Applied power as a function of time is ramped up at the onset of an RF welding process in a manner that is predetermined to match source and load impedance as reflected by maximized forward power during at least the majority of the welding process. The ramp-up portion takes the form of a non-linear curve, such as an S-shaped curve, as opposed to one or more discrete steps. The applied power may then be maintained at or near that maximum required value at least a majority of the remainder of the heating portion of the welding process. The shape of the non-linear ramp-up portion of the applied power curve may be predetermined using, for example, virtual motor control using applied power as a virtual axis.