Origin of Power Converters. Tsai-Fu Wu

Originally, the Ćuk converter has two separate inductors. Analyzing the operation of the converter will realize that the two inductors can be coupled with each other. Other examples are sepic and Zeta converters, of which there are two inductors in each converter and they can be coupled and wound on the same core. A converter with coupled inductors will reduce one degree of dynamic order. Can all of converters with two or more inductors be constructed with coupled inductors? How to place a secondary winding in a proper path in the converter is another issue, which needs to discuss further.

Figure 1.15 PWM converters with coupled inductors: (a) buck type, (b) boost type, (c) Ćuk type, and (d) buck‐flyback type.

      Figure 1.15d shows a buck and a flyback combined converter with coupled inductors to form an isolated output V_oA, which is the flyback‐type output, while output V_o is just the regular buck output without isolation. Comparing the converters shown in Figure 1.15a and d reveals that the coupled winding can be connected back to the converter itself or to a separate network, which can be isolated from the primary side. It is quite diversified when introducing coupled winding(s) to the converters. What is the mechanism behind in developing such kind of converters?

1.4 Approaches to Converter Development

      In last section, many well‐known PWM converters were introduced, but many questions were also brought up. A general question is that how to develop the converters systematically. In this section, several typical approaches are described briefly for later discussion.

From the converters shown in Figures 1.7 and 1.8a, one can observe that the active and passive switches have a common node. Thus, a switching cell concept was introduced to explain the configurations of the converters. There are two types of switching cells, P cell and N cell, as shown in Figure 1.16, and each has two terminals for connecting to source or output and one current terminal for connecting to inductor to form a PWM converter. For examples, buck converter can be derived from P cell, while boost converter can be derived from N cell. This is a kind of intuitive approach with induction but without manipulation on the converters. In fact, with a little bit of manipulation by relocating capacitor C₁ in the sepic and Zeta converters shown in Figure 1.8b and c from the forward path to the return path, a P cell and an N cell can be identified, and the converters can be derived accordingly. Typically, this approach is used to explain the existing converter configurations, but it is hard to develop new converters. It is based on a cell level.

Similarly, based on observation and induction, the converters shown in Figures 1.7 and 1.8 can be explained with two canonical switching cells, namely, Tee canonical cell and Pi canonical cell, as shown in Figure 1.17. By exhaustively enumerating all of possible combinations of Z_in, Z_out, and Z_x, and including LC network, source, and load, the converters shown in Figures 1.7 and 1.8 can be derived. Additionally, the converters with extra LC filters and inverse versions of the converters can be derived. Figure 1.18 shows the buck and boost converters and their inverse versions, in which the input‐to‐output transfer ratios shown in the bottom of the converters are corresponding to continuous conduction mode, and D is the duty ratio of the active switch. Moreover, the converters with the same higher step‐up voltage transfer ratio but with different circuit configurations, as shown in Figure 1.19, can be developed. Although this approach can derive new PWM converters and is straightforward, it is still tedious and lacks of mechanism to explain the converters with identical transfer ratio but with different configurations. Again, it is based on a cell level.

Figure 1.16 (a) P cell and (b) N cell.

Figure 1.17 (a) Tee canonical cell and (b) Pi canonical cell.

Figure 1.18 (a) Buck and inverse buck and (b) boost and inverse boost.

Figure 1.19 With the same input‐to‐output transfer ratio of (2D − 1)/(1 − D) but with different configurations (a) and (b).

Based on a cell level, another approach to developing new converters with higher step‐up and step‐down voltage ratios by introducing switched‐capacitor or switched‐inductor cells to the PWM converters shown in Figures 1.7 and 1.8 was proposed. Typical switched‐capacitor and switched‐inductor cells are shown in Figure 1.20, and their derived converters have been shown in Figure 1.10. Applications of this approach are quite limited, and the chance of deriving new converters is highly depending on experience. Otherwise, it might need many trial and errors. When inserting a cell into a PWM converter, one has to use volt‐second balance principle to verify if the converter is valid. This approach still needs a lot of ground work to derive a valid converter.

Another synthesis approach based on a converter cell concept, 1L and 2L1C, was proposed. The synthesis procedure is supported with graph theory and matrix representation and based on a prescribed set of properties or constraints as criteria to extract a converter from all of the possible combinations, reducing the number of trial and errors. A structure of PWM DC–DC converters included in the synthesis procedure is depicted in Figure 1.21, and possible positions of inserting an inductor into a second‐order PWM converter are shown in Figure 1.22. Typical converter properties include number of capacitors and inductors, number of active–passive switches,