Negative bias temperature instability (NBTI) has become a major factor determining circuit reliability. The effect of the NBTI on the circuit performance depends on the duty cycle which represents the stress and recovery conditions of each device in a circuit. In this paper, we propose an analytical model to perform more accurate duty cycle estimation at the gate-level. The proposed model allows accurate (average error rate: 3%) computation of the duty cycle without the need for expensive transistor-level simulations Furthermore, our model estimates the waveforms at each node, allowing various aging effects to be applied for a reliable gate-level circuit aging analysis framework.