A conversion device includes an A/D converter (8) and a control module for auto-adjustment of the DC component. This module includes an analog comparator (5) which performs a comparison between the analog signal (11) at the input of the A/D converter (8) and a reference voltage (10) produced on the basis of voltages which feed the resistance ladder (9) of the converter. In order that the control does not introduce noise into the signal supplied, the comparator (5) of the control module has a non-linear response with a reduced output/input gain for a range of the differential control signal centered around zero.