Mixed-eccentricity (ME) fault diagnosis has not been so far documented for permanent-magnet (PM) synchronous motors (PMSMs). This paper investigates how the static eccentricity (SE), dynamic eccentricity (DE), and ME in three-phase PMSMs can be detected. A novel index for noninvasive diagnosis of these eccentricities is introduced for a faulty PMSM. The nominated index is the amplitude of sideband components with a particular frequency pattern which is extracted from the spectrum of stator current. Using this index makes it possible to determine the occurrence, as well as the type and percentage, of eccentricity precisely. Meanwhile, the current spectrum of the faulty PMSM during a large span is inspected, and the ability of the proposed index is exhibited to detect eccentricity in faulty PMSMs with different loads. A novel theoretical scrutiny based on a magnetic field analysis is presented to prove the introduced index and generalize the illustrated fault recognition method. To show the merit of this index in the eccentricity detection and estimation of its severity, first, the correlation between the index and the SE and DE degrees is determined. Then, the type of the eccentricity is determined by a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -nearest neighbor classifier. At the next step, a three-layer artificial neural network is employed to estimate the eccentricity degree and its type. After all, a white Gaussian noise is added to the simulated current, and the robustness of the proposed index is analyzed with respect to the noise variance. In this paper, the PMSM under magnetic fault (demagnetization) and electrical faults (short and open circuits) is modeled, and the current spectrum of the faulty PMSM under demagnetization, short circuit, and open circuit faults is analyzed. It is demonstrated that the proposed index, due to eccentricity fault, is not generated in the current spectrum due to magnetic and electrical faults. Indeed, it is exposed that the introduced index is only created due to eccentricity fault and it is not sensitive to other faults. To model the PMSM eccentricities, a time-stepping finite-element method, which takes into account all geometrical and physical characteristics of the machine components, nonuniform permeance of the air gap, and nonuniform characteristics of the PM material, is employed. This model facilitates the access to the demanded signals in order to have accurate processing. A comparison of simulation and experimental results validate the proposed index.