An energy-scavenging interface comprising a first input terminal and a second input terminal (25") configured to be connected to respective terminals of a first storage element, and a first output terminal and a second output terminal (26") configured to be connected to respective terminals of a second storage element, wherein the first and second input terminals (25', 25") are configured to receive an electrical input signal (V IN), and the first and second output terminals are configured to supply to the second storage element an output signal (I OUT, V OUT), the energy-scavenging interface further comprising: a first switch (30a, 31a) and a second switch (30b, 31b) connected in series to one another, between the first input terminal (25'; 25") and the second output terminal (26"); a third switch (36a, 38a) and a fourth switch (36b, 38b), connected in series to one another, between the first input terminal (25'; 25") and the first output terminal; a first electrical-signal detecting device, coupled to conduction terminals of the second switch (30b; 31b) and configured for detecting whether the electric current in the first storage element reaches a threshold value (I TH); and a control logic (60, 70) configured for: - controlling the first and second switches (30a, 30b; 31a, 31b) in an on-state and the third switch (36a; 38a) in an off-state for a first time interval having at least one first time duration (T DELAY) during which the first storage element stores electric current and until the electrical current stored by the first storage element reaches the threshold value (I TH);- acquiring, once the first time interval (T DELAY) has elapsed and once the threshold value (I TH) has been reached, a scaled copy (I p/ K) of a peak value (I p) of the electric current stored in the first storage element; - controlling the first switch (30a; 31a) in an off-state and the third and fourth switches (36a, 36b; 38a, 38b) in Z an on-state to generate the output signal that supplies the second storage element; - maintaining the first switch (30a; 31a) in the off-state and the third and fourth switches (36a, 36b; 38a, 38b) in the on-state as long as the value of current of the output signal (I OUT) is higher than the value of said scaled copy (I p/ K) of the peak value, wherein said scaled copy (I p /K) corresponds to the peak value (I p) reduced by a scale factor, the first time duration (T DELAY) and the scale factor chosen to be of values such as to optimize the matching efficiency to the input port of the energy scavenging interface. - controlling the first and second switches (30a, 30b; 31a, 31b) in an on-state and the third switch (36a; 38a) in an off-state for a first time interval having at least one first time duration (T DELAY) during which the first storage element stores electric current and until the electrical current stored by the first storage element reaches the threshold value (I TH);- acquiring, once the first time interval (T DELAY) has elapsed and once the threshold value (I TH) has been reached, a scaled copy (I p/ K) of a peak value (I p) of the electric current stored in the first storage element; - controlling the first switch (30a; 31a) in an off-state and the third and fourth switches (36a, 36b; 38a, 38b) in Z an on-state to generate the output signal that supplies the second storage element; - maintaining the first switch (30a; 31a) in the off-state and the third and fourth switches (36a, 36b; 38a, 38b) in the on-state as long as the value of current of the output signal (I OUT) is higher than the value of said scaled copy (I p/ K) of the peak value, wherein said scaled copy (I p /K) corresponds to the peak value (I p) reduced by a scale factor, the first time duration (T DELAY) and the scale factor chosen to be of values such as to optimize the matching efficiency to the input port of the energy scavenging interface.