There is proposed an automatic gain control circuit (300a) comprising an entirely analogue feedback loop intended to adjust, in real time, the gain of the circuit according to a plurality of possible reaction time values, so as to provide an output signal having constant mean power (POUT) on the basis of a given input signal (PIN). Such a loop comprises: a variable-gain amplifier block (301); analogue means of adjustment (302) of the gain taking account of a characteristic reaction time modifiable with the aid of capacitive means (304) when they are connected to the means of adjustment; a switching element (303) which makes it possible, in the closed position, to connect the capacitive means and, in the open position, to disconnect capacitive means; analogue means of control (305) of the switching element, which are activated as a function of the level of the input signal (PIN).