Circuitry (20) and a method are provided for limiting peak current while supplying a constant voltage to a load (42). The circuit (20) comprises an input terminal (32) for coupling to the voltage supply, current sense circuitry (26) coupled to the input terminal (32), a capacitor (30) coupled to an output terminal (40), a converter power stage (22) coupled between the current sense circuitry (26) and the output terminal (40); and a converter controller (24) having inputs coupled to the output terminal (40) and the current sense circuitry (26), and an output coupled to the converter power stage (22) for switching the converter power stage (22) from a voltage mode to a current mode.