# Design of Nanosecond Pulse Laser Diode Array Driver Circuit for LiDAR
## 2 Circuit Principle
### Pulse LD Driving Circuit Model  
When the LD is turned on, photons are emitted when holes and electrons recombine. Through multiple oscillations in its resonant cavity and subsequent reflection enhancement, stable wavelength laser light is emitted. Its conductive characteristics are similar to those of ordinary diodes, with common electrical parameters including the threshold current, operating current, operating voltage, maximum output power, pulse width, etc. The output laser power exhibits a linear relationship with the current flowing through the diode. In many applications, the output light intensity is controlled by a current source [31; 32; 33]. For TOF LiDAR, pulse lasers with a higher peak power can achieve longer-range measurements. Additionally, to ensure eye safety, the average output power of the laser needs to be limited, which means reducing the pulse width. Therefore, when designing the laser emission circuit, it is necessary to maximize the peak power of the pulse laser and minimize the pulse width. When using high-voltage pulses with a pulse width on the order of nanoseconds to drive a LD, the voltage across its terminals needs to rapidly increase to tens of volts within a time frame shorter than the pulse width, and then return to zero volts as soon as the pulse time ends (to avoid affecting the repetition rate of pulse emission). In this high-frequency scenario, certain parameters in the circuit loop can significantly affect the quality of the pulse waveform. Typically, due to soldering, packaging, connecting wires, component leads, and the diode itself, equivalent inductance on the order of nH, known as stray inductance, is generated in the loop in LD drive circuits. The stray inductance \(L\) can have a notable impact on the pulse shape. Additionally, the equivalent inter-electrode capacitance \(C\), usually on the order of pF, also affects the pulse shape [34]. Figure 2a is a schematic diagram of a simplified circuit for pulsed LDs, where the switch is turned on and off to enable the LD to output pulsed laser light; Figure 2b is the equivalent circuit of  
Figure 1: Principle block diagram of pulse LD array drive circuit. the LD, consisting of equivalent series inductance \(L\), equivalent parallel capacitance \(C\), and equivalent resistance \(R\). As shown in Figure 2b, when the switch is turned on, Equation (1) can be written according to [PERSON]'s law, resulting in a second-order differential equation for the voltage \(v_{ON}\) across the LD. \[\left\{ \begin{array}{ll}\frac{v_{ON}}{R}+C\frac{dv_{ON}}{dt}=i&\Rightarrow \frac{d^{2}v_{ON}}{dt^{2}}+\frac{1}{RC}\cdot\frac{dv_{ON}}{dt}+\frac{1}{LC} \cdot v_{ON}=\frac{U}{LC}\end{array} \right. \tag{1}\]  
When the switch is turned off, Equation (2) can be written according to Kirchhoff's Law, resulting in a second-order differential equation for the voltage \(v_{OFF}\) across the LD. \[\left\{ \begin{array}{ll}\frac{v_{OFF}}{R}+C\frac{dv_{OFF}}{dt}=i&\Rightarrow \frac{d^{2}v_{OFF}}{dt^{2}}+\frac{1}{RC}\cdot\frac{dv_{OFF}}{dt}+\frac{1}{LC} \cdot v_{OFF}=0\end{array} \right. \tag{2}\]  
When \(L>4R^{2}C\), solving the second-order differential equations represented by Equations (1) and (2), the characteristic roots of these two second-order differential equations are two distinct real roots. Expressions for \(v_{ON}\) and \(v_{OFF}\) can be obtained, as shown in Equation (3). \[\left\{ \begin{array}{ll}v_{ON}=U\bigg{\{}1-\frac{1}{2}\cdot\exp\left[-\frac{ 1}{2 RC}\cdot t+\sqrt{\left(\frac{1}{2 RC}\right)^{2}-\frac{1}{LC}}\cdot t\right] -\frac{1}{2}\cdot\exp\left[-\frac{1}{2 RC}\cdot t-\sqrt{\left(\frac{1}{2 RC} \right)^{2}-\frac{1}{LC}}\cdot t\right]\bigg{\}}\\ v_{OFF}=U\bigg{\{}\frac{1}{2}\cdot\exp\left[-\frac{1}{2 RC}\cdot t+\sqrt{\left( \frac{1}{2 RC}\right)^{2}-\frac{1}{LC}}\cdot t\right]+\frac{1}{2}\cdot\exp \left[-\frac{1}{2 RC}\cdot t-\sqrt{\left(\frac{1}{2 RC}\right)^{2}-\frac{1}{LC} }\cdot t\right]\bigg{\}}\end{array} \right.