Abstract: In order to enable information such as the results of physical measurements performed downhole in an oil well during testing or production to be transmitted in real time to a receiver on the surface, the bottom portion of a tubular string (12) is fitted with a transmitter device that transmits an electromagnetic wave which is conveyed to the receiver on the surface by the ground surrounding the well. The transmitter device includes a power source (32) disposed in an annular cavity (34) formed at an intermediate level between an outer insulating coupling (36) and an inner insulating coupling (38). The power source (32) is electrically connected between two tubular walls (39, 40) delimiting the cavity (34) so as to apply a modulated alternating electrical signal directly to said walls.