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Silicon microring resonator has been recognized as a competitive structure for the electro-optic modulator due to its potential for high-density integration. There are two silicon-ring-based modulation methods: push-pull coupling modulation and index modulation. Previous investigations show that the push-pull coupling modulation seems to outperform the index modulation because of its ultralarge optical modulation bandwidth and chirp-free property. However, there is no performance comparison for these two schemes in power consumption, which has emerged as an important parameter for photonics integrated circuit design. This paper thus studies the power efficiency of these two methods. The analysis of the static characteristics of the ring shows that the index modulation requires a much lower driving voltage than that of the push-pull coupling modulation when the modulator is operated at low frequencies. The dynamic analysis based on the coupled-mode theory in time indicates that the required driving voltage of the push-pull coupling modulation is still higher than that of the index modulation when the modulation frequency is not very high. To solve this problem, we propose a chirp-free two-ring modulator consisting of a push-pull coupling modulator embedded into a ring with the same resonance. We demonstrate that the two-ring modulator can reach its transmission null before the push-pull coupling modulator becomes critical coupled. As a result, the power requirement of the two-ring modulator is lower than that of the push-pull coupling modulator.