## 3 The Proposed SET Hardened LDO Regulator
### Simulations  
As mentioned above, the number of splits is limited by the size of the transistors. In our original unhardened design, the size of \(MN5\) and \(MN6\) is \(W/L=2\)\(\upmu\)m/\(1\)\(\upmu\)m, \(M=8\). The size of \(MN7\) is \(W/L=2\)\(\upmu\)m/\(300\) nm, \(M=72\). The size of \(MP1\) and \(MP4\) is \(W/L=1.25\)\(\upmu\)m/\(500\) nm, \(M=4\). In an SMPS circuit, \(MP1\) and \(MP4\) can be split into eight parts at most. We analyzed the performance when \(n=2\), \(n=4\), and \(n=8\) in the following analysis. To measure the hardening effect, the same double exponential current source with a peak value of 2 mA and a decay time of 2 ns was injected into the drain of \(MN6\_1\) to simulate the single particle hit. We simulate the total current sum of \(MN7\_1\) to \(MN7\_n\) in the SMPS circuit, as well as the frequency of the VCO output signal, considering how they change under the impaction of the same SET as the unhardened circuit. Figure 9 illustrates the transient simulation results of the SMPS circuit when the split factor is 2. It can be seen that in the increase in the resistance value of the split resistor, the change in the total current inducted by the SET becomes smaller and the stopping time is shortened. However, even if the resistance value reaches 288 k\(\Omega\), the total current of \(I_{tail}\) decreased from 2.43 mA to 1.22 mA when particle strike occurred, which is not enough for the EA to operate correctly. So it still cannot be fully immune to SET and will cause VCO oscillation to stop. The hardening effect is not obvious when \(n=2\) in SMPS design. Figure 10 presents the transient simulation results of a hardened circuit when the split factor is four. As the resistance value of the split resistor increasing, the change in the total current due to SET becomes smaller. When the resistance value reaches 24 k\(\Omega\), the total current of \(I_{tail}\) decreases from 2.43 mA to 1.66 mA, no VCO oscillating stop occurs, and it can fully realize the immunity to SET. For our original unhardened design, the minimum split factor for effective hardening is when \(n=4\). Figure 11 shows the transient simulation results of SMPS circuit when \(I_{tail}\) is split into eight parts. When the split factor \(n=8\), SET immunity can be achieved with a 4 k\(\Omega\) or 5 k\(\Omega\) split resistor. The total current of \(I_{tail}\) decreases from 2.43 mA to 1.54 mA and 1.62 mA, respectively. Figure 10: SET induced disturbance in (**a**) total current sum of \(MN7\_1\), \(MN7\_2\), \(MN7\_3\) and \(MN7\_4\). (**b**) VCO oscillation frequency with SMPS circuit when the split factor is 4. Figure 9: SET-induced disturbance in (**a**) total current sum of \(MN7\_1\) and \(MN7\_2\); (**b**) VCO oscillation frequency with SMPS circuit when the split factor is 2. From Figures 9-11, we can figure out that both the split factor and the resistance value affect the hardening effect of the SMPS circuit. Notably, a higher split factor requires more resistors. So we should compare the hardened effect in terms of total resistance value. We consider the total resistance value needed for the hardening of \(MN6\). Naturally, the resistance value needed for the overall circuit should be multiplied by two because the overall hardened structure is symmetric. Figure 12 illustrates the relation between the total resistance in the SMPS structure for hardening \(MN6\) and the VCO oscillating recovery time at different split factors. The VCO oscillating recovery time's decreasing trend for \(n=2\) (black square in the figure) clearly shows that it is unlikely to achieve SET immunity. When the total resistance reaches about 40 k\(\Omega\) with \(n=4\) and \(n=8\), VCO oscillating does not stop when SET occurs. Figure 13 presents the SET induced LDO output disturbance with different SMPS configurations. The voltage variation is less than 40 mV, while it is 207 mV in unhardened LDO (see Figure 3a). For the three combinations that can achieve the SET immunity, we simulated their power consumption.