A welding apparatus includes first and second die members opposing one another. The first and second die members include opposing respective first and second perimeter-welding electrodes and opposing respective first and second tube-welding electrodes. The first perimeter-welding electrode and first tube-welding electrode define a first welding surface. The second perimeter-welding electrode and second tube-welding electrode define a second welding surface. A single source of high frequency energy is electrically connected to the perimeter-welding electrodes and to the tube-welding electrodes. Dielectric material is selectively disposed on the first welding surface such that the material is disposed on some but not all the first welding surface for reducing a strength of a high frequency electric field between the first and second perimeter-welding electrodes as compared to a strength of the high frequency electric field between at least a portion of the first and second tube-welding electrodes.