Active magnetic bearing comprising: a plurality of electromagnetic actuators (17, 18, 20, 22), each actuator (17, 18, 20, 22) receiving for control thereof an input current (I x1, I x2, I y1, I y2) and being able to exert a radial force on a shaft of a rotary machine, with respect to the rotation axis (Z-Z') of said shaft, the shaft being able to be held without contact between the electromagnetic actuators (17, 18, 20, 22) and to undergo radial motion when it is in rotation; and means for supplying input current (I x1, I x2, I y1, I y2) of each actuator (17, 18, 20, 22), the supply means comprising means (46; 72) for controlling the input current (I x1, 1 x2, I y1, I y2) of each actuator (17, 18, 20, 22), according to the position of the shaft with respect to the actuators (17, 18, 20, 22); wherein each electromagnetic actuator (17, 18, 20, 22) comprises an excitation coil comprising an input terminal and an output terminal; wherein the control means (46; 72) comprises a plurality of control members; wherein the supply means further comprises means for damping the radial motion of the shaft, the damping means comprising at least one passive filter (50, 52) of the band-pass type; characterised in that: each control member is connected between the input terminal and the output terminal of one of the excitation coils; the damping means are connected between the input terminal and the output terminal of each coil; and the passive filter or filters (50, 52) of the damping means are connected between one of the control members and the excitation coil connected to said control member, with the passive filter or filters (50, 52) connected in parallel with said excitation coil and comprising a passive energy-dissipation component (54. 56). a plurality of electromagnetic actuators (17, 18, 20, 22), each actuator (17, 18, 20, 22) receiving for control thereof an input current (I x1, I x2, I y1, I y2) and being able to exert a radial force on a shaft of a rotary machine, with respect to the rotation axis (Z-Z') of said shaft, the shaft being able to be held without contact between the electromagnetic actuators (17, 18, 20, 22) and to undergo radial motion when it is in rotation; and means for supplying input current (I x1, I x2, I y1, I y2) of each actuator (17, 18, 20, 22), the supply means comprising means (46; 72) for controlling the input current (I x1, 1 x2, I y1, I y2) of each actuator (17, 18, 20, 22), according to the position of the shaft with respect to the actuators (17, 18, 20, 22); wherein each electromagnetic actuator (17, 18, 20, 22) comprises an excitation coil comprising an input terminal and an output terminal; wherein the control means (46; 72) comprises a plurality of control members; wherein the supply means further comprises means for damping the radial motion of the shaft, the damping means comprising at least one passive filter (50, 52) of the band-pass type; each control member is connected between the input terminal and the output terminal of one of the excitation coils; the damping means are connected between the input terminal and the output terminal of each coil; and the passive filter or filters (50, 52) of the damping means are connected between one of the control members and the excitation coil connected to said control member, with the passive filter or filters (50, 52) connected in parallel with said excitation coil and comprising a passive energy-dissipation component (54. 56).