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2 Discovery of Original Converter
A general question was brought up in last chapter on how to develop or derive PWM converters systematically. There are several approaches to developing converters based on switching cells, canonical converter cells, and switched capacitor/inductor cells, but they left a lot of questions behind without answers. In this book, our attempt is adopting from Charles Darwin's believe of evolution on which he published the book entitled On the Origin of Species. Similarly, we are intended to identify the origin of power converters, from which all of PWM power converters are evolved. The evolution mechanism and principle will be explored in later chapters. In this chapter, three approaches to creating the original converter, the buck converter, are discussed. Based on the original converter, we present three fundamental PWM converters that are used frequently in decoding and synthesizing converters. Their operational modes are discussed correspondingly to verify the evolved converters.
2.1 Creation of Original Converter
Charles Darwin's dilemma is that if species are evolved from their ancestor species and if we keep tracking back to the origin, who is the original one and how to create or generate it? The same questions bother us: if PWM converters are evolved, which one is the origin and what is the mechanism to create it? In literature, there are many converters with various transfer codes, such as D/(1 − 2D), (1 − D)/(1 − 2D), D/(2 − D), D/2(1 − D), D2/(1 − D), etc., in which all of the combinational codes include the duty ratio D and it is just the transfer code of the buck converter in continuous conduction mode (CCM). Thus, we can intuitively reveal that buck converter is the original converter. In this book, we propose three approaches to creating the original converter.
2.1.1 Source–Load Approach
Based on the natural law, Faraday's law, there exists only voltage source, and the output load is usually supplied with voltage form. Thus, the source and load can be configured by the circuit shown in Figure 2.1a. To control the power flow from the source to the load, a control gear or a switch is adopted to link the source and load, as shown in Figure 2.1b. Since source voltage Vi is not necessarily always equal to load voltage Vo, there might exist an inrush current through the switch when switch S1 is turned on. An inductor is therefore inserted in series with the switch, as shown in Figure 2.1c, to limit current slew rate. However, when switch S1 is turned off, there is no path for inductor current to flow continuously, resulting in high voltage spike imposing on the other components. Thus, a freewheeling diode D1 is introduced to provide a path for the inductor current, as shown in Figure 2.1d, and it is the buck converter. How to prove that the buck converter is the origin of converters is left for later discussion.
2.1.2 Proton–Neutron–Meson Analogy
There was a legend about Dr. Hideki Yukawa who was the 1949 Nobel Prize winner in Physics area. Dr. Yukawa used to get stuck at the interaction between protons inside nuclei. Protons carrying positive charges are supposed to repel each other, but how come they stick together tightly? One day, when he walked from his home to laboratory, he found out that the two dogs used to bark each other, but today they stick to each other without barking or fighting. He was curious and walked closely to take a look, and he revealed that they were biting on the same pig's bone. Finally, he realized that the neutrons inside a nucleus play the role of pig's bone to tight protons (dogs) closely. However, if they always stick to each other, which is equivalent to a static balance, how can they interact? This became his research topic, and he figured out that there exist mesons appearing in pair (π+, π−), which govern the interactions between protons and neutrons inside nuclei. When meson π+ is in action, meson π− will be deactivated, and vice versa. In other words, when π− is in action, π+ will be deactivated.
Figure 2.1 Derivation of the original converter, buck converter, with a source–load approach.
With this understanding, derivation of the buck converter can be analogous as follows. The input voltage source and output voltage sink can be treated as two protons, as shown in Figure 2.2a, since they have the same polarity. An inductor, which looks like a rawhide bone, plays the role of a neutron to tight two voltages (similar to protons or dogs), as shown in Figure 2.2b. With this configuration, the output voltage will finally equal to the input voltage, which is a static balance, and there is no further interaction. Thus, it requires to introduce an active–passive switch pair (S1, D1), like meson pair (π+, π−), into the circuit to control power flow from the input to the output, as shown in Figure 2.2c. When switch S1 is turned on, diode D1 is in reverse bias, and on the other way, when S1 is turned off, D1 will conduct to freewheel