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In this paper, a method to build equivalent models of radiating printed circuit boards based on complex E-field measurements taken in the close vicinity of the device under test is explored. It is shown that the inverse problem to be solved to retrieve the currents from the field data is ill-posed. An innovative regularization approach implementing a penalty on abrupt spatial variations of the currents is proposed to alleviate this difficulty. Various schemes to mesh the equivalent current distribution are also explored. Combining these with measurements, it is shown that accurate estimation of equivalent current models can be achieved, thereby allowing the identification of the emission sources. The method is tested for different circuit configurations with both synthetic and real data. Obtained results demonstrate the efficiency of the method.