Microring optical modulators are being explored extensively for energy-efficient photonic communication networks in future high-performance computing systems and microprocessors, because they can significantly reduce the power consumption of optical transmitters via the resonant circulation of light. However, resonant modulators have traditionally suffered from a trade-off between their power consumption and maximum operation bit rate, which were thought to depend oppositely upon the cavity linewidth. Here, we break this linewidth limitation using a silicon microring. By controlling the rate at which light enters and exits the microring, we demonstrate modulation free of the parasitic cavity linewidth limitations at up to 40 GHz, more than 6x the cavity linewidth. The device operated at 28 Gb/s using single-ended drive signals less than 1.5 V. The results show that high-Q resonant modulators can be designed to be simultaneously low-power and high-speed, features which are mutually incompatible in typical resonant modulators studied to date.