## 1 Introduction  
The peak detection and sample hold (PDSH) circuit is important in the pulsed time of flight (ToF) light detection and ranging (LiDAR) system [1; 2; 3; 4; 5]. The PDSH circuit captures the pulse signal and obtains the accurate amplitude of the signal, which provides precise distance information for the ToF LiDAR system. However, with the development of ToF LiDAR systems, the pulse width that needs to be detected reduces, while the accuracy requirement intensifies significantly [6]. Especially when the pulse width approaches the nanosecond domain, the LiDAR system requires a very fast response [7]. Furthermore, in the nanosecond domain, the parasitic parameters, such as parasitic capacitance and parasitic resistance, deteriorate the magnitude response, and accordingly affect the distance information required by the ToF or LiDAR system [8; 9]. Therefore, designing PDSH circuits for nanosecond pulse peak detection is both important and challenging [10; 11; 12; 13; 14]. The most widely used CMOS-based PDSH circuit in industry is shown in Figure 1[15]. The circuit charges a capacitor through a switch, either a diode or a MOS. When the input voltage \(V_{i}\) is greater than the output voltage \(V_{o}\) on the sampling capacitor \(C_{h}\), the switch is turned on, and the input voltage charges the capacitor. Conversely, the switch is turned off, and capacitor \(C_{h}\) maintains the peak voltage, which can be measured using the ADC sampling method [16; 17; 18]. Therefore, the control signal of the switch will directly affect the measurement of the pulse peak. However, the circuit is only valid for ms-scale pulse width detection and needs to be improved for ns-scale pulse width detection. [PERSON] et al. [19] proposed a PDSH circuit using a current-mode latching mechanism and flag generation circuitry to control the switch, which had shallow energy consumption. However, it can only measure the ms-scale pulse width. [PERSON] et al. [20] also designed a CMOS peak detector, which used CMOS to control the charging and discharging of the capacitor. However, the driving ability is relatively small, and the measurement accuracy decreases. The OTA-based PDSH circuit with negative feedback can overcome the shortcomings of the PDSH circuit [21; 22; 23]. [PERSON] et al. [21] proposed an improved PDSH circuit, which would take the output voltage as input to the negative input of the transconductance operational amplifier (OTA) and use the voltage Buffer to output the result. [PERSON] et al. [22] used OPA615 to build the PDSH circuit, analyzed the circuit's bandwidth, and completed the measurement of the pulse peak of 100 ns pulse width and 20 kHz repetition frequency. Moreover, [PERSON] et al. [23] used the same circuit to measure the peak value of a laser pulse with a pulse width of 200 ns. The PDSH circuit based on OTA IC chips has the advantages of easy construction, fast measurement, low cost, and convenient use. As the output current of OTA is variable, the circuit overshoot is slight. The OTA's maximum output current limits the circuit's maximum measurement speed, and the voltage step phenomenon will lead to significant measurement errors. To overcome the error caused by the voltage step of the PDSH circuit based on OTA, a CMOS PDSH circuit was proposed by [PERSON] [24], where a current mirror was used instead of a diode to nonlinear solute problems caused by the diode. However, it also produces new problems, such as significant overshoot, large pedestal voltage, and tradeoffs between measurement accuracy and speed. [PERSON] et al. [25] proposed the two-phase peak detector to overcome the tradeoff between measurement accuracy and speed. Nevertheless, it can only measure the us-scale pulse width. Recently, [PERSON] et al. [2] presented an auto-adjust charging current CMOS PDSH circuit, which reduced errors caused by the pedestal voltage and overshoot voltage. Similarly, [PERSON] et al. [3] proposed using a controlled current source instead of a current mirror to reduce the error.