Reduction of modulator energy consumption to 10fJ/bit is essential for the sustainable development of communication systems. Lumped modulators might be a viable solution if instructed by a complete theory system. Here, we present a complete analytical electro-optic response theory, energy consumption analysis, and eye diagrams on absolute scales for lumped modulators. Consequently the speed limitation is understood and alleviated by single-drive configuration, and comprehensive knowledge into the energy dependence on structural parameters significantly reduces energy consumption. The results show that silicon modulation energy as low as 80.8 and 21.5fJ/bit can be achieved at 28 Gbd under 50 and 10 Ω impedance drivers, respectively. A 50 Gbd modulation is also shown to be possible. The analytical models can be extended to lumped modulators on other material platforms and offer a promising solution to the current challenges of modulation energy reduction.