to a large phase deviation that will be fully presented at the next time step ($t$=$j$+1). The first two steps in implementing $\varphi(t)$ are necessarily conducted in the $initial$ $step$ event, so that the two vectors are generated only once during the simulation.

The third step, as shown in Fig. 1, is to generate the required $\varphi(t)$. $\varphi(t)$ at an arbitrary time, can be expressed as the sum of the accumulated phase deviation $\Sigma\Delta \varphi[k]$ up to the last virtual time step, and the phase deviation produced from the last virtual time step to the absolute time. The parameter $k$ is employed to count the past number of virtual time steps, and it is updated every $\Delta t$ by using the $timer$ function in Verilog-A. It should be noted that the initial value of $k$ is set to -1 since the $timer$ function is called at the beginning of each time period. The absolute time is fetched by calling the $\$ abstime$ function. The relationship between $\varphi(t)$, $\Delta f[k]$ and $\Sigma\Delta \varphi[k]$ is presented in Fig. 2. Specifically, the slope of $\varphi(t)$ is the instantaneous frequency deviation $\Delta f[k]$, so that the phase deviation generated from the last virtual time 