Systems and methods for providing controlled AC TIG arc welding processes is provided. In AC TIG arc welding power source embodiments, configurations of main and auxiliary bridge circuits allow for the directional switching of the output welding current through the welding output circuit path and selectively provide one or more high impedance paths to rapidly decay the arc current. The high impedance path aids in the low spatter transfer of molten metal balls from consumable to a workpiece, via an arc generated by a tungsten electrode, and further aids in the maintaining or the re-establishing of an arc between the tungsten electrode and the workpiece during welding.