Step-down (Buck) Converter

13.3 Step-down (Buck) Converter

E – 13.3.1 Basic Converter

The step-down dc–dc converter, commonly known as a buck

(a)

converter, is shown in Fig. 13.4a. It consists of dc input voltage source V S , controlled switch S, diode D, filter inductor L,

v O filter capacitor C, and load resistance R. Typical waveforms in the converter are shown in Fig. 13.4b under assumption

V that the inductor current is always positive. The state of the

converter in which the inductor current is never zero for any period of time is called the continuous conduction mode (CCM). It can be seen from the circuit that when the switch S

is commanded to the on state, the diode D is reverse biased. i O

When the switch S is off, the diode conducts to support an uninterrupted current in the inductor.

The relationship among the input voltage, output voltage, and the switch duty ratio D can be derived, for instance, from the inductor voltage v L waveform (see Fig. 13.4b).

According to Faraday’s law, the inductor volt–second product

0 DT

over a period of steady-state operation is zero. For the buck converter

(b)

FIGURE 13.2 DC chopper with RLE load: (a) circuit diagram and (b) waveforms.

(V S −V O )DT = −V O (1 − D)T (13.3) Hence, the dc voltage transfer function, defined as the ratio of

D the output voltage to the input voltage, is

=D (13.4)

Load

It can be seen from Eq. (13.4) that the output voltage is always smaller than the input voltage.

The dc–dc converters can operate in two distinct modes FIGURE 13.3 The dc step-up chopper.

with respect to the inductor current i L . Figure 13.4b depicts the CCM in which the inductor current is always greater than zero. When the average value of the input current is low (high R) and/or the switching frequency f is low, the con-

The dc choppers can also provide peak output voltages verter may enter the discontinuous conduction mode (DCM). higher than the input voltage. Such a step-up configuration is In the DCM, the inductor current is zero during a portion presented in Fig. 13.3. It consists of dc input source V S , induc- of the switching period. The CCM is preferred for high effi- tor L connected in series with the source, switch S connecting ciency and good utilization of semiconductor switches and the inductor to ground, and a series combination of diode D passive components. The DCM may be used in applications and load. If the switch operates with a duty ratio D, the output with special control requirements, since the dynamic order of voltage is a series of pulses of duration (1 −D)T and amplitude the converter is reduced (the energy stored in the inductor is

V S /(1 − D). Neglecting losses, the average value of the output zero at the beginning and at the end of each switching period). voltage is V S . To obtain an average value of the output voltage It is uncommon to mix these two operating modes because of greater than V S , a capacitor must be connected in parallel with different control algorithms. For the buck converter, the value

252 D. Czarkowski S

Almost all of this ac component flows through the filter capac- itor as a current i . Current i causes a small voltage ripple

+v L –

across the dc output voltage V

O . To limit the peak-to-peak

C value of the ripple voltage below certain value V r , the filter V S

capacitance C must be greater than

8V r Lf 2 At D = 0.5, V r /V O = 1%, L = 25 µH, and f = 100 kHz,

(a)

the minimum capacitance is C min = 25 µF. Equations (13.5) and (13.6) are the key design equations for the buck converter. The input and output dc voltages (hence,

v L the duty ratio D), and the range of load resistance R are usually determined by preliminary specifications. The designer needs

V S –V O to determine values of passive components L and C, and of the switching frequency f. The value of the filter inductor L is

–V

calculated from the CCM/DCM condition using Eq. (13.5). The value of the filter capacitor C is obtained from the voltage ripple condition Eq. (13.6). For the compactness and

i L low conduction losses of a converter, it is desirable to use small passive components. Equations (13.5) and (13.6) show that it can be accomplished by using a high switching frequency f. The switching frequency is limited, however, by the type of semi- conductor switches used and by switching losses. It should

be also noted that values of L and C may be altered by effects of parasitic components in the converter, especially

i C by the equivalent series resistance of the capacitor. The issue of parasitic components in dc–dc converters is discussed in

Section 13.7.

13.3.2 Transformer Versions of Buck Converter

i S In many dc power supplies, a galvanic isolation between the

dc or ac input and the dc output is required for safety and reliability. An economical mean of achieving such an isola- tion is to employ a transformer version of a dc–dc converter. High-frequency transformers are of a small size and weight and

0 DT

2T t

provide high efficiency. Their turns ratio can be used to addi-

tionally adjust the output voltage level. Among buck-derived dc–dc converters, the most popular are: forward converter,

(b)

FIGURE 13.4 Buck converter: (a) circuit diagram and (b) waveforms. push–pull converter, half-bridge converter, and full-bridge converter.

of the filter inductance that determines the boundary between

A. Forward Converter

CCM and DCM is given by The circuit diagram of a forward converter is depicted in Fig. 13.5. When the switch S is on, diode D 1 conducts and diode

D 2 is off. The energy is transferred from the input, through

2f the transformer, to the output filter. When the switch is off, the state of diodes D 1 and D 2 is reversed. The dc voltage transfer

For typical values of D

function of the forward converter is

boundary is L b = 25 µH. For L > L b , the converter operates

in the CCM.

The filter inductor current i L in the CCM consists of a dc

component I O with a superimposed triangular ac component. where n =N 1 /N 2 .

13 DC–DC Converters 253 S

S /2

FIGURE 13.5 Forward converter.

V S /2

In the forward converter, the energy-transfer current flows FIGURE 13.7 Half-bridge converter. through the transformer in one direction. Hence, an additional

winding with diode D 3 is needed to bring the magnetizing

current of the transformer to zero. This prevents transformer The filter capacitor can be obtained from

saturation. The turns ratio N 1 /N 3 should be selected in such

a way that the magnetizing current decreases to zero during a

C min − 2D)V = 2 (13.10) 32V r Lf

fraction of the time interval when the switch is off.

Equations (13.5) and (13.6) can be used to design the filter components. The forward converter is very popular for low

C. Half-bridge Converter

power applications. For medium power levels, converters with bidirectional transformer excitation (push–pull, half-bridge, Figure 13.7 shows the dc–dc half-bridge converter. The opera- and full-bridge) are preferred due to better utilization of tion of the PWM half-bridge converter is similar to that of the magnetic components.

push–pull converter. In comparison to the push–pull converter, the primary of the transformer is simplified at the expense of two voltage-sharing input capacitors. The half-bridge con-

B. Push–Pull Converter

verter dc voltage transfer function is

The PWM dc–dc push–pull converter is shown in Fig. 13.6. The switches S 1 and S 2 operate shifted in phase by T/2 with the

(13.11) same duty ratio D. The duty ratio must be smaller than 0.5.

When switch S 1 is on, diode D 1 conducts and diode D 2 is

off. Diode states are reversed when switch S 2 is on. When both where D ≤ 0.5. Equations (13.9) and (13.10) apply to the filter controllable switches are off, the diodes are on and share equally components. the filter inductor current. The dc voltage transfer function of the push–pull converter is

D. Full-bridge Converter

2D Comparing the PWM dc–dc full-bridge converter of Fig. 13.8

to the half-bridge converter, it can be seen that the input capacitors have been replaced by two controllable switches.

where n =N 1 /N 2 . The boundary value of the filter inductor is The controllable switches are operated in pairs. When S 1 and S 4 are on, voltage V S is applied to the primary of the trans-

(1 − 2D)R

(13.9) former and diode D 1 conducts, With S 2 and S 3 on, there is 4f voltage −V S across the primary transformer and diode D 2

FIGURE 13.6 Push–pull converter. FIGURE 13.8 Full-bridge converter.

254 D. Czarkowski is on. With all controllable switches off, both diodes conduct,

D I O similarly as in the push–pull and half-bridge converters. The

dc voltage transfer function of the full-bridge converter is

– where D ≤ 0.5. Values of filter components can be obtained

(a)

from Eqs. (13.9) and (13.10). It should be stressed that the full-bridge topology is a very

versatile one. With different control algorithms, it is very pop- v L ular in dc–ac conversion (square-wave and PWM single-phase

inverters). It is also used in four-quadrant dc drives.

V S –V O