# Fast Performance Evaluation for Switched-Capacitor Converter Based on Convolutional Neural Networks
## 2 Power Loss and Efficiency Analysis of Switched-Capacitor DC/DC Converters  
SCC converts a voltage to another by means of changing rapidly between the capacitors using switches. For simplicity, the following assumptions are made:  
* All switches share identical electrical characteristics, such as on-resistance \(R_{ds(on)}\), etc. * All internal (energy transfer) capacitors handling the same voltage share an identical capacitance \(C\) and equivalent series resistance \(ESR\). * The dead time of the converter is neglected. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Topology** & **Efficiency** & **Accuracy** \\ \hline [PERSON] et al. [16] & Simple & High & Medium \\ [PERSON] et al. [17] & Complicated & Low & High \\ [PERSON] et al. [18] & Medium & High & Low \\ This paper & Complicated & High & High \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison with existing methods. The power loss of an SCC can be divided into three parts: conduction loss, switching loss, and gate driving loss. As is evident in Equation (1), the gate driving loss can be calculated using the switching period \(T_{s}\), gate charge \(Q_{g}\), and gate driving voltage \(V_{gs}\)  
\[P_{\text{gate}}=\sum_{Q_{i}}\frac{V_{gs}Q_{g}}{T_{s}} \tag{1}\]  
where \(Q_{i}\) denotes the \(i\)th switch. Switching loss can be expressed as  
\[P_{SW}=\sum_{Q_{i}}\frac{\frac{1}{2}I_{DS}V_{DS}\Big{(}t_{on}+t_{off}\Big{)}}{ T_{S}} \tag{2}\]  
where \(I_{DS}\) and \(V_{DS}\) are the current and voltage across the MOSFET at switching moment, respectively. The conduction loss, which is generated from charging and discharging between energy-transfer capcitors, plays a major part in high current applications such as data center power supply and mobile phone quick charging. The conduction loss is composed of power dissipation in the \(ESR\) of the capacitor and the \(R_{ds(on)}\) of MOSFET. \[P_{conduction}=\sum_{C_{i}}\int_{0}^{T_{s}}\frac{i(t)^{2}R_{ESR}dt}{T_{s}}+ \sum_{Q_{i}}\int_{0}^{dT_{s}}\frac{i(t)^{2}R_{ds(on)}dt}{T_{s}} \tag{3}\]  
However, the current waveform of an SCC is difficult to obtain, making \(P_{SW}\) and \(P_{conduction}\) hard to calculate. The conventional performance evaluation method is based on the well-known equivalent circuit, as shown in Figure 1, which is expressed by a cascade connection of an ideal DC transformer and an output impedance route. The conversion ratio \(M\) of the DC transformer is equal to the input and output voltage ratio \(V_{out}/V_{in}\) at no load, and is only determined by the topology configuration. The output resistance \(R_{out}\) is correlated with the operation efficiency. The most longstanding SCC evaluation method is based on the analysis of output resistance, \(R_{out}\). Referring to the conventional practices in inductor-based power converters, academic efforts have focused on obtaining the output resistance using state equations to analyse the instantaneous equivalent circuits of all phases. However, the element number of the state vector is equal to the number of charge-transfer capacitors in an SCC. In more complex topologies, it is not feasible to solve high-order differential equation to obtain the analytical expression of the output resistance. Confronted with the analytic calculation challenge, several approximation methods have been proposed. The fast switching limit (FSL) and slow switching limit (SSL) approach is the most versatile of the approximate approaches for SCC performance evaluation [19]. The FSL is prominent at high switching frequencies. The FSL impedance is calculated supposing that the voltage of each capacitor and sources are constant. In the FSL, current flow occurs in a frequency-independent constant pattern. The total output impedance of the converter is a combination of the conduction resistance of the switches as well as the ESR of the capacitors. As for low switching frequency, SSL plays an important part in performance evaluation. The SSL impedance is calculated with the following three assumptions:  
Figure 1: Equivalent model of SCC.