## 1 Introduction  
Phase-locked loop (PLL) is widely used to generate stabilized clocking in satellite communication systems. The cosmic radiation environment that the satellite-based PLL is exposed to makes it necessary to consider radiation resistance besides performance metrics in its design [1]. The particle impaction in the cosmic environment can lead to catastrophic failure of satellite communications. The single-event effect (SEE) is caused by a single particle that deposits a certain number of charges on the silicon substrate, which instantly interferes with the operation of the integrated circuit [2]. In addition to the single-event upset (SEU), which can flip the output of a digital logic circuit, SEE includes single-event transient (SET), which propagates through the circuit [3]. SET is a voltage disturbance caused by a collected radiation-induced charge in a circuit node that travels through the circuit. A voltage-controlled oscillator (VCO) is the core module in the PLL, and its phase noise directly affects the performance of the PLL [4]. The power supply noise is the crucial source of phase noise in the VCO [5]. Therefore, the conventional design of VCO is focused on noise suppression of the power supply. A low-dropout regulator (LDO) is a common method to provide high-quality power supply to the VCO [6; 7]. LC VCO as a widely used component in high-speed communication applications, and many studies have been conducted on the SETs of LC VCO in the cosmic radiation environment [8; 9; 10; 11; 12; 13; 14]. When a single particle hits a sensitive node in VCO, it can lead directly to frequency deviation and signal distortion of the VCO outputs and even a temporary stop of oscillation [2; 15]. LDO as a structure to suppress VCO power supply noise has been studied for its SET characteristics in different semiconductor processes [16; 17]. Those studies found that loop stability [18], input voltage [19], and load conditions [20] all affect the SETs of linear regulators significantly. Radiation Hardening by Design (RHBD) is one solution to SET mitigation. Unlike Radiation Hardening by Process (RHBP), RHBD is implemented in the CMOS process to achieve circuit-level hardening by applying a schematic and layout change. Three-mode redundancy (TMD) is widely used in analog and mixed-signal circuit hardening, [PERSON]. [21] used the TMD to harden the LC VCO, while [PERSON]. [22] used this technology to harden ring VCO. It shows great hardening effects but at the cost of a significant increase in circuit surface area and power consumption. Filtering can reduce SET amplitude and duration on the circuit and system levels. [PERSON]. [23] used filtering in LDO hardening design; however, the introduction of capacitors also increases the circuit surface area and power consumption. Ref. [24] proposed a fast transient response circuit under narrow-band conditions to improve the recovery speed of the LDO in the environment of radiation. This approach does not change the response loop in the LDO but introduces extra circuits that can be sensitive nodes. Resistive decoupling was first applied as a technique for hardening memory cells. Ref. [25] proposed an improvement in the SET response by adding a resistor in series with the base of the power transistor in the linear regulator. Ref. [26] used this method on the charge pump (CP) of PLL. Time-skewed space-split is an implementation of sensitive node-splitting technology, which is usually used to harden switched capacitor circuits. Ref. [27] used this method to harden the power transistor in LDO. Research on the SETs of LDOs is mainly focused on commercial LDO chips and the SETs of on-chip LDOs have been less studied, especially those applied to LC VCOs. This paper analyzes the SET-sensitive nodes of LDO applicable to LC VCO and proposes a radiation-hardened LDO design based on sensitive node splitting and resistive decoupling under the restrictions of surface area and power efficiency. This paper is organized as follows. Section 2 analyzes the SET effect for LDO in LC VCO.