= 1.5 mA, while sweeping $\phi_\text{ext}$, are depicted in Fig. 3 as an example. They are compared with the measured time domain signal from [@time], since time domain measurements are not included in [@ref1]-[@muduli2010nonlinear]. The general nature of these simulated time domain signals agree with the measured one. Especially, the phase fluctuation generated by the proposed $\varphi(t)$ function, has continuous changes and is very similar to that of the measured time domain signal [@time]. Aside from the discrepancies between the modeled (theoretical) and measured linewidth, this comparison demonstrates that the proposed MTJ STO model can reproduce the phase fluctuation generated by MTJ STOs, so as to achieve a reliable MTJ STO model.

The time domain signals in Fig. 3. are further analyzed to validate that the model implemented in Verilog-A is equivalent to the analytical model given in [@Tingsu_2014TEDI].

For different $\phi_\text{ext}$, the time domain signals shown in Fig. 3 present different characteristics including the operating frequency, phase noise (linewidth), amplitude, and DC biasing points. Time domain signals with large output power (voltage amplitude) appear at the in-plane external field angles between $40^o$ and $55^o$ (corresponding in-plane effective field angles between $47^o$ and $68^o$). Among these, the signal generated at 