A delta-sigma modulation circuit has a sampling period and, in operation, generates a delta-sigma modulated signal based on the analog input signal. The delta-sigma modulation circuit includes: a first integrator; an analog-to-digital converter; a feedback-loop coupled between an input of the first integrator and the output interface; a second integrator coupled between the first integrator and the analog-to-digital converter. The delta-sigma modulation circuit has loop-delay compensation circuitry having a plurality of switches. The loop delay compensation circuitry, in operation, controls the plurality of switches based on a time interval of a duration of half the sampling period and generates a loop-delay compensation signal.