Developing the fundamentals for the electrical diagnostics of surface dielectric barrier discharges (SDBDs) is of enormous importance for several applications, for example, flow control and gas cleaning. The main challenge is to account for the discharge expansion along the dielectric surface. Typically, a linear expansion with the amplitude of the applied voltage is observed. In this work, we report on a step-wise SDBD expansion along the Al2O3 dielectric surface. More specific, the discharge occupied a certain area after ignition, which remained constant until the voltage exceeded the critical amplitude VL. This absence of expansion is seen as a linear dependence of the discharge power on the applied voltage and it was additionally confirmed by photographs with long exposure times. This novel phenomenon is more pronounced for thicker dielectrics. It is suggested that the derivative of the charge-voltage characteristics can be used for the determination of all essential parameters of the simplest equivalent circuit of SDBDs. Moreover, it was shown that the derivative of the charge-voltage characteristics for the positive half-cycle of the discharge agrees numerically with the voltage dependence of the reactor capacitance derived from photographs. This agreement between both measurement methods indicates a similar step-wise expansion of the SDBD even if a voltage amplitude above VL is applied.