# An Overview of Non-Isolated Hybrid Switched-Capacitor Step-Up DC-DC Converters
## 3 Switched-Capacitor Circuits Controlled by Transistors
One of the recently investigated topologies is the _Flying Capacitor Multilevel Inverter_[27; 28; 29; 30; 31], see Figure 13. Initially used as a multilevel inverter, it has also been investigated as a dc-dc SC converter. Figure 13 shows the converter used as a \(3\times\) converter, which means the output voltage (or high-side voltage) is three times the input voltage (or high-side voltage). To perform this conversion, three switching states are required instead of two, as in the previously studied converters. Figure 14 shows the switching states of the converter in Figure 13.  
The _Flying Capacitor Converter_ was not proposed as an SC circuit, but as a dc-ac (or ac-dc) converter, but it can also be used as an SC dc-dc converter, although it requires more sophisticated switching functions. Figure 14: The three states of the switching sequence of the converter shown in Figure 13, **(a)** first switching state, **(b)** second switching state, and **(c)** third switching state. Figure 13: Two common ways of drawing the Flying Capacitor Multilevel Converter (it is the same topology drawn in two different ways), **(a)** drawn in vertical way, **(b)** drawn horizontally. The converter in Figure 13 requires three equivalent circuits to operate. Figure 14 shows those equivalent circuits, and Figure 14a shows the equivalent circuit in which switches \(s_{1}\), \(s_{4}\), and \(s_{6}\) are on while \(s_{2}\), \(s_{3}\), and \(s_{5}\) are off. We call this the first switching state. Figure 14b shows the equivalent circuit in which switches \(s_{2}\), \(s_{3}\), and \(s_{6}\) are on while \(s_{1}\), \(s_{4}\), and \(s_{5}\) are off. We call this the second switching state. Figure 14c shows the equivalent circuit in which switches \(s_{2}\), \(s_{4}\), and \(s_{5}\) are on while \(s_{1}\), \(s_{3}\), and \(s_{6}\) are off. We call this the third switching state. As a short discussion of advantages and disadvantages, the _Fibonacci Converter_ has a voltage gain that increases significantly when the number of power stages increases, in contrast to the _Ladder_ and the _Series-Parallel_, whose voltage gains increase linearly when the number of power stages increases. The _Ladder_ and the _Series-Parallel_ have the advantage of having the same voltage in all capacitors, equal to the input voltage. The _Ladder_ has the advantage against the other two in that switches are also rated to the input voltage. The _Series-Parallel_ and the _Fibonacci_ require transistors of a larger voltage as the number of power stages increases. The _Flying Capacitor_ topology has the same voltage in all switches, but a different voltage across capacitors. It requires three switching states instead of two. One of the most recent contributions to the SC topologies was the proposition of the _Multilevel Modular Capacitor-Clamped DC-DC Converter_ or the MMCC Converter [32]. Figure 15 shows the MMCC Converter. The operation can be explained in the following manner: The digital inputs are divided into two groups with the same firing signal; similar to the former SC converters, it has two equivalent circuits (except for the flying capacitor, which has three). Figure 16a shows the first equivalent circuit; in this state, switches \(s_{1}\), \(s_{3}\), \(s_{4}\), \(s_{7}\), \(s_{9}\), \(s_{11}\), and \(s_{13}\) are on, while \(s_{2}\), \(s_{5}\), \(s_{6}\), \(s_{8}\), \(s_{10}\), and \(s_{12}\) are off. Figure 16b shows the second equivalent circuit; in this state, switches \(s_{1}\), \(s_{3}\), \(s_{4}\), \(s_{7}\), \(s_{9}\), \(s_{11}\), and \(s_{13}\) are off, while \(s_{2}\), \(s_{5}\), \(s_{6}\), \(s_{8}\), \(s_{10}\), and \(s_{12}\) are on. Figure 10:0 Equivalent circuits of the _MMCC Converter_, (**a**) first switching state, (**b**) second switching state. Figure 10:1 The MMCC Converter topology. During the first switching state, capacitor \(C_{1}\) gets charged to the input voltage \(v_{g}\). During the second state, \(C_{1}\), in series with the input voltage, charges \(C_{2}\) to twice the input voltage.