The paper considers high-frequency resistance spot welding systems. These systems have full-wave center-tapped output rectifiers. The frequency varies from 1000 Hz to 10 kHz. The paper presents an equivalent circuit for these systems, which allows to investigate the influence of electromagnetic parameters of the transformer on power consumption, on the efficiency, and on the welding current. This circuit is necessary to create low-cost power sources for welding the parts made of zirconium, titanium, or radiation-resistant steels. The equivalent circuit of three-winding transformers is used, which has a number of advantages compared to the classical equivalent circuit. The three-winding welding transformer is replaced by two two-winding ones. We take into account the mutual influence of the magnetic leakage fields of these two-winding transformers on electromagnetic processes in the resistance spot systems. The study of the transformer’s parameters includes both 2D eddy-current FEA analysis for estimating the leakage impedance and the circuit simulation, which gives the output current power consumption. The effectiveness of the developed equivalent circuit of the source was tested experimentally.