Excimer and exciplex UV/VUV sources excited by Dielectric Barrier Discharges represent a promising technology for industrial applications where powerful and efficient UV sources are needed. According to previous work, the most suited power supply waveform for coaxial DBD Excilamps is a unipolar pulsed voltage excitation of some kilovolts at some hundred of kilohertz with a duty cycle around one percent. We present here new concepts for energy supplying of coaxial DBDs, based on the direct control of the current in the lamps. These concepts have been tested by means of simulation models developed in our department and the time evolution of the UV radiation is presented for various considered current waveforms. Based on these results, a power supply topology has been designed for an efficient power transfer to the Excilamp. It is based on a converter which controls the current flowing through the DBD. The results concerning the coupling of this converter with a DBD load are commented.