the linewidth has a Lorentzian lineshape), changing every $\Delta t$. $\Delta t$ is the virtual time step, which reflects how offen the frequency fluctuation happens and can be defined by the user. Moreover, the user-set $\Delta t$ is necessary in order to implement the Verilog-A model, because the circuit simulator provides an adaptive time step determined by the local truncation error (LTE) [@Kundert] so that the real simulation time step cannot be fully controlled by the user nor the programmer. Hence, the real simulation time step cannot be used to update the frequency fluctuations. To obtain the correct linewidth, the dataset of $\Delta f [~]$ follows a normal distribution with a mean of 0 and a standard deviation of $\sqrt{\frac{2 \Delta \omega}{\Delta t}}$, resulting in a phase variance that is growing linearly with time in a rate consistent with the specific level of white frequency noise for the specific linewidth $2\Delta \omega$ [@silva2010]. The virtual time step $\Delta t$ is related to the upper cut-off frequency for white noise in the frequency noise spectrum, and should be set to a value smaller than one order of magnitude lower than the inverse cut-off frequency in order to produce white frequency noise 