This paper presents how the parasitic elements of the step-up transformer impact the DBD operation, while supplied with a current-mode converter. The initial analysis is performed with the state-plane technique and then the steady-state values are calculated with an iterative method. Results show that the increase of power in the DBD can be achieved by the reduction of the magnetizing inductance and the parasitic capacitance in the transformer, without changing the power converter ratings. This result offers the opportunity to achieve a revision of the transformer specifications; and it is advantageous in terms of dimensions and price of the latter. Experimental results are performed with UV excilamps verifying the analysis. The need of a more complex DBD model has been also pointed out, to extend the validity of the presented method in the case of short current pulses.