# Combination of LiCs and EDLCs with Batteries:
## 2 Proposed Hybrid Energy Storage System
### The Multiple Input Converter Implementation
\[Rs\ \leq\frac{v_{0}}{I} \tag{5}\]  
\[1=\frac{1}{2}C_{s}v^{2}\times 2f \tag{6}\]  
\[Cs=\frac{1}{v_{0}^{2}f} \tag{7}\]  
For the MOSFET driver circuit, \(V_{DD}\) and \(V_{SS}\) are the output voltage levels of the controller and the ground of the controller; this is to ensure an adequate reference ON and OFF state so the driver could understand the ON and OFF states of the controller. A capacitor \(C_{1}\) is added with a parallel ceramic capacitor of low equivalent series resistance to facilitate high frequency switching. \(H_{IN}\) and \(L_{\text{IN}}\) are the inputs of the MOSFET driver for the high side and low side switch signals, respectively. _SD_ is the shutdown pin, which acts as a fail-safe when there is an error in the operation of the converter; it shuts down the driver operation to prevent further damage to the MOSFET driver, and _GND_ is the common ground. Again \(C_{2}\) is an electrolytic capacitor, and a complementary ceramic capacitor is used to ensure stable voltage across \(V_{CC}\) and _GND_. \(L_{O}\) is the gate drive signal for the low side switch, while \(H_{O}\) is the gate drive signal for the high side switch. Since an N-channel MOSFET was used for the high side switching, the gate signal voltage had to be higher than the voltage at the drain of the switch; therefore, a floating gate voltage was used. This was achieved by using a bootstrap circuit, which was implemented simply using \(C_{B}\) and \(V_{B}\). \(V_{S}\) is tied to the source of the high side switch and therefore becomes the effective reference ground for the bootstrap capacitor, and \(V_{B}\), which is the bootstrap voltage, gets its charge from forward biasing the diode \(D_{B}\). This makes the switching signal of the high side switch have a voltage \(V_{B}\) higher than the voltage (\(V_{DS}\)) at the drain of the corresponding high side switch. The values for the various circuit parameters presented in Figure 4b,c are presented in Table 3.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Device** & **Manufacturer ID** & **Parameter** & **Value** \\ \hline \multirow{6}{*}{\(\text{Q}_{\text{H}}=\text{Q}_{\text{L}}\)} & & \begin{tabular}{c} Drain-source voltage \\ Gate source voltage \\ ON-state resistance \\ \end{tabular}  & \begin{tabular}{c} 300 V \\ \(\pm\)30 V \\ 110 m\(\Omega\) \\ 36 A \\ \end{tabular}  \\ \hline \(\text{D}_{\text{H}}=\text{D}_{\text{L}}\) Schottky diode & DSTF30100S & \begin{tabular}{c} Peak reverse voltage \\ Forward current \\ \end{tabular}  & \begin{tabular}{c} 100 V \\ 30 A \\ \end{tabular}  \\ \hline \(L_{1}=L_{2}=L_{3}\) Ring core inductor & B82726S2243A020 & \begin{tabular}{c} Inductance \\ Voltage, current \\ \end{tabular}  & \begin{tabular}{c} 0.75 mH \\ 250 V, 24 A \\ \end{tabular}  \\ \hline Co (electrolyte) & LH.NOVA & Capacitance, voltage & 33 \(\mu\)F, 400 V \\ \hline Cs (mica) & CD19 FD242 GO3 & Capacitance, voltage & 2400 pF, 500V \\ \hline \(R\)s & CF14J715 IR0 & Resistance, power & 51 \(\Omega\), 2 W \\ \hline \(D\)s & 1N4004-TP & \begin{tabular}{c} Peak reverse voltage \\ Forward current \\ \end{tabular}  & 400 V \\ \hline \(\text{D}_{1}=\text{D}_{2}\) Fast switching diode & 1N4148 TR & \ \begin{tabular}{c} Peak reverse voltage \\ Forward current \\ \end{tabular}  & \begin{tabular}{c} 100 V \\ 150 mA \\ \end{tabular}  \\ \hline \(C_{\text{B}}\) (tantalum) & TAP226K025 SRW & Capacitance, voltage & 22 \(\mu\)F, 25 V \\ \hline \(C_{1}=C_{2}\) (electrolyte) & ESK226M025 AC3 AA & Capacitance, voltage & 22 \(\mu\)F, 25 V \\ \hline C (ceramic) & & Capacitance, voltage & 224 pF, 25V \\ \hline \multirow{6}{*}{**Parameter**} & & **Nominal Value** & \\ \cline{2-4}  & & **Minimum (V)** & **Maximum (V)** \\ \hline \(V_{\text{DD}}\) & & \(V_{SS}+3\) & \(V_{SS}+20\) \\ \(V_{SS}\) & & \(-5\) & 5 \\ \(D\)C & & \(10\) & 20 \\ \(V_{CC}\) & & \(10\) & 20 \\ \(V_{S}\) & & - & 600 \\ \(H_{O}\) & & \(V_{S}\) & \(V_{B}\) \\ \(L_{O}\) & &