This paper is aimed at the modelling of an electrical discharge controlled by mean of a dielectric barrier, at atmospheric pressure; we focus our study on the homogeneous “regime”. This model is based on the use of equivalent electrical circuits and is taking into account the main phenomena of the discharge. We also offer a method for the determination of the parameters of the model; the comparison of the experimental waveforms with the simulated ones is validating the accuracy of the proposed model in the case of discharges in nitrogen or helium. Our model is exploited to point out the drastic importance of the electrical characteristics of the power supply with respect to the main waveforms of the discharge. (including computer-aided circuit design and analysis)