chap06.pdf

Converter Circuits

We have already analyzed the operation of a number of different types of converters: buck, boost,

buck–boost, , voltage-source inverter, etc. With these converters, a number of different functions can

be performed: step-down of voltage, step-up, inversion of polarity, and conversion of dc to ac or vice-

versa.

It is natural to ask, Where do these converters come from? What other converters occur, and

what other functions can be obtained? What are the basic relations between converters? In this chapter,

several different circuit manipulations are explored, which explain the origins of the basic converters.

Inversion of source and load transforms the buck converter into the boost converter. Cascade connection

of converters, and simplification of the resulting circuit, shows how the buck–boost and converters

are based on the buck and the boost converters. Differential connection of the load between the outputs

of two or more converters leads to a single-phase or polyphase inverter. A short list of some of the better

known converter circuits follows this discussion.

Transformer-isolated dc–dc converters are also covered in this chapter. Use of a transformer

allows isolation and multiple outputs to be obtained in a dc-dc converter, and can lead to better converter

optimization when a very large or very small conversion ratio is required. The transformer is modeled as

a magnetizing inductance in parallel with an ideal transformer; this allows the analysis techniques of the

previous chapters to be extended to cover converters containing transformers. A number of well-known

isolated converters, based on the buck, boost, buck–boost, single-ended primary inductance converter

(SEPIC), and are listed and discussed.

Finally, the evaluation, selection, and design of converters to meet given requirements are con-

sidered. Important performance-related attributes of transformer-isolated converters include: whether the

transformer reset process imposes excessive voltage stress on the transistors, whether the converter can

supply a high-current output without imposing excessive current stresses on the secondary-side compo-

nents, and whether the converter can be well-optimized to operate with a wide range of operating points,

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Converter Circuits

that is, with large tolerances in and Switch utilization is a simplified figure-of-merit that mea-

sures the ratio of the converter output power to the total transistor voltage and current stress. As the

switch utilization increases, the converter efficiency increases while its cost decreases. Isolated convert-

ers with large variations in operating point tend to utilize their power devices more poorly than noniso-

lated converters which function at a single operating point. Computer spreadsheets are a good tool for

optimization of power stage designs and for trade studies to select a converter topology for a given appli-

cation.

6.1

CIRCUIT MANIPULATIONS

The buck converter (Fig. 6.1) was developed in Chapter 1 using basic principles. The switch reduces the

voltage dc component, and the low-pass filter removes the switching harmonics. In the continuous con-

duction mode, the buck converter has a conversion ratio of M = D. The buck converter is the simplest and

most basic circuit, from which we will derive other converters.

6.1.1

Inversion of Source and Load

Let us consider first what happens when we interchange the power input and power output ports of a con-

verter. In the buck converter of Fig. 6.2(a), voltage is applied at port 1, and voltage appears at port

2. We know that

This equation can be derived using the principle of inductor volt-second balance, with the assumption

that the converter operates in the continuous conduction mode. Provided that the switch is realized such

that this assumption holds, then Eq. (6.1) is true regardless of the direction of power flow.

So let us interchange the power source and load, as in Fig. 6.2(b). The load, bypassed by the

capacitor, is connected to converter port 1, while the power source is connected to converter port 2.

Power now flows in the opposite direction through the converter. Equation (6.1) must still hold; by solv-

ing for the load voltage one obtains

So the load voltage is greater than the source voltage. Figure 6.2(b) is a boost converter, drawn back-

wards. Equation 6.2 nearly coincides with the familiar boost converter result,

except that

is replaced by D.

Since power flows in the opposite direction, the standard buck converter unidirectional switch

6.1 Circuit Manipulations

133

realization cannot be used with the circuit of Fig. 6.2(b). By following the discussion of Chapter 4, one

finds that the switch can be realized by connecting a transistor between the inductor and ground, and a

diode from the inductor to the load, as shown in Fig. 6.2(c). In consequence, the transistor duty cycle D

becomes the fraction of time which the single-pole double-throw (SPDT) switch of Fig. 6.2(b) spends in

position 2, rather than in position 1. So we should interchange D with its complement in Eq. (6.2), and

the conversion ratio of the converter of Fig. 6.2(c) is

Thus, the boost converter can be viewed as a buck converter having the source and load connections

exchanged, and in which the switch is realized in a manner that allows reversal of the direction of power

flow.

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Converter Circuits

6.1.2

Cascade Connection of Converters

Converters can also be connected in cascade, as illustrated in Fig. 6.3 [1,2]. Converter 1 has conversion

ratio

such that its output voltage is

This voltage is applied to the input of the second converter. Let us assume that converter 2 is driven with

the same duty cycle D applied to converter 1. If converter 2 has conversion ratio

then the output

voltage V is

Substitution of Eq. (6.4) into Eq. (6.5) yields

Hence, the conversion ratio M ( D ) of the composite converter is the product of the individual conversion

ratios and

Let us consider the case where converter 1 is a buck converter, and converter 2 is a boost con-

verter. The resulting circuit is illustrated in Fig. 6.4. The buck converter has conversion ratio

The boost converter has conversion ratio

So the composite conversion ratio is

6.1 Circuit Manipulations

135

The composite converter has a noninverting buck–boost conversion ratio. The voltage is reduced when

D < 0.5, and increased when D> 0.5.

The circuit of Fig. 6.4 can be simplified considerably. Note that inductors and along with

capacitor form a three-pole low-pass filter. The conversion ratio does not depend on the number of

poles present in the low-pass filter, and so the same steady-state output voltage should be obtained when

a simpler low-pass filter is used. In Fig. 6.5(a), capacitor is removed. Inductors and are now in

series, and can be combined into a single inductor as shown in Fig. 6.5(b). This converter, the noninvert-

ing buck–boost converter, continues to exhibit the conversion ratio given in Eq. (6.9).

The switches of the converter of Fig. 6.5(b) can also be simplified, leading to a negative output

voltage. When the switches are in position 1, the converter reduces to Fig. 6.6(a). The inductor is con-

nected to the input source

and energy is transferred from the source to the inductor. When the

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