## 5 Conclusions  
This paper presented an enhanced method to reconstruct the radiated emissions of an EUT in an RC via knowledge of the values of the electric field sampled on the walls. By enforcing the equivalence principle, the number of equivalent sources used to represent the emissions is strongly reduced with respect to other choices. The analytical formulation of the method is based on the use of the modal expansion of the electromagnetic field in a rectangular cavity. The method has been validated using both numerical simulations and experimental measurements performed in an anechoic environment. Future work will deal with the extension of the proposed method to a scenario where the electric field is sampled using a spectrum analyzer or an EMI receiver, so only the amplitude of the electric field samples is known. Another fundamental aspect that will be investigated is the influence of the loading effect of the chamber, due to the presence of lossy EUTs, on the accuracy of the proposed method. Conceptualization, A.D.L., G.C., P.R. and V.M.P. ; methodology, G.C. ; software, A.D.L. ; validation, A.D.L. and V.M.P. ; formal analysis, G.C. and P.R. ; data curation, A.D.L. and V.M.P. ; writing--original draft preparation, A.D.L., G.C., P.R. and V.M.P. ; writing--review and editing, A.D.L., G.C., P.R. and V.M.P. ; visualization, A.D.L., G.C., P.R. and V.M.P. ; supervision V.M.P. All authors who have contributed substantially to the work reported have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The authors declare no conflict of interest. Appendix A Appendix A Appendix A Appendix A.1. Electric Field Generated by a Sub-Surface Orthogonal to y Axis  
Let us consider the rectangular faces of the equivalence surface orthogonal to the y axis and one of its sub-surfaces (S) having dimensions (\(2\Delta_{x}\), \(2\Delta_{z}\)), and centered in (\(x_{H}\),\(y_{H}\),\(z_{H}\)). In this case, the equivalent magnetic (\(M_{eq}^{i}\)) and electric (\(j_{eq}^{i}\)) currents are (A1):  
\[\left\{ \begin{array}{ll}\overline{M_{eq}^{i}}=M_{eqx}^{i}\hat{x}+M_{eqz}^{i} \hat{z}&\\ \overline{j_{eq}^{i}}=J_{eqx}^{i}\hat{x}+J_{eqz}^{i}\hat{z}&\end{array} \right. i=1,\ldots,N_{eq}^{(y)} \tag{11}\]  
where \(N_{eq}^{(y)}\) is the total number of sub-areas after the discretization of the considered face. The electric field radiated by the equivalent currents in a generic point \(P(x,y,z)\) is reported in (A2)-(A4). \[\overline{E}_{IRR}(x,y,z)= -\frac{1}{j\omega\omega}\frac{32}{abc_{m}\omega_{R}}\sum\limits_{ m,n,p}\frac{1}{k_{m,n,p}^{2}-g_{TE}^{2}}\sin(k_{x}\Delta_{x})\sin(k_{y}y_{H}) \sin(k_{z}\Delta_{z})\left[-\frac{J_{eqx}^{i}\sin(k_{x}x_{H})\cos(k_{z}z_{H}) }{k_{x}}\right.\] \[\left.+\frac{J_{eqx}^{i}\cos(k_{x}x_{H})\sin(k_{z}z_{H})}{k_{z}} \right]\left\{ \begin{array}{ll}k_{x}\cos(k_{x}x)\sin(k_{y}y)\sin(k_{z}z)\hat {x}&\\ k_{y}\sin(k_{x}x)\cos(k_{y}y)\sin(k_{z}z)\hat{y}&,\\ k_{z}\sin(k_{x}x)\sin(k_{y}y)\cos(k_{z}z)\hat{z}&\end{array} \right.\] \[\overline{E}_{TE}(x,y,z)= \frac{32}{ab\omega_{m}\omega_{R}}\sum\limits_{m,n,p}\frac{1}{k_{ m,n,p}^{2}-g_{TE}^{2}}\sin(k_{x}\Delta_{x})\sin(k_{z}\Delta_{z})\left\{\cos (k_{y}y_{H})\left[\frac{M_{eqx}^{i}\cos(k_{x}x_{H})\sin(k_{z}z_{H})}{k_{x}k_{z }}\right.\right.\] \[\left.\left.-\frac{M_{eqx}^{i}\sin(k_{x}x_{H})\cos(k_{z}z_{H})}{ k_{x}^{i}}\right]\right.\] \[+j\omega\mu\frac{k_{y}}{k_{x}^{i}k_{x}}\int_{k_{z}}^{i}j_{eqz}^{i }\cos(k_{x}x_{H})\sin(k_{y}y_{H})\sin(k_{z}z_{H})\Big{\}}\left\{ \begin{array}[ ]{ll}-k_{y}\cos(k_{x}x)\sin(k_{y}y)\sin(k_{z}z)\hat{x}&\\ k_{x}\sin(k_{x}x)\cos(k_{y}y)\sin(k_{z}z)\hat{y}&\\ \end{array}