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In past work, the authors have proposed a radial magnetic bearing architecture where the rotor was kept suspended only by means of magnetic forces produced by permanent magnets working in attraction mode and the rotor was actively controlled only in one degree of freedom (d.o.f.), i.e., its axial direction. Although the presented architecture is simpler than those bearings with active control in two or more d.o.f., it presented limitations mainly of low radial stiffness. So, in this context this paper discusses ways to enhance the radial stiffness in this kind of bearing and presents simplified analytical methods used to find magnets and actuator optimal dimensions that gives both ring magnets radial stiffness and actuator force/current ratio maximum intensities.