## 2 Responses of Single-Event Transients in the LDO
### Responses of SET in LDO  
The LDO used in this study is shown in Figure 2a. The differential pair used in the error amplifier is an n-MOS transistor, and the power transistor is p-MOS transistor. SETs are simulated using a double exponential current source [30]. Figure 2b shows the implementation of the LDO circuit in this paper. A start-up circuit is not presented in the schematic. Double exponential current sources with a peak value of 2 mA and a decay time of 2 ns are injected at the drains of \(MN6\), \(MP1\), \(MP3\), and \(MP5\), respectively. To evaluate the impact of these current pulses, the output voltage of the regulator \(V_{reg}\), and the frequency of the VCO were analyzed. The simulation results are shown in Figure 3a-c.  
Figure 2: Low-dropout regulator (LDO) structure: (**a**) Supply-regulated VCO. (**b**) Unhardened regulator schematic. Figure 3a shows the transient response of the LDO output voltage \(V_{reg}\) and VCO oscillation frequency when the particle strike occurs on the \(MN6\). The LDO output voltage changed from 700 mV to 493 mV, and the VCO oscillation frequency changed from 8.589 GHz to zero. The oscillation recovery time was 492 ns. Figure 3b,c present the transient simulation of the LDO output voltage \(V_{reg}\) and VCO oscillation frequency when the particle strike occurs on the \(MP1\), \(MP3\) and \(MP5\). The LDO output voltage changed from 700 mV to 546 mV, 529 mV, and 732 mV, respectively. The oscillation recovery times were 278 ns and 5.7 ns for \(MP1\) and \(MP3\). It can be seen that when a single particle strikes on \(MN6\), \(MP1\), and \(MP3\), the LDO voltage decreased, which caused the VCO to stop oscillating, exhibiting a greatly varied non-oscillating duration. To maintain the oscillation of the VCO, the tail current source in the VCO should provide enough current to meet its oscillation conditions. When the power supply of the VCO is directly connected to the main power supply, the power supply can provide enough current to keep the VCO working as long as the tail current source of the VCO is in normal condition. However, when the regulator provides the power supply to the VCO, it will cause the VCO to stop oscillating if the regulator does not work correctly when injected with charges. The transfer function between the LDO output voltage \(V_{reg}\) and the LDO input voltage \(V_{ref}\) is shown in Equation (2). \[\frac{V_{reg}}{V_{ref}}=\frac{A_{EA}\cdot A_{P}}{1+A_{EA}\cdot A_{P}} \tag{2}\]  
where  
\[A_{P}=g_{mMP5}({K}//\frac{1}{sC}//\tau_{VCO}) \tag{3}\]  
\[A_{EA} =G_{mEA}r_{oEA}\] \[\approx g_{mMN4}\{[(1+g_{mMN2}r_{oMN2})r_{oMN4})+r_{oMN2}]//r_{oMP3}\} \tag{4}\] \[\approx g_{mMN4}[(g_{mMN2}r_{oMN2}r_{oMN4})//r_{oMP3}]\]  
\[g_{mMN4}=\frac{2\cdot\frac{1}{2}I_{tail}}{V_{gsMN4}-V_{thMN4}}=\frac{I_{tail}} {V_{gsMN4}-V_{thMN4}} \tag{5}\]  
Power-supply rejection ratio (PSRR) is a term that quantifies the ability of a circuit to suppress fluctuations on the power supply. \[\Delta V_{reg}=\Delta V_{ddhv}\cdot A_{p}+\Delta(V_{ref}-V_{reg})\cdot A_{EA} \cdot A_{P} \tag{6}\]  
\[PSRR_{DC}=\frac{\partial V_{reg}}{\partial V_{ddhv}}=\frac{A_{p}}{1+A_{EA} \cdot A_{P}}\approx\frac{1}{A_{EA}} \tag{7}\]  
Figure 3: Single-event transient (SET) induced disturbance in LDO output voltage and VCO oscillating frequency when the particle strike occurs on: (**a**) \(MN6\); (**b**) \(MP1\); (**c**) \(MP3\) and \(MP5\). When a particle impacts the LDO, the output voltage \(V_{reg}\) of the LDO will change and no longer follow its reference voltage \(V_{ref}\). The re-following process, realized slowly with the regulation of the loop, is closely related to the response time of the loop, which indicates that the bandwidth of the entire loop determines its regulation speed. When a single particle hits the \(MP1\) or \(MN6\), the tail transistor \(MN7\) in the error amplifier no longer works in its saturation region, disabling the entire error amplifier.