,6)\) is  
Figure 6: Single-hole cavity model with built-in dielectric plate. (**A**) Rectangular opening (**B**) Circular opening. Figure 7: Equivalent circuit model of single-hole cavity with built-in dielectric plate. \[\rho_{1}=0\] \[\rho_{2}= \begin{bmatrix}\frac{Y_{0}-Y_{0}-Y_{qp}}{Y_{0}+Y_{0}+Y_{qp}}& \frac{2Y_{g0}}{Y_{0}+Y_{0}+Y_{qp}}\\ \frac{2Y_{0}}{Y_{0}+Y_{g0}+Y_{qp}}&\frac{Y_{0}-Y_{0}}{Y_{0}+Y_{qp}+Y_{qp}}\\ \end{bmatrix} \] \[\rho_{3}= \begin{bmatrix}0&1\\ 1&0\end{bmatrix} \] \[\rho_{4}= \begin{bmatrix}\frac{Y_{g0}-Y_{pcb}}{Y_{g0}+Y_{pcb}}& \frac{2Y_{g0}}{Y_{0}+Y_{pcb}}\\ \frac{2Y_{pcb}}{Y_{0}+Y_{pcb}}&\frac{Y_{0}-Y_{pcb}}{Y_{g0}+Y_{pcb}}\\ \end{bmatrix}  \tag{18}\] \[\rho_{5}= \begin{bmatrix}\frac{Y_{pcb}-Y_{q0}}{Y_{g0}+Y_{pcb}}& \frac{2Y_{q0}}{Y_{g0}+Y_{pcb}}\\ \frac{2Y_{pcb}}{Y_{g0}+Y_{pcb}}&\frac{Y_{0}-Y_{pcb}}{Y_{g0}+Y_{pcb}}\\ \end{bmatrix} \] \[\rho_{6}=-1\]  
where \(Y_{0}=1/Z_{0}\) is the equivalent admittance of the electromagnetic waves in free space; \(Y_{g0}=1/Z_{g0}\) is the equivalent admittance of the electromagnetic waves in the cavity; \(Y_{ap}=1/Z_{ap}\) is the equivalent admittance of the perforated cavity wall; \(Y_{PCB}=1/Z_{PCB}\) is the equivalent admittance of the dielectric plate, and \(Z_{0}\approx 377\)\(\Omega\) is the wave impedance.