chap03 - 3 Steady-State Equivalent Circuit Modeling Losses...

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3 Steady-State Equivalent Circuit Modeling , Losses , and Efficiency Let us now consider the basic functions performed by a switching converter, and attempt to represent these functions by a simple equivalent circuit. The designer of a converter power stage must calculate the network voltages and currents, and specify the power components accordingly. Losses and efficiency are of prime importance. The use of equivalent circuits is a physical and intuitive approach which allows the well-known techniques of circuit analysis to be employed. As noted in the previous chapter, it is desir- able to ignore the small but complicated switching ripple, and model only the important dc components of the waveforms. The dc transformer is used to model the ideal functions performed by a dc-dc converter [1–4]. This simple model correctly represents the relationships between the dc voltages and currents of the con- verter. The model can be refined by including losses, such as semiconductor forward voltage drops and on-resistances, inductor core and copper losses, etc. The resulting model can be directly solved, to find the voltages, currents, losses, and efficiency in the actual nonideal converter. 3.1 THE DC TRANSFORMER MODEL As illustrated in Fig. 3.1, any switching converter contains three ports: a power input, a power output, and a control input. The input power is processed as specified by the control input, and then is output to the load. Ideally, these functions are performed with 100% efficiency, and hence or,
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40 Steady-State Equivalent Circuit Modeling, Losses, and Efficiency These relationships are valid only under equilibrium (dc) conditions: during transients, the net stored energy in the converter inductors and capacitors may change, causing Eqs. (3.1) and (3.2) to be violated. In the previous chapter, we found that we could express the converter output voltage in an equa- tion of the form where M ( D ) is the equilibrium conversion ratio of the converter. For example, M ( D ) = D for the buck converter, and M ( D ) = 1/(1 – D ) for the boost converter. In general, for ideal PWM converters operating in the continuous conduction mode and containing an equal number of independent inductors and capac- itors, it can be shown that the equilibrium conversion ratio M is a function of the duty cycle D and is independent of load. Substitution of Eq. (3.3) into Eq. (3.2) yields Hence, the converter terminal currents are related by the same conversion ratio. Equations (3.3) and (3.4) suggest that the converter could be modeled using dependent sources, as in Fig. 3.2. An equivalent but more physically meaningful model (Fig. 3.3) can be obtained through the realization that Eqs. (3.1) to (3.4) coincide with the equations of an ideal transformer. In an ideal transformer, the input and output powers are equal, as stated in Eqs. (3.1) and (3.2). Also, the output volt- age is equal to the turns ratio times the input voltage. This is consistent with Eq. (3.3), with the turns ratio taken to be the equilibrium conversion ratio M ( D ) .
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chap03 - 3 Steady-State Equivalent Circuit Modeling Losses...

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