The device comprises, connected to the antenna, a rectifier (RD) delivering a primary DC supply voltage (VNR) at its output terminal (BS), stabilizing means (1,ST) for generating a stabilized DC voltage (VDD) from the said primary voltage. First means (R3, R4, R5) calculate a first prespecified voltage threshold corresponding to a prespecified level of the stabilized DC supply voltage. Comparison means (CP) are also provided, the output terminal (BS2) of which is connected to the processing means, a first input of which is connected to the output of the first calculating means, and a second input of which is connected to the output terminal (BS) of the rectifier. Furthermore, a load (RBL) with chosen impedance is connected between the said output terminal of the rectifier and earth by way of a controllable switching means (T200) whose control input is joined to the output terminal of the comparison means (CP).