Switched-capacitor (SC) DC-DC converters have several advantages over inductive DC-DC converters in that they are easily integrated on-chip and can scale to desired power levels, rendering themselves promising for integrated voltage regulators, especially for small, low-power systems. However, many SC DC-DC converters offer only a few conversion ratios, limiting their use for systems in which either the input or output voltages vary. This is particularly important in wireless systems where battery voltage degrades slowly. [1] proposed a technique to reconfigure cascaded SC converters to achieve arbitrary binary ratios: p/2N, 0<;p<;2N, where N is the number of cascaded stages. This structure was improved in [2] by reversing the cascading order to increase output conductance and in [3] by using a positive feedback approach. However, this design still provides less output conductance than previous works offering only a small fixed number of ratios [4,5]. This paper presents an SC DC-DC converter that can be reconfigured to have any arbitrary rational conversion ratio: p/q, 0<;p<;q≤2N+1. The key idea of the design, which we refer to as a rational DC-DC converter, is to incorporate negative voltage feedback into the cascaded converter stages using negative-generating converter stages (“voltage negators”); this enables reconfiguring of both the numerator p and denominator q of the conversion ratio. With help from the current supply of the voltage negators, output conductance becomes comparable to conventional few-ratio SC DC-DC designs. Hence, the proposed design achieves a resolution higher than previous binary SC converters while maintaining the conversion efficiency of dedicated few-ratio SC converters. Using only 3 cascaded converter stages and 2 voltage negator stages, the rational converter implemented in 0.18μm CMOS offers 79 conversion ratios and achieves >90% efficiency when downconverting from 2V to a 1.1-to-1.86V output voltage range.