Injection-locked ring oscillators (ILROs) are extensively employed for multi-phase clock generation in wireline and optical links. However, existing injection-locking theorems primarily rely on linearized phase-domain or nonlinear time-domain models, which fail to account for amplitude-to-phase conversion effects inherent in ILROs. This paper introduces an enhanced analytical model based on an extension of Adler's equation, explicitly incorporating amplitude-to-phase conversion. Simulation results demonstrate strong alignment with the proposed analytical predictions, validating the model's accuracy in capturing the locking range and phasor relationships.