Origin of Power Converters. Tsai-Fu Wu
similar to those of the proton–neutron–meson model. Thus, the buck converter can be derived accordingly.
It can be noted that with a source–load approach, the buck converter derivation is constructed one component by one component. While, with the proton–neutron–meson approach, the active–passive switch pair is introduced to the converter at a time, like a meson pair.
2.1.3 Resonance Approach
Power transfer between energy storage elements, capacitors and inductors, has three types of configurations, as shown in Figure 2.3. The two types shown in Figure 2.3a and b will result in electrical energy loss up to half the initially stored energy when turning on switch S1 and under the condition of capacitance C1 = C2 or inductance L1 = L2. To conserve the total electrical energy during power transfer, the only valid configuration is shown in Figure 2.3c where the power transfer is from capacitor to inductor or vice versa and it is conducted in resonant manner. Practical examples applying this configuration are shown in Figure 2.4, in which Figure 2.4a shows a current output and Figure 2.4b shows a voltage one, and the diode D1 is introduced to the converter to circulate the energy stored in inductor L1 when switch S1 turns off. With the freewheeling diode D1, the converter shown in Figure 2.4b can be controlled with PWM to tune its input‐to‐output voltage transfer gain. This converter, namely, buck converter, consists of the minimum number of components for power transfer with resonance.
Figure 2.2 Analogy of the buck converter derivation to proton–neutron–meson model of a nucleus.
Figure 2.3 Three types of configurations of power transfer between capacitors and inductors.
Figure 2.4 Practical examples applying the configuration shown in Figure 2.3c: (a) with current output and (b) with voltage output.
In the above discussions, the buck converter has been derived with different approaches. Its power transfer is straightforward from input to output when turning on active switch S1, and when turning off the switch, the energy stored in inductor L1 is continuously releasing to the output. The power flow can be controlled with PWM, and its output is always limited within the input voltage in the steady state. From dynamic point of view, the buck converter is a kind of minimum‐phase system, and it is easy to achieve high stability margin. With all of these positive natural properties together, the buck converter has the potential to be the original converter for evolving the rest of PWM converters. This viewpoint will be proved through decoding and synthesizing processes in later chapters.
2.2 Fundamental PWM Converters
Before embarking on the proof of the original converter, we review the operational principle of the buck converter and derive its input‐to‐output voltage transfer ratios in CCM and discontinuous conduction mode (DCM). Additionally, we show the derivation of buck‐boost and boost converters from the buck converter to get some feeling about the potential of the buck converter acting as the original converter.
2.2.1 Voltage Transfer Ratios
From power transfer point of view, the resonance approach can describe the derivation of the buck converter with more physical insight. For resonance, it requires at least a second‐order LC network. In addition to the buck converter, there are other two well‐known PWM converters, boost and buck‐boost, each of which is also with a second‐order LC network. As discussed previously, the buck converter is considered as the candidate of the original converter. Thus, let us see if it is possible to evolve buck‐boost and boost converters from the buck converter. For illustrating the evolution, operation mode and transfer ratio of the buck converter need to be discussed first.
Given a buck converter shown in Figure 2.5a and assuming all of the components are ideal, when switch S1 turns on, the voltage across inductor L1 is Vi − Vo, while when switch S1 turns off, diode D1 will conduct, and the voltage across L1 is −Vo, as illustrated in Figure 2.5b. Thus, based on the volt‐second balance principle, we can have the following equation:
Figure 2.5 (a) The buck converter, (b) inductor voltage VL1 and current iL1, and (c) those in DCM operation.
where D is the duty ratio of switch S1 and Ts is the switching period. Since inductor current iL1 never drops to zero, this operation mode is called CCM. From (2.1), we can derive the input‐to‐output voltage transfer ratio below:
(2.2)
If inductor current iL1 drops to zero before turns on switch S1 again, as shown in Figure 2.5c, the operation mode is called DCM. Again, based on the volt‐second balance principle, we can have the following equation:
where d1 is the duty ratio of switch S1, d2 is the duty ratio of diode D1, and (1 − d1 − d2)Ts is the dead time. From (2.3), we have the following input‐to‐output voltage transfer ratio under DCM operation: