A method of forming a bag assembly by RF welding includes generating from a single source of RF energy a high frequency electric field having a first strength between tube-welding electrodes of opposing die members and a second strength less than said first strength between perimeter-welding electrodes of the opposing die members. Subjecting a tube assembly and corresponding portions of sheets surrounding the tube assembly to the high frequency electric field of said first strength for a predetermined amount of time to weld the sheets to a tube along a tube-weld. Corresponding portions of the sheets between the perimeter-welding electrodes are subjected to the high frequency electric field of said second strength for said predetermined amount of time to weld the sheets together along a bladder perimeter-weld. The subjecting steps are performed simultaneously so that the bag assembly is formed in one welding operation.