# An Overview of Non-Isolated Hybrid Switched-Capacitor Step-Up DC-DC Converters
## 3 Switched-Capacitor Circuits Controlled by Transistors  
We studied several SC topologies with transistors and have described the most common. For example, Figure 10a shows a possible circuit extension in Figure 9. It can be called the _Series-Parallel Converter_, one of the converters studied in [20]. Figure 10 also shows the equivalent circuits in the two switching states of the converter. As their name indicates, one of the switching states (see Figure 10b) corresponds to a state in which all capacitors (except the output capacitor) are in parallel, while Figure 10c shows an  
Figure 10: The _Series-Parallel Converter_ and their equivalent switching states, (**a**) topology, (**b**) equivalent circuit when capacitors are in parallel, and (**c**) equivalent circuit when capacitors are in series. equivalent circuit when all capacitors (except the output capacitor) are in a series connection. This operation can be summarized as follows from Figure 10a: We can divide the switches into two groups; group \(A\) is made by switches \(s_{2}\), \(s_{3}\), \(s_{5}\), \(s_{6}\), \(s_{8}\), \(s_{9}\), \(s_{11}\), and \(s_{12}\), and group \(B\) is made by \(s_{1}\), \(s_{4}\), \(s_{7}\), \(s_{10}\), and \(s_{13}\). We drive the converter with a single firing signal, a square signal (50% of duty cycle), meaning the switches of group \(A\) are all closed, and the switches of group \(B\) are all open when the firing signal is one (high). This produces the equivalent circuit shown in Figure 10b. On the other hand, when the firing signal is zero (low), the switches of group \(A\) are all open while the switches of group \(B\) are all closed; this produces the equivalent circuit shown in Figure 10c. When the circuit behaves in the same way as in Figure 10b, capacitors \(C_{1}\), \(C_{2}\), \(C_{3}\), and \(C_{4}\) get connected in parallel to the input voltage and charged to the input voltage level. In the other state, those capacitors (\(C_{1}\), \(C_{2}\), \(C_{3}\), and \(C_{4}\)) get in series with the input voltage source charging \(C_{5}\) with five times the input voltage. This converter, which is the _Series-Parallel Converter_, multiplies the input voltage for a certain value. In the case of Figure 10, the input voltage is multiplied by five, and this value can be extended with more capacitors and switches. The _Series-Parallel Converter_ is one of the possible extensions to the circuit in Figure 9. Another possible extension is shown in Figure 11; it is known as the _Fibonacci Converter_[21] (another of the converters studied in [20]). Figure 11 also shows the equivalent circuits of the Fibonacci Converter. The converter may seem to be operated with two firing signals, square signals with a phase shift of 180\({}^{\circ}\), or with a single firing signal in which some of the transistors are driven on when the firing signal is high, while other transistors are driven on when the firing signal is low. Their traditional operation can be described in the following manner. Again, we can divide the switches into two groups: group \(A\) is made by odd switches (\(s_{1}\), \(s_{3}\), \(s_{5}\), \(s_{7}\), \(s_{9}\), \(s_{11}\), and \(s_{13}\)), and group \(B\) is made by even switches (\(s_{2}\), \(s_{4}\), \(s_{6}\), \(s_{8}\), \(s_{10}\), and \(s_{12}\)). We can also drive the converter with a single firing signal, a square signal (50% of duty cycle), meaning the switches of group \(A\) are all closed, and the switches of group \(B\) are all open when the firing signal is one (high), which produces the equivalent circuit shown in Figure 11b. On the other hand, when the firing signal is zero (low), the switches of group \(A\) are all open, while the switches of group \(B\) are all closed; this produces the equivalent circuit in Figure 11c. When the circuit behaves as in Figure 11b, capacitor \(C_{1}\) gets charged with the input voltage at the next switching state (see Figure 11c).