the transient simulation results as a function of $I_\text{DC}$ at $\phi_\text{ext}=45^o$ is depicted in Fig. 4(b). The rise in $I_\text{DC}$ causes a decline in the operating frequency and an increase in the output power, which matches the theoretical results and experiments.

Effort has been made in this work to achieve the compact MTJ STO model and improve the simulation speed. Therefore, the time required for transient simulations of the proposed model is of interest. To benchmark the simulation speed, a 1 $\mu$s simulation with a maximum time step of 5 ps is performed. By averaging the runtime of 10 simulations containing approximately 470900 transient steps, a simulation takes only 52.6 s. The simulations are performed on a server with 2$\times$AMD Opteron 6172, and occupy one core. Regarding the micromagnetics-based model, which is most efficiently simulated on graphic processing units (GPUs) or supercomputer clusters, the typical runtime is roughly 24 hours for a similar device. Compared with the micromagnetics-based model discussed in Part I [@Tingsu_2014TEDI], the proposed model offers rapid simulations with a similar degree of accuracy.

Hybrid simulation of the MTJ STO model with CMOS circuits
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Hybrid simulation of the MTJ STO model with CMOS circuits is of great 