A resistance annealing furnace for annealing a metal wire, strand, string, wire rod or strap having at least two electric axes provided with respective pulleys to convey the metal wire and a DC voltage generator suppliable with an AC voltage to generate an annealing voltage applied between the two electric axes so as to provoke the annealing due to Joule effect. The DC voltage generator has active supplying means supplied with the AC voltage so as to generate an intermediate DC voltage, a pulse width modulator to transform the intermediate voltage into a first PWM voltage with the same amplitude, a voltage transformer to transform the first PWM voltage into a second PWM voltage with a smaller amplitude, and a voltage rectifier stage to transform the second PWM voltage into the annealing voltage.