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GTAW welding with pulsed current has been misinterpreted in some of the classic literature and scientific articles. General conclusions are presented, stating that its use provides greater penetration compared to the use of constant current and that the simple pulsation of the current promotes beneficial metallurgical effects. Therefore, this manuscript presents a critical analysis of this topic and adopts the terminology of thermal pulsation for the situation where the weld undergoes sensitive effects, regarding grain orientation during solidification. For comparison purposes, an index called the form factor (ratio between the root width and the face width of the weld bead) is adopted. It is shown that the penetration of a welding with pulsed current can be worse than constant current depending on the formulation of the adopted procedure. Moreover, metallurgical effects on solidification, such as grain orientation breakage, only occur when there is adequate concatenation between the pulsation frequency and the welding speed. Finally, a thermal simulation of the process showed that the pulsation frequency limits the welding speed so that there is an overlap of the molten pool in each current pulse, and continuity of the bead is obtained at the root. For frequencies of 1 Hz and 2.5 Hz, the limit welding speed was 3.3 mm/s and 4.1 mm/s, respectively.