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, DC voltage conversion ratio, continuous input and/or output current, possible coupling of inductors, etc. This approach seems general and has a broad vision in synthesizing converters, but it needs a lot of efforts or even trial and errors in selecting a valid converter when considering many properties simultaneously. For the main purpose of deriving a converter, maybe, we have to consider the static performance, such as input‐to‐output voltage transfer ratio and continuous inductor current, first, and if users would like to know more about the dynamics of the converter, they can analyze them further.
Figure 1.20 (a) Switched‐capacitor and (b) switched‐inductor cells.
Figure 1.21 Structure of PWM converters used in the derivation procedure.
Figure 1.22 Possible positions of the inductor in a second‐order PWM converter based on 1L converter cell.
In the above discussed approaches, the converters are derived or synthesized based on cell or component levels. They select a proper converter configuration and add certain cell or component to the converter to form a new converter topology. Essentially, they exhaustively enumerate all of possible combinations and extract converters based on certain constraints or properties. Valid converters are verified with the volt‐second balance principle. Applications of these approaches to developing new converters are quite limited because the chance of obtaining a valid converter is depending highly on experience. Is it possible to start from valid converters and with certain manipulation to develop new converters? To answer this question, several viable approaches are briefly discussed.
The three well‐known valid PWM converters, buck, boost, and buck‐boost, are shown in Figure 1.7. With a synchronous switch technique, the buck‐boost converter can be derived from buck and boost converters in cascade connection. The derivation procedure is illustrated in Figure 1.23, in which the buck and boost converters in cascade connection is shown in Figure 1.23a. Without considering ripple current, it can be proved that capacitor C1 can be eliminated, and inductors L1 and L2 are just connected in series to become L12, as shown in Figure 1.23b. If switches S1 and S2 are synchronized and have identical duty ratio, the active–passive switch pairs, S1&D1 and S2&D2, can be replaced with two single‐pole double‐throw (SPDT) switches, as also shown in Figure 1.23b, in which node “A” corresponds to an active switch and node “B” is to a passive switch. Thus, the circuit shown in Figure 1.23b can be simplified to that shown in Figure 1.23c, and the two switch pairs can be combined to S12. Replacing the switch pair with an active switch and a passive one yields the buck‐boost converter shown in Figure 1.23d. Note that at the output of Figure 1.23b, the positive polarity is located at the upper node, while that in Figure 1.23c and d, the positive polarity is in the lower node. How to determine the polarity is not straightforward. And it usually needs several words to explain the polarity transition. Similarly, the Ćuk converter that can be proved to be a cascade connection of boost and buck converter can be also derived with the same procedure. Again, the change of output polarity needs extra explanation, and it is not so obvious and convincible.
Figure 1.23 Evolution of the buck‐boost converter from the buck and boost converters with a synchronous switch technique.
The derivation procedure based on the synchronous switch technique is so far only applied to two switch pairs, because its combination of switch pairs, location of inductor/capacitor, and determination of output voltage polarity are not straightforward. This approach is essentially based on a preliminary observation of converter operation and configuration, but it lacks of principle or mechanism in decoupling and decoding PWM converters. Thus, it cannot be extended to derive other PWM converters, such as the sepic and Zeta converters shown in Figure 1.8b and c.
Based on the synchronous switch concept, the graft switch technique (GST) was proposed. Instead of starting from converter manipulation, the GST starts to deal with how to graft two switches operated in unison or synchronously and with at least a common node, from which four types of grafted switches are developed, as shown in Figure 1.24. They are T‐type, inverse T‐type, Π‐type, and inverse Π‐type grafted switches, which can be used to integrate the active switches in the converters. An illustration example in deriving the buck‐boost converter is shown in Figure 1.25. Again, the buck and boost converters in cascade connection shown in Figure 1.23a is still adopted. After simplifying the L1C1L2 filter, we can obtain a circuit shown in Figure 1.25a. By exchanging the connection of
