## 4 Simulations Results
### Single Event Effect Simulations  
The model used for SEE simulations and widely accepted by the scientific community [29; 30; 31] is shown in Equation (6), where _tinj_ is the injection instant, _ta_ is the collection time constant of the junction, _tb_ is the ion track establishment time constant, and \(Q\) is the critical charge. \[ISET = \frac{Q}{ta-tb}\Big{[}e^{-(\frac{t-\text{ini}}{ta})}-e^{-(\frac{t- \text{ini}}{tb})}\Big{]} \tag{6}\]  
SEEs were modeled as double exponential current pulses at sensitivity nodes, and two different sets of values, with a Linear Energy Transfer (LET) of 5 and 60 MeV\(\times\)cm\({}^{2}\)/mg, were used [32]. The two sets of values were expressed for different time constants versus critical charge Q and LET. The strike of an ionizing particle could be modeled by inserting a current pulse on each P-N junction, with the direction of the injected current depending on the device type [33], as shown in Figure 12. Moreover, the effects generated by the injected currents were strongly sensitive to the circuit conditions, requiring the analysis of the system in different states. Both VCOs based their frequency tuning on accumulation-mode MOSFETs varactors, and the output nodes resulted as the most sensitive nodes in the whole architectures. Indeed, the strike of an ionizing particle generated a voltage variation in the node that was then translated in a frequency deviation by varactors. In this subsection, SEE simulations results are discussed, respectively, for RO and LC controlled oscillators. Figure 11: Allan deviation of (**a**) frequency and (**b**) amplitude for RO-VCO (**red line**) and LC-VCO (**blue line**) calculated in typical condition at the same oscillation frequency. Figures 13 and 14 show the effects generated by a particle strike for the two values of LET provided for the model in Equation (5). Particles with 5 and 60 MeV\(\times\)cm\({}^{2}\)/mg are representant in the following figures with the label hit\({}_{1}\) and hit\({}_{2}\), respectively. The two exponential current generators excited sensitive nodes of RO-VCO at 25 ns and 30 ns, and the LC-VCO ones at 10 ns and 15 ns. Figure 14: Differential amplitude variations due to the hit of the two LET values provided for the model. (**a**) shows the differential amplitude in the RO-VCO, while (**b**) shows the differential amplitude in the LC-VCO. Figure 12: The model used for the correct stimulation of the P-N junction with the double exponential current pulses generators. Figure 13: Two sets of values with a Linear Energy Transfer (LET) of 5 and 60 MeV\(\times\)cm\({}^{2}\)/mg were used for Single Event Effect (SEE) simulations, and the free-running frequency was plotted for the control voltage value equal to 0 V (**red line**) and V\({}_{\rm DD}\) (**blue line**). (**a**) shows the free-running frequency in the RO-VCO, while (**b**) shows the free-running frequency in the LC-VCO. In Figure 13, the free-running frequency versus time is plotted for minimum (red line) and maximum (blue line) values of control voltage, and in Figure 14, the differential output amplitudes for the maximum value of the control voltage, respectively, for RO-VCO and LC-VCO are shown. In Table 2, the data extracted from Figures 13 and 14 are listed, where the column called clock cycles shows the number of clock cycles in which the frequency assumes different values respect to the nominal due to the strike of the particle. In the last two columns, the maximum variations for frequency and amplitude are reported. As it is shown in the last two columns of Table 2, when the VCOs were hit by the ionizing particle with a LET of 5 MeV\(\times\)cm\({}^{2}\)/mg (called hit\({}_{1}\) in Table 2), both architectures showed nearly the same amplitude and frequency variations. Instead, when a particle with higher LET (called hit\({}_{2}\) in Table 2) did hit the two VCOs, the amplitude variations of the LC-tank were greater than that of the RO, while the frequency variations were lower in the LC-tank-based architecture.