An analytic model is developed to study the dynamic response of carrier-depletion silicon ring modulators. Its validity is confirmed by a detailed comparison between the modeled and the measured small signal frequency response of a practical device. The model is used to investigate how to maximize the optical modulation amplitude (OMA) and how the OMA could be traded for the bandwidth by tuning the coupling strength and the operation wavelength. Our calculation shows that for a ring modulator with equal RC time constant and photon lifetime, if its operation wavelength shifts from the position of the maximum OMA towards the direction that is away from the resonance, the 3dB modulation bandwidth increases ~2.1 times with a penalty of 3 dB to the OMA.