Circuits and methods to sense the current through a coil of an integrated switching converter, applicable to boost and to buck converters, have been achieved. The present invention uses a "replica biasing" technique to avoid a resistor for current measurement. The current through a pass device is mirrored into a replica, having a scale of n and being much smaller in size, of said pass device. The current through the replica is mirrored to another branch of the circuit and back again to achieve a fast stabilization of the current. The current through the replica is mirrored again to an output branch of the circuit, which conducts exactly a fraction 1/n of the current flowing through the pass device. The self-biasing current loop of the invention adapts quickly to the actual current level through the pass device of the switching converter. Accuracies better than 5% are achieved over a wide range of dynamic range.