DCM Control Method of Boost Converter
based on Conventional CCM Control
Le Hoai Nam, Koji Orikawa, Jun-ichi Itoh
Department of Electrical, Electronics and Information Engineering
Nagaoka University of Technology
Nagaoka, Japanlehoainam@stn.nagaokaut.ac.jp
Abstract— This paper proposes current control method
for DCM to achieve same control performance as CCM. The
proposed control loop is designed based on the conventional
current control loop in CCM. By using only one PIcontroller and introduction of two correction factors, theproposed control method can control both CCM and DCM
current exactly to design values. In this paper, the operationof the proposed control method is confirmed by simulationand experiment. The simulation results of the current
response in both CCM and DCM agree with design values.
In the experimental results, due to the delay in feedback,error 11.3% in rise time and error 2.5 point in overshootoccur. Furthermore, the voltage regulation experiment withthe proposed current controller as a inner control loop is
conducted. As load varies, the recovery time for the output
voltage regulation is about 20 ms and the overshoot –undershoot voltage is below 3%.

I. INTRODUCTION
The research in electric power conversion has grown
rapidly in recent years due to energy crisis. DC-DC
converters present in most power conversion systems ordevices such as: fuel cell systems in mobile devices [1],photovoltaic(PV) systems [2], lithium-ion battery inhybrid vehicles (HEVs) [3][4], smart power system forservers [5], e.t.c. Because the minimization of those DCDC converters not only increases the mobility of mobile
devices but also simplifies the layout for PV systems orbattery systems in HEVs, many studies have focused on
shrinking the DC-DC converter circuit as much as
possible. Besides, passive components such as inductors
and capacitors account for the majority of the volume of
DC-DC converters, so the miniaturization of thesepassive components leads to compact DC-DC converter
generation. One of methods to minimize these passive
components is to switch the circuit at high frequency [6].
However, switching at high frequency leads to theincrease of frequency-dependent losses such as switchingloss in MOSFET or recovery loss in diode [7]. The
increase of conversion loss accounts for larger cooling
sink, and this makes the minimization of DC-DC
converters further difficult. In order to eliminate theincrease of loss when switching at high frequency, theconcept of resonant converters has been proposed [8].
Some researchers have introduced DC-DC converters
operating at frequencies of hundreds of MHz, while
maintaining the power conversion efficiency high [9][10].
However, in those resonant converter, because switch's

iL

L
Vout

Vin

C

R

SW

Fig. 1. A unidirectional boost converter
DCM
Feedforward
Control
Voltagecontroller

vout*
vout

CCM
Current
controller

iL*
iL

d

SW

1
0
CarrierFig. 2. Conventional CCM/DCM control method.

duty is limited in narrow range, the problems such as theuncontrollability of output voltage or the overheat whenresonant converter operates in boot mode [11], aredifficult to be solved. This limits the practicalapplications for resonant converters. On the other hand,
the minimization of the inductor can be accomplished by
the utility of Discontinuous Current Mode (DCM).
Fig. 1 shows a unidirectional boost converter which is
generally applied in PV system to regulate the output
voltage while preventing the power from flowing backinto the input side. When the inductor is minimized, theripple of the input current becomes higher, and this leads
to the discontinuity of input current. This can beunderstood that only a small amount of energy can be
stored in a minimized inductor, so all stored energy ininductor will be released before a new switching period
begins. In order to design controller for DCM similar tothe conventional Continuous Current Mode (CCM),
many researches have been conducted [12][13][14], but a
specific method to accomplish this has not been discussed.
Furthermore, the inductor current alternates between
CCM and DCM depending on the variation of the load,
and this likely leads to the unstable operation of theconverter. Many CCM/DCM control methods have beenstudied in past years to deal with the nonlinearity in DCM,
such as Adaptive Tuning method [15], Bi-frequency
Pulse-Train Control technique [16], Peak Current Mode
Bifrequency Control Technique [17], Current-ModeSynthetic Control Technique [18], Switching-Frequency
Control [19], e.t.c [20][21][22]. However, those control
methods either lead to the complication of the control
system, or the increase in cost for the auxiliary circuit
such as the variable frequency pulse generator.
Fig. 2 shows a conventional control system which
composes of an Automatic Voltage Regulator (AVR) andtwo Automatic Current Regulators (ACR) [23]. Many
designers prefer to utilize PI controller for both AVR andACR because of its simple design. In conventional
inductor current PI control method, the PI parameters for
CCM can be designed simply based on the linear CCM
transfer function. On the other hand, due to the nonlinear
characteristic of the DCM transfer function, the current
control loop in DCM is designed based on the reducedorder model [12][23]. This leads to the feed forward
current control in DCM. As a result, the DCM current
response cannot be controlled as same as the CCM
current response. In this case, DCM current control iseffective in only critical conditions.
This paper proposes a control method in which only
one PI controller is necessary to regulate both CCM and
DCM. By introduction two correction factors into theconventional inner current control loop in CCM, thecurrent response of DCM is controlled exactly to that ofCCM. Besides, it is not necessary to detect the current
mode. In this paper, first, the principle of the proposed
CCM-DCM control method is described. Second, theintroduction of two correction factors DCM and KDCM aredescribed. Then, the transition between CCM and DCM
is explained. Finally, the operation of the boost converter
which the proposed control method is applied, isconfirmed by simulation and experiment.
II. PROPOSED CCM-DCM CONTROL SCHEME
A. Conventional inner current loop design in CCM
Fig. 3 shows typical boost converter configuration.
The average small signal modeling technique is used tomodel the boost converter for the inner current control
loop design [6]. In this chapter, the output voltage isassumed to be constant, because the response of theinductor current is much higher than that of the output
voltage in ACR design step.
Fig. 4 shows inductor current waveform in DCM,
where d and d’ denote the duty ratio of the first and thesecond interval respectively. Equation based on the
average model of the boost converter in CCM and DCM
is given by (1),di
L L  dVin  d Vin  Vout  ………………..………….(1)dt
where Vin is the input voltage, Vout is the output voltage,i L is the average inductor current during a switching
period Tsw, and L is the inductance. In case of CCM, therelationship between d and d’ is given by (2).
d  d   1 ……………………………………………....(2)Substituting (2) into (1), (3) is obtained.
di
L L  Vin  Vout  dVout …………………………….…(3)dtHere, the averaged control to inductor current transfer

D

iL

Vout

L

Vin
SW

Fig. 3. Typical boost converter configuration in ACR design

ipk
iL
0 iL

dTsw

d’Tsw
Tsw

Fig. 4. Inductor current waveform in DCM
d

iL*

PICCM
iL

1/VoutVin

Vout
Feedforward

Fig. 5. Conventional inner current loop in CCM
d[n]
iL*

PIDCM

d[n]

1/Voutd[n-1]

iL

Fig. 6. Proposed inner current loop in DCM

function in CCM is given by (4),i ( s) Vout
GCCM ( s)  L……………………………...(4)d ( s)
sL
Fig. 5 shows ACR-CCM designed based on (3) and (4).
The integral period Ti and proportional gain Kp of PICCM
controller are designed based on the second-orderstandard form (5),2ωn…………………...(5)2s 2  2ωn s  ωn
where ωn is the natural angular frequency, ζ is thedamping factor, and both of which are designed toachieve the desired inductor current response. The closed
loop transfer function of ACR-CCM is derived by (6).
Kp
1  sTi i ( s)LTi
H CCM  ACR ( s)  L………….….(6)Kp
Kp
iL * ( s )
2
s 
s
L
LTi
In order to make the design of PI parameters simple, alow pass filter whose role is to filter the commandcurrent iL * is necessary for matching (5) and (6).
However, a low pass filter is not essentially needed.
G2 nd orderdelay(s) d[n]iL*[n]

PICCM-ACR

1/VoutLimiterSW10~1iL[n-1]To Fig.9
KDCM[n]DCM[n]

Vout

SW2
1

Vin
Carrier0Fig. 7. Configuration of the proposed CCM/DCM current controller.

Using a low pass filter depends on designers. The PI
parameters are then obtained by matching (5) and (6).
K p  2 n L …………………………..………………(7)

Ti 

2
……………………………………………….(8)nB. Small signal modeling in DCM
In case of DCM, the relationship between d and d’ isgiven by (9).
d  d   1 ……………………………………………..(9)In order to derive the averaged control to inductor current
transfer function in DCM, it is necessary to represent thesecond interval d’ in Fig. 4 as a function of the firstinterval d. Based on [12] and the waveform shown in
Fig. 4, this can be done as follow
i pk
iL 
(d  d ) ……………………………………..(10)2where ipk is the inductor peak current during a switching
period Tsw. Neglect the voltage drop by the switch, thevoltage across the inductor during the first interval d canbe assumed as Vin. The inductor peak current can be
written asVi pk  in dTsw ………………………………..………..(11)L
Substituting (11) into (10) and solving the resulting
equation for d’ yields
2 LiL
d'
 d ……………………...………..…..…(12)dTswVin
Substituting (12) into (1), (13) is obtained.
di
2 LiL  Vin  Vout   dVout …………………….(13)L L 
dt dTsw  Vin 
In case of DCM, the averaged control to inductor
current transfer function in DCM cannot be derived
simply from (13) because of its nonlinearity compared to(3). Therefore, (13) is linearized at steady point, then the
averaged control to inductor current transfer function in
DCM can be derived by linearized equation (14)~i ( s) Vout
2
GDCM ( s)  ~L……..(14)Ld ( s)(Vout / Vin  1)Vouts2
2 LI LTsw~~
where iL is the small signal of inductor current, d is thesmall signal of duty, IL is the value of the inductor current
at steady point. Eq. (14) indicates that not only the gainof the DCM transfer function differs from that of theCCM transfer function, but also the control targetchanges from the full values i L and d in CCM into the~~small values iL and d in DCM. Therefore, in order toachieve the DCM current control by the conventional
CCM-ACR, both the control gain and the control targetof the PICCM controller needs to be modified. The
modification of control target and control gain isachieved by introducing two corrector factors DCM and
KDCM into conventional current control loop in CCM.
C. Proposed CCM/DCM current control loop
1) Derivation of the first correction factor DCM
The modification of the control target from CCM to
DCM is achieved by compensating the output of the
CCM feedforward part using the correction factor DCM
that given in (16) [22]. The procedure to calculate thiscorrection factor DCM is as follows.
When considering the control system in z-domain, the~control target of DCM d n is given by~
d [n]  d[n]  d[n  1] …………………......……….....(15)where d[n] is the output duty to control inductor current,d[n-1] is the value of the duty in one sampling period
before. Eq. (15) indicates that, the output duty is the sum
between the value of the duty in one sampling period
before and the difference duty controlled by the PI
controller in DCM.
Fig. 6 shows the proposed DCM current control loop.
The objective to change Fig. 5 into Fig. 6, is achieved bymultiplying the output of the CCM feedforward part withthe correction factor DCM.
Vout
 DCM [n] d [n  1] ……………….……...…(16)Vout  Vin
2) Derivation of the second correction factor KDCM
The modification of the control gain from CCM to
DCM is achieved by compensating the output of the
PICCM using the correction factor KDCM that given by (21).
The procedure to calculate this correction factor KDCM is
as follows.
The discretized control gains (17), (18) are obtained bydiscretizing (4) and (14) in sampling period Tsw. Note thatthe sampling period equals to the switching period.
V T
GCCM ( z )  out sw …………………………………..(17)LV
2 LI LTsw
GDCM ( z )  out…………........…..(18)
L (Vout / Vin  1)Vout
In order to change the control gain from |GCCM(z)| toTABLE IVALUES OF TWO CORRECTION FACTOR IN CCM AND DCM
Current Mode
CCM
DCM
1
αDCM
Voutd[n-1]/(Vout-Vin)
KDCM
1(Vout-Vin)/(Vind[n-1])|GDCM(z)|, a correction factor KDCM is multiplied with theoutput of the PICCM controller. KDCM is given by (19).
G ( z)(Vout / Vin  1)VoutTsw………... (19)K DCM  CCM

GDCM ( z )2 LI LD. Transition between CCM and DCM
As mentioned above, the proposed control method canachieve both CCM and DCM control without detect theinductor current. The approach for this can be explained
as follow. From Table I , both correction factors DCM
and KDCM have to be set to 1 when the circuit operates in
CCM and be set to (16) , (21) respectively in DCM.
Fig. 8 shows two correction factors DCM and KDCM as
functions of duty d. Let consider the transition of DCM
first. As shown in Fig. 8, the transition point falls right
into the boundary between CCM and DCM, which means
DCM can trade between CCM value and DCM value
without detecting the circuit operating mode. This can be
explained as when the circuit operates in CCM , the duty
d follows as
V  Vind  out………………..………………………..(22)
Vout
Neglect the parasitic characteristic of switch and diode,(22) is always established whenever the circuit operates
in CCM. Substituting (22) into (16), it is understood that
DCM is set to 1 because of the steady operation of CCM.
On the other hand, as shown in Fig. 8, KDCM do notchange into 1 automatically when the circuit has alreadyswitched from DCM to CCM. However, because DCM
can change states automatically, the transition of KDCM is
accomplished by observing the value of DCM. To be
specific, whenever DCM becomes 1, KDCM is also set to 1,otherwise KDCM follows as (21). Because DCM can tradevalues between CCM and DCM without detecting current
mode, the transition of KDCM based on DCM state is also
accomplished without sensing which mode the circuit isoperating.
III. SIMULATION RESULTS
Simulation are carried out to verify the proposed
CCM/DCM control method.
Fig. 9 shows the simulation system. The switching
device in the upper arm SW1 is used when the boost

5
DCM

4.5

Correction factor value

The KDCM in (19) is simplified by using the equation of IL
at steady state as below [12]. Note that (20) is obtaineddiby simply let the inductor current differential part L indt(13) be zero.
d 2 [n  1]TswVoutVin…….………...…. .(20)I L  iL [n  1] 
2(Vout  Vin ) L
Substituting (20) into (19), KDCM is also given by (21).
V  Vin1……………..………….(21)K DCM [n]  outVind [n  1]
Fig. 7 shows the proposed CCM-DCM current control
loop, which controls both CCM and DCM by using only
one PICCM and two correction factors DCM and KDCM.
Table I shows the values of two correction factors incase of CCM and DCM.

CCM

KDCM

4
3.5
3
2.5
2
1.5

Transition
point

1
0.5

αDCM

0
0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Duty
Fig. 8. Relationship between duty and correction factors at
steady point
iL

L

SW1
Vout

Vin
SW2

Vin

Periodic average

iL

Vout

Fig. 9. Boost converter for ACR Simulation and Experiment.
TABLE IISIMULATION AND EXPERIMENTAL PARAMETERS
Input voltage Vin
70 V
100 V
Output voltage Vout
56 W
Rated output power Pout
Boost chopper inductor L
360 mH
Switching frequency fsw
20 kHz
20 kHzSampling frequency fsamp
Damping factor ζ
0.7
ACR
Natural angular frequency ωn2500/3000/3500 rad/s
ACR

converter operates in CCM. When the DCM operation istested, the switch SW1 is always kept at off-state.
Table II lists the system parameters and ratings. In
order to avoid the appearance of the delay time infeedback, the sampling of the average inductor current isachieved by simply taking advantage of the periodic
average block in simulator.
Fig. 10 shows the simulation results of the step
response. Fig. 10(a) and Fig. 10(b) show the current
waveform of CCM and DCM respectively. Fig. 10(c)shows the step response of the average inductor current inboth CCM and DCM. It can be concluded from Fig. 10(c)that the DCM current response is the same as the CCM
current response. In order to verify the operation of the
proposed CCM-DCM control method in many cases, themeasurement of the overshoot and the rise time of thecurrent response are conducted while varying the natural

2

iL

1.0

1.5

Rise time [ms]Current [A]

2.0

0.0

-1.0
0

0.5

1.0

1.5
2.0
2.5
Time [ms]

3.0

3.5

CCM
DCM
Design Value

1

0.5

4.0

2000

(a) CCM current waveform.
2.4

4000

7

iL
1.6

0.8

CCM
DCM
Design Value

6

Overshoot[%]

Current [A]

2500
3000
3500
Natural angular frequency [rad/s](a) Rise time.

5
4

0.0
0

0.5

1.0

1.5

2.0
2.5
Time [ms]

3.0

3.5

2000

2500
3000
3500
4000
Natural angular frequency [rad/s](b) Overshoot.
Fig. 11. Rise time and overshoot of the current response
in simulation.

(b) DCM current waveform.
Command0.8

Current [A]Overshoot
0.6
CCM

0.4
Rise time

0.2
0

0.5

1.0

DCM

1.5
2.0
2.5
Time [ms]

3

4.0

3.0

3.5

4.0

(c) CCM and DCM average current response
Fig. 10. Simulation results of step response.

frequency of the PICCM controller.
Fig. 11 shows the overshoot and the rise time of thecurrent response in simulation while varying the natural
frequency of the PICCM controller. It is confirmed that therise time and the overshoot of both CCM and DCM
current are agreed with the design values.
IV. EXPERIMENTAL RESULTS
The experimental conditions are the same as those of
the simulation as shown in Table II. In experiment, theaverage inductor current is sampled by using a Low Pass
Filter (LPF) with cutoff frequency of 2 kHz. Note that theswitch SW1 is always kept at off-state in case of DCM.
Fig. 12 and Fig.13 show the experimental step
response of the inductor current response at ωn = 3000
rad/s and ωn = 3500 rad/s, respectively. Both the inductor
current and the average values of the inductor current in
CCM and DCM are demonstrated in same waveform.
There is a slight difference in the shape of the current
response between CCM and DCM. This difference can be
explained as follows. The state of SW1 is different
between CCM and DCM. As a result, the on-resistance in

MOSFET and the voltage drop by diode change the shapeof the current response.
Fig. 14 shows the overshoot and the rise time of thecurrent response in experiment while varying the natural
frequency of the PICCM controller. There are errors
between CCM/DCM current response and the design
values. In the rise time results, the maximum error is
11.3%, while it is 2.5 point in the overshoot results. It canbe seen from Fig. 13 that in both CCM response and
DCM response, the experimental results of the rise time
tend to become smaller than the design values, while theexperimental results of the overshoot tend to become
higher than design values. This error tendency can be
explained as follows. When a LPF is used to obtain the
average values of any signal, the time constant in LPF
becomes the delay time between the input and output of
LPF. This delay time increases the total delay time in the
feedback of the controller. As a result, the rise time of thesystem response becomes shorter, while the overshootbecomes higher than the design values. Next step is toconfirm the validity of the proposed CCM/DCM current
controller in the output voltage regulation system.
Fig. 15 shows the boost converter whose the output
voltage needs to be regulated for proper operation . Notethat the upper switch is changed into a diode in order to
let the circuit operate in DCM at light load. This also
prevents the current flowing back into the source, which
damages the source in such PV systems. Besides, the PI
parameters in AVR are as follows
K p  2 nC ……………………………...………….(23)

Ti 

2

n

………………………………………..…….(24)

Table III lists the system parameters and ratings in1 (A/div)

1 (A/div)

0

0
Iin

Iin*

Iin

Iin*

0.2 (A/div)0.2 (A/div)

Iin_average

Iin_average
400 (us/div)

400 (us/div)00(a) CCM current waveform and average current response.

(a) CCM current waveform and average current response.

1 (A/div)

1 (A/div)

0

0
Iin

Iin*

Iin

Iin*

0.2 (A/div)
Iin_average

0.2 (A/div)
Iin_average

400 (us/div)

400 (us/div)00(b) DCM current waveform and average current response.
Fig. 12. Experimental results of step response(ωn = 3000 rad/s )(b) DCM current waveform and average current response.
Fig. 13. Experimental results of step response(ωn = 3500 rad/s )Rise time [ms]2

Error：11.3%

1.5

CCM
DCM
Design Value

1

0.5
2000

2500
3000
3500
Natural angular frequency [rad/s](a) Rise time.

4000

7

Overshoot[%]

AVR experiment. Note that the natural angular frequency
in AVR should be designed smaller at least 10 times thanthat of ACR in order to achieve the stable operation of
the control system.
Fig. 16 shows the experiment results of load transient
response between CCM (heavy load) and DCM(lightload). Fig. 16(a) shows the output voltage response andthe input current response when load varies from 40% in
DCM to 100% in CCM. The recovery time for the output
voltage regulation is about 20 ms and the undershootvoltage is 2 V, which is below 3% of the output voltage.
Fig. 16(b) shows the output voltage response and the
input current response when load varies from 100% in
CCM to 40% in DCM. The recovery time for the output
voltage regulation is about 20 ms and the overshootvoltage is 2 V, which is below 3% of the output voltage.
There are two things needs to be noted in Fig. 16. First,
when load varies the input voltage also slightly changes.
In the experiment, a three-phase diode bridge rectifier andan input side smoothing capacitor are applied as thevoltage source, so when the load varies, the voltage dropby the diode bridge and the smoothing capacitor alsochanges. This results in the variation of the input voltage
when the load varies. Second, the input current quite
oscillates not only in DCM but also in CCM. This is
explained that, the accuracy of the average input current
sampling mainly depends on three factors: the ripple ofthe input current, the speed of the D/A converter, and thetime constant of LPF. According with the minimization

CCM
DCM
Design Value

6

Error: 2.5 point

5
4
3
2000

2500
3000
3500
4000
Natural angular frequency [rad/s](b) Overshoot.
Fig. 14. Rise time and overshoot of the current responsein experiment

of the boost chopper inductor, the ripple current becomes
higher. The average value of the input current needs to besampled in order to achieve the proper operation of ACR.
Therefore, a LPF is applied in order to obtain averagevalue of the input current. However, this LPF introduces
a considerable delay time into the feedback, while themismatch in each sampling point in the D/A converter
lead to the feedback into ACR is just a delayed value ofthe actual current. This results in the oscillation of the
input current. However, in both cases, the output voltage
is regulated at the command. On the other hand, in order
to avoid the oscillation of duty in CCM which mightcause the current mode determination inaccuracy, insteadof comparing with 1, DCM is compared with 0.9 todetermine the state of KDCM . This achieves theCCM/DCM current control without detecting the input
current or the parameters of the boost converter circuit.
Fig. 17 shows the experiment results of load transient
at light load. Fig. 17(a)(b) shows the output voltage
response and the input current response when load varies
from 20% in DCM to 40% in CCM and vice versa. The
recovery time for the output voltage regulation is about
15 ms and the overshoot voltage is least than 1 V, which
is below 2% of the output voltage. Both Fig. 16 and Fig.
17 confirm the validity of the proposed CCM/DCM
current control method.

iL
Vin

Vin

R

Vout

iL

LPF

Fig. 15. Boost converter for AVR Experiment.
TABLE III
EXPERIMENTAL PARAMETERS
Input voltage Vin
40 V
Output voltage Vout
70 V
Rated output power Pout
49 W
Boost chopper inductor L
180 mH
Smoothing Capacitor C
680 mF
Switching frequency fsw
50 kHz
50 kHzSampling frequency fsamp
5 kHz
LPF cutoff frequency fcutoff
Damping factor ζ
0.7
ACR
Natural angular frequency ωn3000 rad/s
ACR
Damping factor ζ
0.7
AVR
Natural angular frequency ωn
300 rad/s
AVR

Vin

Vout

10 (V/div)Iin

1 (A/div)

Iin_average0

10 (ms/div)(a) From 40% load in DCM to 100% load in CCM.

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C
SW

V. CONCLUSION
In this paper, a control method for both CCM and
DCM was proposed. In the proposed method, the controlof CCM and DCM current is achieved by using only one
PI controller and introduction of two correction factors.
Besides, the CCM/DCM current control can be achieved
without sensing the input current or any circuit
parameters. Therefore, the simplification of theCCM/DCM control system is possible. The validity ofthe proposed current control is confirmed by both
simulation and experiment.
Future works will be focused on designing theminimized inductor and evaluating the conversion
efficiency.

L

Vin

Vout

10 (V/div)Iin

1 (A/div)

Iin_average0
10 (ms/div)(b) From 100% load in CCM to 40% load in DCM.
Fig. 16. Experimental results of load transient response
from 40% load in DCM to 100% load in CCM and vice versa.
With the proposed current control method, the input current
smoothly alternates between CCM and DCM, so this ensures thestability of the output voltage regulation when load varies.

Vin

Vout

10 (V/div)Iin

1 (A/div)0

10 (ms/div)(a) From 20% load in DCM to 40% load in DCM.

Vin

1 (A/div)0

Vout

10 (V/div)Iin

10 (ms/div)(b) From 40% load in DCM to 20% load in DCM.
Fig. 17. Experimental results of load transient response
from 20% load in DCM to 40% load in DCM and vice versa.
With the proposed current control method, the input current in
DCM is controlled exactly to the conventional CCM, so thisensures the stability of the output voltage when load varies.
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