Читать книгу Origin of Power Converters - Tsai-Fu Wu - Страница 34

The above decoding process is based on CCM operation of the converters. In order to confirm the decoding process is also working for DCM operation, the input–output voltage transfer ratios of the converters in DCM operation are discussed as follows.

For the buck converter shown in Figure 2.6a and operated in DCM, the input–output voltage transfer ratio was derived and expressed in (2.4). Similarly, the transfer ratio of the buck‐boost converter in DCM operation can be derived as

(2.10)

by substituting the transfer ratio D shown in (2.8) with the ratio, d₁/(d₁ + d₂), of the buck converter in DCM operation. The transfer ratio of the boost converter, therefore, can be derived as

(2.11)

Again, if

(2.12)

and d₂ is replaced with (1 − D), the boost converter is, therefore, in CCM operation, and the transfer ratio will become the one shown in (2.9).

Based on the transfer ratio of the buck converter in DCM operation, those of the buck‐boost and boost converters can be derived correspondingly. The transfer ratios of the buck‐boost and boost converters in DCM operation can be also derived directly based on volt‐second balance principle, and they come out the same expressions as those shown in (2.10) and (2.11). This confirms that the decoding and synthesizing processes can be applied for both DCM and CCM operations. In the rest of the chapters, for simplicity, the discussion of decoding and synthesizing processes will be based on CCM operation only. From now on, the transfer ratio will be treated as a transfer code for further decoding processing.

From the above discussion, we observed that the original PWM code is D, and the derived codes include (1 − D), 1/(1 − D), and D/(1 − D), which can be adopted as fundamental codes in decoding transfer codes. Buck converter is the origin, and the evolved converters are buck‐boost and boost converters up to this moment. In the evolution process, the evolved converters are not always directly evolved from the original converter, but they can be evolved from the evolved converters or their descendant converters, like that the boost converter is evolved from the buck‐boost converter instead of the buck converter, while the buck‐boost converter is evolved from the buck converter.