Enhanced mathematical model for studying fundamental behaviors of injection locked relaxation oscillator

This article proposes the analytical model for studying behaviors of injection locked relaxation oscillator (ILRO). The proposed model enhanced from N. Soltani's model can be used to demonstrate behaviors of the ILRO in case the input frequency is higher than the natural frequency, namely, necessarily physical conditions for locking, locked ranges, detuning behaviors and frequency division. The proposed model is verified by simulation results of the ILRO based on 0.35um-CMOS technology of TSMC.