The present invention is directed to a DRAM circuit that implements a self-refresh scheme to substantially reduce its power dissipation level during self-refresh operations. A ramped power supply voltage in replacement of a substantially invariant power supply voltage is used to power a sense amplifier in the DRAM circuit for amplifying a voltage difference between two bit lines coupled to the sense amplifier. As a result, the heat produced by the self-refresh operation is only a fraction of the heat produced by the conventional self-refresh powered by the substantially invariant power supply voltage.