## 2 Power Stage  
A circuit block diagram of the battery charger proposed in this study is shown in Figure 1. It was composed of the electromagnetic interference (EMI) filter, bridge rectifier, power factor correction stage, PSFB converter, transformer, current-doubler rectifier (CDR),  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Literature** & **[13]** & **[17]** & **[14]** & **[15]** & **[18]** & **[16]** & **This Study** \\ \hline Application & Charger & Charger & Charger & Charger & Converter & Charger & Charger \\ \hline Load type & Super-capacitor & Lithium-ion battery & LiFePO4 & Liquid-state LiFePO4 & Resistance load & Battery module & Solid-state lithium battery \\ \hline Power topology & No mentioned & Full-bridge phase-shifted CDR & PSFB CDR & PSFB CDR & & & \\  & & & (No resonant inductor) & (No resonator inductor) & PSFB CDR & No mentioned & PSFB SR CDR \\ \hline Control & Set-point-modulation cooperative charging method & No mentioned & P & PI and P & No & P & Fuzzy-aided PI & Fuzzy-aided P-PI \\ \hline \hline \end{tabular}
\end{table}
Table 1: Technical comparisons of literatures.  
synchronous rectification (SR), filter capacitor, and standby power supply. The standby power supply provided the DC power for driving the cooling fans and the control chips of the proposed control system. Moreover, the input side of the charger was connected to a single-phase (1-\(\phi\)) AC source, while the output side was connected to a solid-state lithium battery pack. Additionally, the output current of the charger was monitored for overcurrent protection to prevent potential damage. The detected current signal was fed into the PSFB controller.  
The PSFB converter circuit integrated with a current-doubler filter and synchronous rectification is illustrated in Figure 2. The circuit components was composed of the four power MOSFETs (\(Q_{x}\)-\(Q_{d}\)), blocking capacitor (\(C_{b}\)), transformer (\(T_{r}\)), synchronous rectification (SR) MOSFETs (\(Q_{s71}\) and \(Q_{s72}\)), current-doubler inductors (\(L_{c41}\) and \(L_{c42}\)), filter capacitor (\(C_{o}\)). Moreover, the input power supply to the PSFB converter is denoted as \(V_{i}\), and the output voltage and current are represented as \(V_{o}\) and \(I_{o}\), respectively. The calculated formulas for the component values and specifications are referenced from [19] and are described as follows.  
It is assumed that two current-doubler inductors have the same value, which can be given by  
\[L_{c41}=L_{c42}=V_{o}\left(1-d_{psfb}\right)/(\Delta i_{c41}f_{sw}), \tag{1}\]  
Figure 1: A circuit block diagram of the proposed battery charger.  
Figure 2: PSFB converter circuit integrated with the CDR and SR.  
where \(f_{sw}\) is the operating frequency of \(Q_{a}\)-\(Q_{d}\). The duty cycle ratio is \(d_{ppb}\), it can be expressed as  
\[d_{psfb}=(V_{o}/V_{j})\,(n_{p}/n_{s}), \tag{2}\]  
where \(n_{p}\) denotes the number of primary-side winding turns of the transformer, \(n_{s}\) represents the numbers of secondary-side winding turns of the transformer. Moreover, in (1), \(\Delta i_{lod1}\) denotes the peak-to-peak current of the inductor \(L_{cd1}\), and it can be expressed as  
\[\Delta i_{cd1}=\Delta i_{cd2}=k\,l_{o}/2, \tag{3}\]  
where \(k\) represents the percentage of the inductance's peak-to-peak ripple current relative to the average current.  
The root mean square (rms) current flowing through the power MOSFETs (\(Q_{a}\)-\(Q_{d}\)) is given by  
\[i_{Qd(rms)}=\sqrt{0.5}\,(I_{o}/2)\,\,(n_{s}/n_{p}), \tag{4}\]  
The rms current flowing through \(Q_{sr1}\) and \(Q_{sr2}\) is given by  
\[i_{Qsr(rms)}=I_{o}\sqrt{0.25+\left(d_{psfb}/2\right)}, \tag{5}\]  
The voltage stress of \(Q_{sr1}\) and \(Q_{sr2}\) is given by  
\[V_{Q_{cr}}=V_{o}/d_{psfb}, \tag{6}\]  
The capacitance value of the output capacitor \(C_{o}\) can be expressed as  
\[C_{o}=V_{o}\,\left(1-2\,d_{psfb}\right)/\left(16\,L_{cd1}\,\Delta V_{co}\,f_{ sw}^{2}\right), \tag{7}\]  
where \(\Delta V_{co}\) represents the voltage ripple across the output capacitor.