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This work presents a new sensorless control technique for active magnetic bearings (AMB). We consider a single-axis AMB composed of a rotor and a pair of electromagnets. It is driven by a pair of pulsewidth-modulated (PWM) switching power amplifiers. We connect the amplifier input and output terminals and the magnet coils to a simple network composed of a transformer and a sample-and-hold circuit. Then, we show that when the sampling takes place at a certain moment of each PWM cycle, the electronics gives a full state feedback that can stabilize the rotor. Although there is not an explicit controller, the closed-loop poles can be arbitrarily placed, and good performance is achieved with reasonable parameter values of the driving electronics. We include an implementation example with experimental results.