Systems and methods providing an energy limited arc re-ignition voltage for AC arc welding processes to re-ignite an arc during polarity transitions. In arc welding power source embodiments, configurations of bridge and superposition circuits allow for the directional switching of the welding output current through the welding output circuit path and provide a voltage between the electrode and the workpiece of the welding output circuit path that is sufficient to re-ignite the arc during polarity transition of the output current. The superposition circuit provides a capacitor for storing energy from a dedicated charging source which produces the voltage level for re-igniting the arc during the zero crossing of the output current in both polarities.