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13 DC–DC Converters 247

–

(a)

(b)

0DTT t

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

(b) waveforms.

–

Load

FIGURE 13.3 The dc step-up chopper.

The dc choppers can also provide peak output voltages

higher than the input voltage. Such a step-up conﬁguration is

presented in Fig. 13.3. It consists of dc input source V

, induc-

tor L connected in series with the source, switch S connecting

the inductor to ground, and a series combination of diode D

and load. If the switch operates with a duty ratio D, the output

voltage is a series of pulses of duration (1−D)T and amplitude

/(1 −D). Neglecting losses, the average value of the output

voltage is V

. To obtain an average value of the output voltage

greater than V

, a capacitor must be connected in parallel with

the load. This results in a topology of a boost dc–dc converter

that is described in Section 13.4.

13.3 Step-down (Buck) Converter

13.3.1 Basic Converter

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

converter, is shown in Fig. 13.4a. It consists of dc input voltage

source V

, controlled switch S, diode D, ﬁlter inductor L,

ﬁlter capacitor C, and load resistance R. Typical waveforms

in the converter are shown in Fig. 13.4b under assumption

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.

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

waveform (see Fig. 13.4b).

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

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

converter

−V

)DT =−V

(1 −D)T (13.3)

Hence, the dc voltage transfer function, deﬁned as the ratio of

the output voltage to the input voltage, is

≡

= D (13.4)

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

with respect to the inductor current i

. 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-

verter may enter the discontinuous conduction mode (DCM).

In the DCM, the inductor current is zero during a portion

of the switching period. The CCM is preferred for high efﬁ-

ciency and good utilization of semiconductor switches and

passive components. The DCM may be used in applications

with special control requirements, since the dynamic order of

the converter is reduced (the energy stored in the inductor is

zero at the beginning and at the end of each switching period).

It is uncommon to mix these two operating modes because of

different control algorithms. For the buck converter, the value

248 D. Czarkowski

–V

–

(a)

–V

0DT T 2T

(b)

FIGURE 13.4 Buck converter: (a) circuit diagram and (b) waveforms.

of the ﬁlter inductance that determines the boundary between

CCM and DCM is given by

(1 −D)R

(13.5)

For typical values of D = 0.5, R = 10 , and f = 100 kHz, the

boundary is L

= 25 µH. For L > L

, the converter operates

in the CCM.

The ﬁlter inductor current i

in the CCM consists of a dc

component I

with a superimposed triangular ac component.

Almost all of this ac component ﬂows through the ﬁlter capac-

itor as a current i

. Current i

causes a small voltage ripple

across the dc output voltage V

. To limit the peak-to-peak

value of the ripple voltage below certain value V

, the ﬁlter

capacitance C must be greater than

min

(1 −D) V

(13.6)

At D = 0.5, V

= 1%, L = 25 µH, and f = 100 kHz,

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,

the duty ratio D), and the range of load resistance R are usually

determined by preliminary speciﬁcations. The designer needs

to determine values of passive components L and C, and of

the switching frequency f. The value of the ﬁlter inductor L is

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

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

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

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

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,

push–pull converter, half-bridge converter, and full-bridge

converter.

A. Forward Converter

The circuit diagram of a forward converter is depicted in

Fig. 13.5. When the switch S is on, diode D

conducts and

diode D

is off. The energy is transferred from the input,

through the transformer, to the output ﬁlter. When the switch

is off, the state of diodes D

and D

is reversed. The dc voltage

transfer function of the forward converter is

(13.7)

where n = N

13 DC–DC Converters 249

–

··

FIGURE 13.5 Forward converter.

In the forward converter, the energy-transfer current ﬂows

through the transformer in one direction. Hence, an additional

winding with diode D

is needed to bring the magnetizing

current of the transformer to zero. This prevents transformer

saturation. The turns ratio N

should be selected in such

a way that the magnetizing current decreases to zero during a

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

power applications. For medium power levels, converters with

bidirectional transformer excitation (push–pull, half-bridge,

and full-bridge) are preferred due to better utilization of

magnetic components.

B. Push–Pull Converter

The PWM dc–dc push–pull converter is shown in Fig. 13.6.

The switches S

and S

operate shifted in phase by T/2 with the

same duty ratio D. The duty ratio must be smaller than 0.5.

When switch S

is on, diode D

conducts and diode D

is off.

Diode states are reversed when switch S

is on. When both con-

trollable switches are off, the diodes are on and share equally

the ﬁlter inductor current. The dc voltage transfer function of

the push–pull converter is

(13.8)

where n = N

. The boundary value of the ﬁlter inductor is

(1 −2D)R

(13.9)

–

FIGURE 13.6 Push–pull converter.

–

··

FIGURE 13.7 Half-bridge converter.

The ﬁlter capacitor can be obtained from

min

(1 −2D)V

32V

(13.10)

C. Half-bridge Converter

Figure 13.7 shows the dc–dc half-bridge converter. The oper-

ation of the PWM half-bridge converter is similar to that

of the push–pull converter. In comparison to the push–

pull converter, the primary of the transformer is simpli-

ﬁed at the expense of two voltage-sharing input capacitors.

The half-bridge converter dc voltage transfer function is

≡

(13.11)

where D ≤ 0.5. Equations (13.9) and (13.10) apply to the ﬁlter

components.

D. Full-bridge Converter

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.

The controllable switches are operated in pairs. When S

and

are on, voltage V

is applied to the primary of the trans-

former and diode D

conducts, With S

and S

on, there is

voltage −V

across the primary transformer and diode D

–

··

FIGURE 13.8 Full-bridge converter.

250 D. Czarkowski

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

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

dc voltage transfer function of the full-bridge converter is

≡

(13.12)

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

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-

ular in dc–ac conversion (square-wave and PWM single-phase

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

13.4 Step-up (Boost) Converter

Figure 13.9a depicts a step-up or a PWM boost converter. It is

comprised of dc input voltage source V

, boost inductor L,

controlled switch S, diode D, ﬁlter capacitor C, and load resis-

tance R. The converter waveforms in the CCM are presented in

Fig. 13.9b. When the switch S is in the on state, the current in

the boost inductor increases linearly. The diode D is off at the

time. When the switch S is turned off, the energy stored in the

inductor is released through the diode to the input RC circuit.

Using the Faraday’s law for the boost inductor

DT = (V

−V

)(1 −D)T (13.13)

from which the dc voltage transfer function turns out to be

≡

1 −D

(13.14)

As the name of the converter suggests, the output voltage is

always greater than the input voltage.

The boost converter operates in the CCM for L > L

where

(1 −D)

(13.15)

For D = 0.5, R = 10 , and f = 100 kHz, the boundary value

of the inductance is L

= 6.25 µH.

As shown in Fig. 13.9b, the current supplied to the output

RC circuit is discontinuous. Thus, a larger ﬁlter capacitor is

required in comparison to that in the buck-derived converters

to limit the output voltage ripple. The ﬁlter capacitor must

provide the output dc current to the load when the diode D

(a)

–V

DT T 2T

(b)

–

–I

–

FIGURE 13.9 Boost converter: (a) circuit diagram and (b) waveforms.

is off. The minimum value of the ﬁlter capacitance that results

in the voltage ripple V

is given by

min

(13.16)

At D = 0.5, V

= 1%, R = 10 , and f = 100 kHz, the

minimum capacitance for the boost converter is C

min

= 50 µF.

The boost converter does not have a popular transformer

(isolated) version.

13 DC–DC Converters 251

13.5 Buck–Boost Converter

13.5.1 Basic Converter

A non-isolated (transformerless) topology of the buck–boost

converter is shown in Fig. 13.10a. The converter consists of

dc input voltage source V

, controlled switch S, inductor L,

diode D, ﬁlter capacitor C, and load resistance R. With the

switch on, the inductor current increases while the diode is

–

(a)

DT T 2T

(b)

–I

–

FIGURE 13.10 Buck–boost converter: (a) circuit diagram and (b)

waveforms.

maintained off. When the switch is turned off, the diode pro-

vides a path for the inductor current. Note the polarity of the

diode which results in its current being drawn from the output.

The buck–boost converter waveforms are depicted in

Fig. 13.10b. The condition of a zero volt–second product for

the inductor in steady state yields

DT =−V

(1 −D)T (13.17)

Hence, the dc voltage transfer function of the buck–boost

converter is

≡

=−

1 −D

(13.18)

The output voltage V

is negative with respect to the ground.

Its magnitude can be either greater or smaller (equal at D =

0.5) than the input voltage as the converter’s name implies.

The value of the inductor that determines the boundary

between the CCM and DCM is

(1 −D)

(13.19)

The structure of the output part of the converter is similar

to that of the boost converter (reversed polarities being the

only difference). Thus, the value of the ﬁlter capacitor can be

obtained from Eq. (13.16).

13.5.2 Flyback Converter

A PWM ﬂyback converter is a very practical isolated ver-

sion of the buck–boost converter. The circuit of the ﬂyback

converter is presented in Fig. 13.11a. The inductor of the

buck–boost converter has been replaced by a ﬂyback trans-

former. The input dc source V

and switch S are connected

in series with the primary transformer. The diode D and the

RC output circuit are connected in series with the secondary

of the ﬂyback transformer. Figure 13.11b shows the converter

with a simple ﬂyback transformer model. The model includes

a magnetizing inductance L

and an ideal transformer with

a turns ratio n = N

. The ﬂyback transformer leakage

inductances and losses are neglected in the model. It should

be noted that leakage inductances, although not important

from the principle of operation point of view, affect adversely

switch and diode transitions. Snubbers are usually required in

ﬂyback converters.

Refer to Fig. 13.11b for the converter operation. When the

switch S is on, the current in the magnetizing inductance

increases linearly. The diode D is off and there is no current

in the ideal transformer windings. When the switch is turned

off, the magnetizing inductance current is diverted into the

ideal transformer, the diode turns on, and the transformed

252 D. Czarkowski

–

(a)

–

(b)

FIGURE 13.11 Flyback converter: (a) circuit diagram and (b) circuit

with a transformer model showing the magnetizing inductance L

magnetizing inductance current is supplied to the RC load.

The dc voltage transfer function of the ﬂyback converter is

≡

n(1 −D)

(13.20)

It differs from the buck–boost converter voltage transfer

function by the turns ratio factor n. A positive sign has

been obtained by an appropriate coupling of the transformer

windings.

Unlike in transformer buck-derived converters, the mag-

netizing inductance L

of the ﬂyback transformer is an

important design parameter. The value of the magnetizing

inductance that determines the boundary between the CCM

and DCM is given by

(1 −D)

(13.21)

The value of the ﬁlter capacitance can be calculated using

Eq. (13.16).

13.6

Cuk Converter

The circuit of the

Cuk converter is shown in Fig. 13.12a.

It consists of dc input voltage source V

, input inductor L

controllable switch S, energy transfer capacitor C

, diode D,

ﬁlter inductor L

, ﬁlter capacitor C, and load resistance R.

(a)

+ v

–

(b)

+ I

–I

0 DT T 2T t

FIGURE 13.12

Cuk converter: (a) circuit diagram and (b) waveforms.

An important advantage of this topology is a continuous

current at both the input and the output of the converter.

Disadvantages of the

Cuk converter include a high number of

reactive components and high current stresses on the switch,

the diode, and the capacitor C

. Main waveforms in the con-

verter are presented in Fig. 13.12b. When the switch is on, the

diode is off and the capacitor C

is discharged by the inductor

current. With the switch in the off state, the diode conducts

currents of the inductors L

and L

whereas capacitor C

charged by the inductor L

current.

To obtain the dc voltage transfer function of the converter,

we shall use the principle that the average current through a

capacitor is zero for steady-state operation. Let us assume that

inductors L

and L

are large enough that their ripple current

can be neglected. Capacitor C

is in steady state if

DT = I

(1 −D)T (13.22)

13 DC–DC Converters 253

For a lossless converter

= V

=−V

= P

(13.23)

Combining these two equations, the dc voltage transfer

function of the

Cuk converter is

≡

=−

1 −D

(13.24)

This voltage transfer function is the same as that for the

buck–boost converter.

The boundaries between the CCM and DCM are deter-

mined by

(1 −D)R

2Df

(13.25)

for L

and

(1 −D)R

(13.26)

for L

The output part of the

Cuk converter is similar to that

of the buck converter. Hence, the expression for the ﬁlter

capacitor C is

min

(1 −D)V

(13.27)

The peak-to-peak ripple voltage in the capacitor C

can be

estimated as

(13.28)

A transformer (isolated) version of the

Cuk converter can

be obtained by splitting capacitor C

and inserting a high-

frequency transformer between the split capacitors.

13.7 Effects of Parasitics

The analysis of converters in Sections 13.2 through 13.6 has

been performed under ideal switch, diode, and passive com-

ponent assumptions. Non-idealities or parasitics of practical

devices and components may, however, greatly affect some

performance parameters of dc–dc converters. In this section,

effects of parasitics on output voltage ripple, efﬁciency, and

voltage transfer function of converters will be illustrated.

A more realistic model of a capacitor than just a

capacitance C, consists of a series connection of capacitance

C and resistance r

. The resistance r

is called an equiva-

lent series resistance (ESR) of the capacitor and is due to

losses in the dielectric and physical resistance of leads and

connections. Recall Eq. (13.6) which provided a value of the

ﬁlter capacitance in a buck converter that limits the peak-to-

peak output voltage ripple to V

. The equation was derived

under an assumption that the entire triangular ac component

of the inductor current ﬂows through a capacitance C.Itis,

however, closer to reality to maintain that this triangular com-

ponent ﬂows through a series connection of capacitance C and

resistance r

The peak-to-peak ripple voltage is independent of the

voltage across the ﬁlter capacitor and is determined only by

the ripple voltage of the ESR if the following condition is

satisﬁed,

C ≥ C

min

= max



1 −D

min

max



(13.29)

If condition (13.29) is satisﬁed, the peak-to-peak ripple voltage

of the buck and forward converters is

= r

i

Lmax

(1 −D

min

)

(13.30)

For push–pull, half-bridge, and full-bridge converters,

C ≥ C

min

= max



0.5 −D

min

max



(13.31)

where D

max

≤ 0.5. If condition (13.31) is met, the peak-to-

peak ripple voltage V

of these converters is given by

= r

i

Lmax

(0.5 −D

min

)

(13.32)

Waveforms of voltage across the ESR V

, voltage across

the capacitance V

, and total ripple voltage V

are depicted

in Fig. 13.13 for three values of the ﬁlter capacitances. For the

case of the top graph in Fig. 13.13, the peak-to-peak value

of V

is higher than the peak-to-peak value of V

because

C < C

min

. Middle and bottom graphs in Fig. 13.13 show the

waveforms for C = C

min

and C > C

min

, respectively. For both

these cases, the peak-to-peak voltages of V

and V

equal to

each other.

Note that when the resistance r

sets the ripple voltage V

the minimum value of inductance L is determined either by the

boundary between the CCM and DCM according to Eq. (13.5)

(buck and forward converters) or Eq. (13.9) (push–pull, half-

bridge, and full-bridge converters), or by the voltage ripple

condition (13.30) or (13.32).

In buck–boost and boost converters, the peak-to-peak

capacitor current I

Cpp

is equal to the peak-to-peak diode

current and is given by

Cpp

1 −D

(13.33)

254 D. Czarkowski

–0.08

0.2 0.4 0.6 0.8 10

0.04

0.08

–0.04

0.04

0.08

–0.04

–0.08

0.04

0.08

–0.04

–0.08

ripple voltage (V) ripple voltage (V)ripple voltage (V)

t/T

FIGURE 13.13 Voltage ripple waveforms V

, V

, and V

for a buck

converter at V

= 12 V, f = 100 kHz, L = 40 µH, r

= 0.05 , and

various values of C: C = 33 µF (top graph), C = C

min

= 65 µF (middle

graph), and C = 100 µF (bottom graph).

under condition that the inductor current ripple is much lower

than the average value of the inductor current. The peak-to-

peak voltage across the ESR is

= r

Cpp

1 −D

(13.34)

Assuming that the total ripple voltage V

is approximately

equal to the sum of the ripple voltages across the ESR and the

capacitance, the maximum value of the peak-to-peak ripple

voltage across the capacitance is

Cmax

≈ V

−V

(13.35)

Finally, by analogy to Eq. (13.16), when the ESR of the ﬁlter

capacitor is taken into account in the boost-type output ﬁlter,

the ﬁlter capacitance should be greater than

min

Cmax

(13.36)

Parasitic resistances, capacitances, and voltage sources affect

also an energy conversion efﬁciency of dc–dc converters.

The efﬁciency η is deﬁned as a ratio of output power to the

input power

η ≡

(13.37)

Efﬁciencies are usually speciﬁed in percent. Let us consider the

boot converter as an example. Under low ripple assumption,

the boost converter efﬁciency can be estimated as

η=

R(1−D)

(1+(V

)+fC

R)+r

+Dr

+(1−D)r

+D(1−D)r

(13.38)

where V

is the forward conduction voltage drop of the diode,

is the output capacitance of the switch, r

is the ESR of the

inductor, and r

is the forward on resistance of the diode.

The term fC

R in Eq. (13.38) represents switching losses in

the converter. Other terms account for conduction losses.

Losses in a dc–dc converter also contribute to a decrease in

the dc voltage transfer function. The non-ideal dc voltage

transfer function M

is a product of the ideal one and the

efﬁciency

= ηM

(13.39)

Sample graphs for the boost converter that corre-

spond to Eqs. (13.38) and (13.39) are presented in

Fig. 13.14.

13.8 Synchronous and Bidirectional

Converters

It can be observed in Eq. (13.38) that the forward voltage

of a diode V

contributes to a decrease in efﬁciency. This

contribution is especially signiﬁcant in low output voltage

power supplies, e.g. 3.3 V power supplies for microprocessors

or power supplies for portable telecommunication equipment.

Even with a Schottky diode, which has V

in the range of

0.4 V, the power loss in the diode can easily exceed 10% of

the total power delivered to the load. To reduce conduction

losses in the diode, a low on-resistance switch can be added

in parallel as shown in Fig. 13.15 for a buck converter. The

input switch and the switch parallel to the diode must be

13 DC–DC Converters 255

Efficiency (%)

Ideal

100

0.2 0.4 0.6 0.8 1.0

0 0.2 0.4 0.6 0.8 1.0

Non-ideal

, M

Ideal

Non-ideal

(a)

(b)

FIGURE 13.14 Effects of parasitics on characteristics of a boost con-

verter: (a) efﬁciency and (b) dc voltage transfer function.

turned on and off alternately. The arrangement of Fig. 13.15

is called a synchronous converter or a synchronous rectiﬁer.

Modern low-voltage MOSFETs have on resistances of only sev-

eral milliohms. Hence, a synchronous converter may exhibit

higher efﬁciency than a conventional one at output currents

as large as tens of amperes. The efﬁciency is increased at an

expense of more complicated driving circuitry for the switches.

In particular, a special can must be exercised to avoid hav-

ing both switches on at the same time as this would short

the input voltage source. Since power semiconductor devices

−

FIGURE 13.15 Synchronous buck converter.

−

FIGURE 13.16 Bidirectional ﬂyback converter.

usually have longer turn-off times than turn-on times, a dead

time (sometimes called a blanking time) must be introduced

in PWM driving signals.

The parallel combination of a controllable switch and a

diode is also used in converters which allow for a current

ﬂow in both directions: from the input source to the load

and from the load back to the input source. Such convert-

ers are called bidirectional power ﬂow or simply bidirectional

converters. As an example, a ﬂyback bidirectional converter

is shown in Fig. 13.16. It contains unipolar voltage and bidi-

rectional current switch–diode combinations at both primary

and secondary of the ﬂyback transformer. When the primary

switch and secondary diode operate, the current ﬂows from the

input source to the load. The converter current can also ﬂow

from the output to the input through the secondary switch

and primary diode. Bidirectional arrangements can be made

for buck and boost converters. A bidirectional buck converter

operates as a boost converter when the current ﬂow is from the

output to the input. A bidirectional boost converter operates

as a buck converter with a reversed current ﬂow. If for any rea-

son (for instance to avoid the DCM) the controllable switches

are driven at the same time, they must be driven alternately

with a sufﬁcient dead time to avoid a shot-through current.

13.9 Control Principles

A dc–dc converter must provide a regulated dc output

voltage under varying load and input voltage conditions.

256 D. Czarkowski

The converter component values are also changing with time,

temperature, pressure, etc. Hence, the control of the output

voltage should be performed in a closed-loop manner using

principles of negative feedback. Two most common closed-

loop control methods for PWM dc–dc converters, namely,

the voltage-mode control and the current-mode control, are

presented schematically in Fig. 13.17.

In the voltage-mode control scheme shown in Fig. 13.17a,

the converter output voltage is sensed and subtracted from

an external reference voltage in an error ampliﬁer. The error

ampliﬁer produces a control voltage that is compared to a

constant-amplitude sawtooth waveform. The comparator pro-

duces a PWM signal which is fed to drivers of controllable

switches in the dc–dc converter. The duty ratio of the PWM

signal depends on the value of the control voltage. The fre-

quency of the PWM signal is the same as the frequency

of the sawtooth waveform. An important advantage of the

voltage-mode control is its simple hardware implementation

and ﬂexibility.

Error

Amplifier

Comparator

And

Latch

dc-dc Converter

Voltage

reference

Voltage

reference

Control

voltage

Control

voltage

Switch or inductor current

Output voltage

Comparator

Sawtooth

waveform

PWM signal

(a)

(b)

Error

Amplifier

FIGURE 13.17 Main control schemes for dc–dc converters: (a) voltage-mode control and (b) current-mode control.

The error ampliﬁer in Fig. 13.17a reacts fast to changes in the

converter output voltage. Thus, the voltage-mode control pro-

vides good load regulation, that is, regulation against variations

in the load. Line regulation (regulation against variations in

the input voltage) is, however, delayed because changes in the

input voltage must ﬁrst manifest themselves in the converter

output before they can be corrected. To alleviate this problem,

the voltage-mode control scheme is sometimes augmented

by so-called voltage feedforward path. The feedforward path

affects directly the PWM duty ratio according to variations in

the input voltage. As will be explained below, the input volt-

age feedforward is an inherent feature of current-mode control

schemes.

The current-mode control scheme is presented in

Fig. 13.17b. An additional inner control loop feeds back

an inductor current signal. This current signal, converted

into its voltage analog, is compared to the control voltage.

This modiﬁcation of replacing the sawtooth wavefrom of the

voltage-mode control scheme by a converter current signal