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A novel brushless compound-structure permanent-magnet synchronous machine (CS-PMSM) with six different topologies is proposed based on the magnetic field modulation principle. As the key part of the brushless CS-PMSM, the radial magnetic-field-modulated brushless double-rotor machine (MFM-BDRM) is investigated on the speed and torque relations of the first-stator magnetic field, the first-PM rotor and the modulating ring rotor by analytical method. Besides, on the basis of analyses of magnetic field distribution in the inner and outer air gap, the back electromagnetic force and torque performance of the radial MFM-BDRM are further studied by finite-element method (FEM). The results indicate that the low power factor is a major problem of the radial MFM-BDRM. Therefore, the influence of parameters, such as combinations of magnetic block number and PM pole pair number, the span ratio and radial thickness of magnetic blocks, and the length of air gap, on the power factor is analyzed. Additionally, to investigate the distribution law of core loss in the radial MFM-BDRM, amplitudes and frequencies of the magnetic fields in each part of the machine are analyzed. Furthermore, considering the weak mechanical strength of modulating ring rotor employing DW310 laminations, an attempt to use iron instead of DW310 in modulating ring rotor is investigated.