## 4 Design Consideration and Simulation
### HPLDDC Current Loop Analysis and Simulation  
Parameter values of Table 2 are listed in Table 7. In Table 7, substitution of \(V_{LD1}\), \(V_{LD2}\), \(I_{LD1}\), and \(I_{LD2}\) from Table 3 into (12) can yield \(r_{hpl}\) = 0.99 \(\Omega\). From Table 4, substation of \(V_{o(max)}\) = 16 V and \(V_{in(min)}\) = 9 V into the formula (\(V_{o(max)}-V_{in(min)}\))/\(V_{o(max)}\) can yield \(D_{bt}\) = 0.437. To yield the \(d\)-\(v_{ca}\) characteristic of SBBC in the boost mode, the testing conditions were defined as \(V_{o(max)}\) = 16 V and \(V_{in(min)}\) = 9 V and, and the SBBC output current, \(I_{o}\), was adjusted from 0.5 to 1.2 A; the measurement points are depicted in Figure 11a. In addition, the curve fitting function of MATLAB was used to obtain a linear polynomial, and the notation, \(d\), was replaced with \(d_{bt}\); hence, Equation (13) can be rewritten as follows:  
\[d_{bt}=0.1v_{caa}+0.35 \tag{19}\]  
Similarly, to yield the \(d\)-\(v_{ca}\) characteristic of SBBC in the buck mode, the testing conditions were defined as \(V_{o}\) = 12 V and \(V_{in(max)}\) = 16 V, and the SBBC output current, \(I_{o}\), was adjusted from 0.5 to 1.2 A; the measurement points are depicted in Figure 11b. In addition, the curve fitting function of MATLAB was used to obtain a linear polynomial, and \(d\) was replaced with \(d_{bt}\); therefore, Equation (13) can be rewritten as follows:  
\[d_{bt}=0.23v_{caa}+0.64. \tag{20}\]  
From Equation (14), \(G_{cltr}\)(s) = \(k_{ca}\), and \(k_{ca}\) in the boost mode equals the constant 0.1 from Equation (19); hence, \(G_{cltr(bt)}\) (s) = 0.1. From Equation (20), in the buck mode, \(G_{cltr}\) (s) can be obtained and defined as \(G_{cltr(bb)}\) (s) = 0.23. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Circuit Element** & **Type-Number** & **Specification** \\ \hline \multirow{3}{*}{\(Q_{1},Q_{2},Q_{3},Q_{4}\)} & \multirow{3}{*}{IRF7478 PBF} & Maximum drain–source voltage is 60 V \\  & & Drain–source turning on resistance is 26 m\(\Omega\) \\  & & Drain current is 7 A at 25 \({}^{\circ}\)C \\ \hline \multirow{3}{*}{\(L_{1}\)} & \multirow{3}{*}{CS127060} & Inductance value: 30 uH \\  & & Material: Sendust \\ \hline \multirow{3}{*}{\(C_{o}\)} & \multirow{3}{*}{EEU-FR1E471Y} & Inductance value: 470 uF \\  & & \(ESR\leq\) 41 m\(\Omega\), \\  & & Aluminum electrolytic capacitance \\  & & Semiconductor laser diode \\ \multirow{3}{*}{Blue-beam HPLDs} & \multirow{3}{*}{PL TB405B} & Material: InGaN-base \\  & & Laser emission: Blue beam. \\ \cline{3-3}  & & See the Table 3 \\ \hline \multirow{3}{*}{Operational amplifier} & \multirow{3}{*}{LM258 ADR} & Range of DC power supply: 3 V to 32 \\  & & VOpen-loop differential voltage gain: 100 dB \\ \cline{1-1} of & & Unity gain bandwidth: 0.7 MHz \\ \cline{1-1} \cline{3-3} SA and CLC & & Operational amplifier, package: SO8 \\ \cline{1-1}  & & Operating temperature: \(-\)40 \({}^{\circ}\)C to 85 \({}^{\circ}\)C. \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Circuit element specification. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(r_{c}\) & 41 m\(\Omega\) & \(r_{L}\) & 68 m\(\Omega\) \\ \(V_{in(max)}\) & 16 V & \(C_{o}\) & 470 uF \\ \(L_{1}\) & 30 uH & \(r_{hpl}\) & 0.99 \(\Omega\) \\ \(D_{bt}\) & 0.437 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parameter values of Table 2.  
Substitution of \(G_{cdt(bt)}\) (\(s\)) = 0.1 and \(G_{cdt(bt)}\) (\(s\)) = 0.23 into Equations (16) and (17), and using Matlab, frequency responses of buck and boost modes, are illustrated in Figure 12. From Figure 12, a resonant frequency point of \(G_{op(bt)}\) (\(s\)) was at 450 Hz; hence, the compensative crossover frequency, \(f_{\zeta}\), must be deviated from this resonant frequency point because the resonant occurrence would cause the HPLDDC instability. Moreover, \(G_{op(bt)}\) (\(s\)) bandwidth (BW) was 7.7 Hz, and it should be expanded for the HPLDDC response speed promotion.