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This work proposes a method for feeding a balanced IRA with an unbalanced transmission line. This method is based on the current distribution on the surface of the antenna. The method of moments (MoM) simulations show that for the IRAs, there are some areas with low current density in comparison to the current density of the feeding points, almost over the entire frequency range. The coaxial cable is attached to the antenna's body all the way from the feeding point to an area of low current density, and extends out of the antenna structure at that point. This tremendously reduces the current density on the body of the coaxial cable. As a result, the current balance between two parts of the antenna is not disturbed. This method is applied to the TEM horn antenna, the reflector IRA, and the Vivaldi antenna. The TEM horn antenna was simulated using the HEMI software, and was fed by an unbalanced coaxial cable, both directly at the feeding point and using this method. This method was also applied to the reflector impulse-radiating antenna. Also, the Vivaldi antenna was fed both by considering the low-current density area and direct feeding. The E-plane far-field pattern of the new feeding method had good agreement with the result generated by the HEMI software for the balanced-fed antenna.