## 1 Introduction  
The measurement of radiated emissions is a fundamental aspect in electromagnetic compatibility; in fact, in order to ensure the correct behavior of several devices in the same environment, it is necessary to establish maximum emission and minimum immunity limits. Historically, the first measurement environment was the open-air test site (OATS), which was subsequently substituted by anechoic alternative test sites as anechoic chambers and TEM or GTEM cells. For this reason, how to correlate the measurements performed in these sites to OATS conditions has been investigated. In this direction, [1, 2, 3, 4, 5, 6, 7] introduced a set of equivalent sources to replace the equipment under test (EUT) and to extrapolate the radiation in free space conditions from the measurements performed in these alternative sites. Nowadays, one of the alternative sites that has been more extensively investigated in electromagnetic compatibility research is the reverberation chamber (RC). An RC is a metallic enclosure where the electromagnetic field is properly stirred to be statistically uniform, unpolarized, and anisotropic. There are two main typologies of stirring actions: mechanical stirring and source stirring. The first is based on the variation of the boundary conditions by rotating metallic paddles [8], or by moving [9] or vibrating [10] the RC's walls. The second kind of stirring technique acts on the source [11] by varying its positions or its frequency and therefore its coupling with the eigenmodes of the chamber. In this second set of actions, the multiple monopole source stirring (MMSS) technique was developed [12], validated [13], and successfully compared to the other techniques [14, 15]. The standard rules [16] support the use of RCs as an alternative site for EMC measurements. In particular, for the radiation emission measurements, the value of the maximum electric field radiated by the EUT is derived from the measurement of its average total radiated power and the estimation of the directivity of the EUT, analytically derived by its geometrical dimensions. Recently, a novel method was proposed [17] to directly reconstruct the emissions of an EUT by an RC. It is based on the measurement of a set of samples of electric fields collected on the walls of the RC, and subsequently on the setting of equivalent sources able to provide the emission values in free space conditions. The main advantage of this method is that the value of the electric field over all the directions is directly obtained, avoiding the estimation of the directivity of the EUT, without moving or rotating neither antennas nor EUT. In the generalized formulation of the method, six equivalent sources are placed at each point of a volumetric grid, placed in the whole volume containing the EUT. The main scope of this paper is to improve the method's computational efficiency through the reduction of the number of equivalent sources, obtained by enforcing the equivalence principle. In fact, the equivalence principle states that the radiation of a device can be described in terms of the only electric and magnetic currents tangential to a closed surface surrounding the device. According to this formulation, only four equivalent current components are necessary for each point of the equivalence surface. Therefore, by passing from a 3D to a 2D distribution of the equivalent sources, the problem complexity is strongly reduced without losing accuracy. The traditional application of the equivalence principle is based on a direct measurement of the tangential electric and magnetic field components on the equivalence surface. In our case, the EUT is inside an RC where the antennas are located on its walls, so we extrapolate the complex value of the equivalent currents by measuring only the electric field component normal to the RC walls. Under the assumption that the power radiated by a device inside an RC and the one radiated in free space are the same, the estimation of the EUT emission can be carried out in three steps.