A phase shifter, which carries out a ninety-degree phase shift of a sinusoidal input signal having an input frequency, at the same input frequency, envisages: a continuous-time all-pass filter stage, which receives the sinusoidal input signal and generates an output signal phase-shifted by 90° at a phase-shift frequency that is a function of a RC time constant of the all-pass filter stage; and a calibration stage, which is coupled to the all-pass filter stage and generates a calibration signal for the all-pass filter stage, such that the phase-shift frequency is equal to the input frequency of the sinusoidal input signal, irrespective of variations of the value of the input frequency and/or of the RC time constant with respect to a nominal value.