For the purpose of designing an intrinsic safety Flyback converter with minimal output voltage ripple based on a specified output current, this paper first classified the energy transmission modes of the system into three sorts, namely, the Complete Inductor Supply ModeCCM (CISMCCM), the Incomplete Inductor Supply ModeCCM (IISMCCM) and the Incomplete Inductor Supply ModeDCM (IISMDCM). Then, the critical secondary selfinductance assorting the three modes are deduced and expressions of the output voltage ripples (OVR) are presented. For a Flyback converter with constant loads and switching frequency, it is shown that the output voltage ripple in the CISMCCM is the smallest and that it has no relationship with the secondary selfinductance. Otherwise, the OVR of the other two modes are bigger than the previously mentioned one. It is concluded that the critical inductance between the CISMCCM and the IISMCCM is the minimal secondary selfinductance to ensure the smallest output voltage ripple. At last, a design method to guarantee the minimum OVR within the scales of the input voltage and load are analyzed, and the minimum secondary selfinductance is proposed to minimize the OVR. Simulations and experiments are given to verify the results.
I. INTRODUCTION
DCDC converters have been widely applied in industrial circles
[1]
. In some special cases, such as coal mines, underground and chemical engineering, the specific requirements of antiexplosive and antispark should be considered when designing a converter. For these reasons, much attention has been paid in the research to intrinsic safety converters.
Intrinsic safety is defined as a protection technique based on the restriction of electrical energy to a level that is too low to ignite an explosive atmosphere
[2]
. Since the stored energy varies directly with the reactive component values at specific output voltages, the key points for designing an appropriate intrinsic safety system are making use of the minimum inductors and capacitors under conditions that satisfy the requirements of the output voltages and their ripples
[3]
. Although, increasing the switching frequency could minimize the size and weight of the electric components, it would lead to some drawbacks at very high switching speeds, such as increasing of the switching losses, switching noise and so on. As a result, researchers focus on analyzing the operating modes and output voltage ripples as well as the relationship between the circuit parameters and trying to improve the intrinsic safety of the converter by choosing appropriate components. Thus, for a DCDC converter with specific output voltage (or current) and OVR, finding the minimum number of inductors and capacitors will be the most important task in a system design procedure.
Researchers are dedicated to the analysis the OVR of DCDC converters
[4]
. Several recent works had focused on the OVR of intrinsic safety nonisolation DCDC converters, such as Buck
[5]
, Boost
[3]
,
[6]
, BuckBoost
[7]
and SEPIC converters
[8]
. They suggest that as the inductance value changes, there will be new energy transfer modes (ETM) in the system, i.e., CISM and IISM. By analyzing the new operation modes, it is shown that the OVR closely relates to the inductance. Computing the amplitude of the OVR has played a very important role in the design of converters. Based on the analysis of the correlations between the ETM and the output voltage ripples, the performances of intrinsic safety converters are further improved by properly designing the parameters of the circuit components.
When compared to the BuckBoost converters and so on, the Flyback converter has the advantages of input/output isolation, low cost and a versatile conversion ratio, which are more appropriate for application under explosive conditions. However, the majority of the studies carried out on converters are concentrated with topology reconstructions and industrial applications, see
[9]

[14]
. They never focus on the design considerations of intrinsic safety Flyback converters. The mechanism of the ETM is neglected, which leads to inaccurate conclusions in terms of the operation modes for the system.
When analyzing the operation modes of Flyback converters, they are traditionally separated it into continuous conduction mode (CCM) and discontinuous conduction mode (DCM)
[1]
,
[15]
. It is generally deemed that the OVR in CCM operation converter is irrelevant to the magnetizing inductance and secondary selfinductance. Nevertheless, the theoretical analysis and experimental results manifest that this conclusion is only correct under certain conditions. However, in some cases, the OVR of a Flyback converter increases significantly while the magnetizing inductance decreases, which is inconsistent with the existing theoretical analysis results.
Traditionally, a Flyback converter is an isolated buckboost converter
[16]
,
[17]
. Taking the turns ratio into account as an extra degreeoffreedom, both the output voltage and the current are affected. This leads the different design methods to assure the minimum OVR from the basic buckboost converter, which needs to be thoroughly analyzed. The ETM of the converter only has a relationship with the secondary selfinductance. As a result, the connection between the output current and the secondary winding should be confirmed by mathematical calculations. Furthermore, the optimal parameters of the circuit components will be obtained.
For the purpose of classifying the ETM of the object, the energy transfer process and the OVR in Flyback converters are analyzed in depth so as to design an intrinsic safety system. The relationship between the ETM, the OVR and the component parameters are deduced, and the minimum secondary selfinductance to guarantee the minimum OVR is obtained. These are of great use for transformer and converter miniaturizations.
This paper is organized as follows. In the next Section, the ETM of the intrinsic safety Flyback converter is analyzed. The critical secondary selfinductances between CCM and DCM, as well as the CISMCCM and IISMCCM are derived in Section III. Section IV provides the OVR of the different operational modes belonging to the Flyback converter. The Maximum and Minimum OVRs (MOVRs) of the regulator are presented in Section V. After that, the design considerations for choosing proper circuit parameters are discussed in Section VI. Simulation and experimental results are given in Section VII. At last, some conclusions are given in Section VIII.
II. ETM OF FLYBACK CONVERTER
The topology of a Flyback converter is shown in
Fig. 1
(a). Assuming that the Flyback transformer has a
k
=
W
_{1}
W
_{2}
turns ratio and a leakage inductance
L_{e}
, let the magnetizing inductance and secondary selfinductance be
L_{M}
and
L_{s}
, respectively. Then, the following equations will be obtained based on the electrical model of the transformer
[18]
:
Operation modes of Flyback converter. (a) Flyback converter. (b) Switch S connects. (c) Flyback converter in CISMCCM. (d) Flyback converter in IISMCCM. (e) Flyback converter in IISMDCM.
where,
V_{in}
and
V_{inn}
denote the input voltage and secondary selfinductance voltage, respectively, and
The energy transfer mode is complicated when switch S turns off and the secondary winding connects to the circuit. Now the ETM is closely related to the quantity of the secondary selfinductance. There will be a critical inductance
L_{sC}
. When
L_{s}
>
L_{sC}
, the converter operates in CCM, and when
L_{s}
<
L_{sC}
, the converter operates in DCM. Diagrams of the different operation modes are shown in
Fig. 1
(b), (c), (d) and (e).
 A. ETM of DCM Flyback Converter
While the converter operates in DCM, the inductance currents and the output voltage waveforms are sketched in
Fig. 2
(c). The ETM may be separated into three subintervals as the switch turns off at time instant
t
_{1}
.
Output voltage, magnetic flux, primary inductor current of transformer, secondary inductor current of transformer and capacitor current waveforms of Flyback converter. (a) The CISMCCM mode. (b) The IISM CCM mode. (c) The IISMDCM mode.
First subinterval (
t
_{1}
~
t
_{2}
): Only the secondary winding inductor discharges energy in this stage.
Fig. 1
(c) shows the equivalent circuit. The inductance
L_{s}
supplies energy to the output capacitor and the load resistance, which leads to an increase of the capacitor voltage. This stage lasts until time instant
t
_{2}
. Meanwhile
i_{s}
declines to
I_{O}
.
Second subinterval (
t
_{2}
~
t
_{3}
): This stage begins when (
i_{s}
<
I_{O}
). In this case, both the secondary selfinductance and the capacitor provide energy for the load resistance. The equivalentcircuit is shown in
Fig. 1
(d).
Third subinterval (
t
_{3}
~
t
_{4}
): This time subinterval begins at the moment is reaches zero. Since the next period has not come, there is only the capacitor supplying energy to the load.
Fig. 1
(e) shows the equivalent schematic.
It is evident that for a Flyback converter performing in DCM, the ETM is divided into the three parts after the switch disconnects, i.e,: the inductance supplies energy, the inductance and capacitor supply energy at the same time, and the capacitor supplies energy.
 B. ETM of CCM Flyback Converter
In the case of CCM operation, according to a comparison between
I
_{smin}
(the minimum magnitude of the secondary winding current
i_{s}
) and
I_{O}
, the operation processes of the converter can be further divided into two kinds of energy transfer modes. When
I
_{smin}
>
I_{O}
, it is called CISMCCM; when
I
_{smin}
<
I_{O}
, it is called IISMCCM. The concrete analyses are as follows:
CISMCCM: In this case,
I
_{smin}
>
I_{O}
. The switch tube S is blocked, the secondary winding inductor supplies energy both to the load and to the capacitor.
Fig. 1
(c) shows the equivalent diagram. The waveforms of the secondside inductor current and the capacitor voltage are portrayed in
Fig. 2
(a).
IISMCCM: In this case,
I
_{smin}
<
I_{O}
. The waveforms, including the capacitor voltage, inductor currents and magnetic flux, are depicted in
Fig. 2
(b). The ETM of the converter can be separated into two parts. The first part is that the inductor completely charges the capacitor and load, the equivalent circuit of which is shown in
Fig. 1
(c). In this case,
i_{s}
>
I_{O}
, the capacitor voltage increases linearly. The second part is that the secondary winding inductor and the output capacitor simultaneously supply current for the load.
Fig. 1
(d) shows the equivalent scheme. At this moment,
i_{s}
<
I_{O}
, and the voltage of the capacitor starts to go down and will not stop until the next clock pulse signal comes.
It is clear that the critical condition of the Flyback converter operates between CISMCCM and IISMCCM is
I
_{smin}
=
I_{O}
.
III. DERIVATION OF THE CRITICAL INDUCTOR
The boundary between the CCM and DCM is specified by the critical inductance
L_{sC}
with regard to
L_{s}
. By considering the output current
I_{O}
and the secondary winding current
I_{s}
, the CCM mode is divided into two operational modes, namely, CISMCCM and IISMCCM. The borderline of these two operational modes is defined by the critical inductance
L_{sk}
.
 A. Critical inductance LsC
As for the Flyback converter, the following equations are always workable with the leakage inductance:
The critical inductance of CCM and DCM is as follows:
 B. Critical inductance Lsk
The minimum secondary inductor current can be written as:
It is clear that the critical condition in CISMCCM and IISMCCM is
I
_{smin}
=
I_{O}
, which leads to:
Since
d
≤1 , it is obtained that
L_{sk}
>
L_{sC}
.
According to the forgoing analysis, the operation mode boundary of the entire system is illustrated in
Table I
.
OPERATION MODE BOUNDARY OF THE CONVERTER
OPERATION MODE BOUNDARY OF THE CONVERTER
IV. OVR OF THE FLYBACK CONVERTER
The amplitudes of the OVRs of the Flyback converter in different operation modes will be calculated in detail.
 A. Calculation of the OVR in CISMCCM
Obviously, in the timesubinterval
T_{on}
, the output voltage is equal to the capacitor voltage. From
Fig. 2
(a), it can be seen that:
Then, the OVR can be expressed as:
In the time frame of
T_{on}
, the capacitor current is 
I_{O}
, and the following can be obtained:
Then, the following is obtained:
From Eq. (10), it can be concluded that the OVR of the converter has no connection with the secondary selfinductance in CISMCCM operation.
 B. Calculation of the OVR in IISMCCM
The OVR in this mode is determined by the voltage waveform in the time subinterval (
t
_{1}
,
t
_{2}
) when switch S is turned off, as can be seen in
Fig. 2
(b). Obviously, the following is obtained:
In addition, the equations of the secondary winding inductor current can be written as:
The application of Eq. (12) to (11), results in:
At the time instant
t
=
t
_{2}
,
i_{C}
(
t
_{2}
) reaches zero. As a result,
i_{s}
(
t
_{2}
)=
I_{O}
. Taking
t
_{2}
as the time benchmark leads to:
Consequently, the OVR in this time subinterval can be written as:
Substitution of the above equations into Eq. (15) yields:
From Eq. (16) the OVR is connected with the value of the secondary selfinductance
L_{s}
. The ripple has a relationship with the turns ratio
k
of the transformer. In order to simplify the analysis and with a view to the proportional relationship between
L_{s}
and
k
, only
L_{s}
is discussed in the following.
Calculating the first partial derivative of Eq. (16) yields:
Calculating the second partial derivative of Eq. (16) leads to:
From Eqs. (16), (17) and (18), it is know that when
L_{s}
<
L_{sk}
,
∂V_{PP}
/
∂L_{s}
< 0. Therefore, the voltage ripple
V_{PP}^{IISMCCM}
decreases with an increase of the inductance
L_{s}
in
L_{sC}
<
L_{s}
<
L_{sk}
. By putting Eqs. (17) and (4) into Eq. (16), the minimum and maximum of
V_{PP}^{IISMCCM}
are obtained as follows:
 C. Calculation of the OVR in IISMDCM
The maximum value of the primary winding inductor current is the current climbing value in the time interval
T_{on}
=
dT
, which is the duration when switch S connects. Because
i_{p}
(
t
_{0}
) is equal to zero at the beginning of every switching period, the following is obtained:
The following equation is true when the Flyback converter works in DCM:
Putting Eqs. (13), (14), (17) and (21) into Eq. (22), leads to:
Calculate the partial derivative with respect to
L_{s}
on Eq.(19) and let it be zero, the result is:
Comparing Eq. (4) with (20), it can be seen that:
Then, calculate the partial derivative with respect to
L_{s}
in Eq.(19), and the following is obtained:
Combine Eqs. (19), (20), (21) and (22). It can then be concluded that when
L_{s}
<
L_{sD}
,
V_{PP}^{IISMDCM}
decreases with an increase in the value of the inductance. However, when in IISMDCM, there is
L_{s}
<
L_{sC}
<
L_{sD}
. Combine Eq. (4) into (19), and consider Eq. (3) when
L_{s}
=
L_{sC}
. Then the minimum value of
V_{PP}^{IISMDCM}
can be obtained:
The above analysis demonstrates that the OVR of a Flyback converter operating in CISMCCM is the smallest, and that the amplitude is irrelevant to the inductance. Meanwhile, the OVRs in IISMCCM and IISMDCM are much bigger and increase with a decrease in the inductance. Therefore, the OVR decreases as the secondary selfinductance increases, and reaches its minimum value when
L_{s}
=
L_{sk}
. In other words, the critical secondary selfinductance
L_{sk}
is the minimum one which makes the OVR of the system become the smallest in the whole operation region. The variations of the OVR based on the secondary selfinductance are sketched in
Fig. 3
.
Variations of OVR based on secondary selfinductance.
V. MAXIMUM AND MINIMUM OUTPUT VOLTAGE RIPPLES
According to the former analysis, when
V_{in}
and load
R
decrease, the value of the OVR increases, and vice versa. In comparison to the variation of the critical inductance, the operation areas of the system can be separated into five regions. Generally speaking, under the conditions of
L
_{sC,max}
<
L
_{sK,min}
or
L
_{sC,max}
>
L
_{sK,min}
, the operation areas can be classified into two regions.
 A. LsC,max
In the case of
L
_{sC,max}
<
L
_{sK,min}
, the operation areas can be separated into five parts. The typical classifications are portrayed in
Fig. 4
.
Classifications of operation modes under L_{sC,max}<L_{sK,min} condition.
1) IISMDCM when L_{s} sK,min
: In the first operation area, the minimum value of MOVR is used to get under the
L_{s}
=
L
_{sC,min}
condition. Taking Eq. (23) into account yields:
2) If L_{sC,min}ssC,max
: In this area, as the system operates in IISMCCM. Calculating the minimum magnitude of MOVR by Eq. (16) yields:
The maximum magnitude of MOVR in this area is obtained as the system operates in IISCMDCM. Therefore, MOVR in this subpart is given by:
3) If L_{sC,max}ssK,min
: In this case, the system only operates in IISMCCM. Calculating the minimum and maximum magnitude of MOVR by Eq. (16) yields:
Considering Eqs. (19) and (31), the minimum value of MOVR leads to:
4) If L_{sK,min}ssK,max
: In this case, the system only operates in IISMCCM. Calculating the minimum and maximum magnitude of MOVR by Eq. (16) yields:
On the other hand, if the converter operates in CISMCCM, the minimum magnitude of MOVR is given by:
Taking Eqs. (19) and (34) into consideration, the maximum OVR will be shown as:
5) If L_{s}>L_{sK,max}
: In this case, the system only operates in CISMCCM. Calculating Eq. (10) leads to:
As stated above, the sequence of the MOVRs can be shown as:
 B. LsC,max>LsK,min
The other five classifications of the operation areas under the
L
_{sC,max}
>
L
_{sK,min}
condition are typically portrayed as in
Fig. 5
.
Different operation modes under L_{C,max}>L_{K,min} condition.
1) IISMDCM when L_{s}sC,min
: Considering Eq. (19), the minimum magnitude of
V
_{PP1,max}
in this operation area is shown as follows:
2) If L_{sC,min}ssK,min
: The system performs in either IISMDCM or IISMCCM. By calculating Eq. (16), the minimum magnitude of MOVR is shown as:
Meanwhile, the maximum magnitude of MOVR will be obtained by Eq. (23):
3) If L_{sK,min}ssC,max
: In this case, the Flyback converter performs in either CISMCCM or IISMCCM. By calculating Eq. (10), the minimum magnitude of MOVR is shown as:
Meanwhile, the maximum magnitude of MOVR will be obtained by Eq. (16):
Taking Eqs. (19) and (27) into consideration, the minimum magnitude of MOVR in this area is given by:
4) If L_{sC,max}ssK,max
: In this case, the system only operates in CISMCCM. The MOVR is obtained as follows:
5) If L_{s}>L_{sK,max}
: In this case, the system only operates in CISMCCM. The expression of MOVR is as follows:
Based on the former analyses, the sequence of the MOVRs can be shown as:
VI. DESIGN CONSIDERATIONS OF THE FLYBACK CONVERTER
As for voltage controlled Flyback converters, the magnitude of the OVR is closely related to the magnetizing inductance and loads at a specific switching period. In most cases, the smaller the OVR is, the better electrical characteristic becomes. According to the expression of the OVR in different operating modes, it is reversely related to
L_{M}
,
C
, and
f
. To ensure the minimum magnitude of the OVR in industrial applications, the switching period of the converter must be decreased. However, owing to the limitations of the manufacturing technology level, the switching frequency is finite. Meanwhile, along with the short switching periods are the high costs and switching losses. As a result, deductions of the minimum OVR with appropriate capacitor and magnetizing inductance are of great importance.
 A. Suggested Inductance in CCM Operation
According to Eqs. (37) and (46), the minimum OVR is ensured when the converter operates in CISMCCM, which means the inductance
L_{s}
should be designed larger than
L_{sK,max}
. Nevertheless, this is not suitable for industrial applications because the high duty cycle of the Flyback converter would leads to lower efficiency and so on. Therefore,
L_{s}
should be chosen so that it is lower than
L_{sK,max}
. It is clear that the minimum OVR was obtained when the condition
L_{s}
>
L_{sK,min}
was ensured:
If the condition
L_{s}
>
L_{sK,min}
is meet, according to Eq. (48), the MOVR is independent from the magnetizing inductance. As a result, the minimum secondary selfinductance
L_{sK,min}
is the right one to ensure the minimum MOVR in IISMCCM.
Calculating Eq. (48) leads to the minimum capacitance:
 B. Consideration of the Secondary SelfInductance in DCM
The OVR has a reverse relation to the load and secondary selfinductance, when the converter is in DCM operation, and independent of input voltage, see Eqs. (28) and (39). Taking Eqs. (38) and (47) into consideration, the OVR obtains its minimum magnitude as
L_{s}
=
L_{sC,min}
. The heavy load would make the peak switching current flow through the secondary winding diode increase remarkably. Therefore, the converter should not operate in DCM with heavy loads at a larger power. However, the condition
L_{s}
<
L_{sC,max}
with a large resistance
R
_{max}
should be meet if the converter needs to operate in DCM.
VII. SIMULATION AND EXPERIMENTAL RESULTS
To further validate these results, simulation and experimental tests were carried out. The parameters chosen for the intrinsic safety Flyback converter are as follows:
V_{in}
=20~30V,
V_{O}
=12V,
R
=15~30Ω,
f
=20
kH
_{z}
,
k
=2, and
V
_{PP,min}
=0.1V. In addition, the primary leakage inductance of the transformer is
L_{e}
=0.02
L_{M}
, that is
η
=0.98. Considering Eqs. (4), (6), (49) and (50),
L_{sC}
=75.8
μH
,
L_{sK,min}
=
L_{sK}
=137.7
μH
, and
C
=200
μF
are obtained.
Fig. 6
(a), (b) and (c) show the experimental results of the variations of the OVR versus secondary the selfinductance for specific values of
V_{in}
and
R
. Change
L_{s}
from 50
μH
to 150
μH
and take the pairs of
R
and
V_{in}
as [
R
=15Ω,
V_{in}
=20V], [
R
=15Ω,
V_{in}
=30V], [
R
=26Ω,
V_{in}
=20V], and [
R
=26Ω,
V_{in}
=30V], separately. The experimental results are depicted in
Fig. 6
(a). It is clear that the OVR in IISMCCM and IISMDCM decrease as the secondary selfinductance increases, while it is kept constant in CISMCCM.
Experimental results of variations of OVR. (a) versus V_{in} and R. (b) versus R. (c) versus V_{in}.
Since the load resistance is the smallest (
R
=15Ω), with the variation of
L_{s}
, the OVR versus
V_{in}
are illustrated in
Fig. 6
(b). It is clear that the OVR decreases with an increase of the
V_{in}
.
Choosing the smallest input voltage (
V_{in}
=20V), with the variation of
L_{s}
, the OVR versus
R
are illustrated in
Fig. 6
(c). It can be seen from the figure that the OVR decreases with an increase in the load.
According to the above results, a detailed example is shown in the following. The parameters chosen for the intrinsic safety Flyback converter are as follows:
V_{in}
=24V,
V_{O}
=12V,
I_{O}
=0.8A,
R
=15Ω,
f
=20
kH
_{z}
, and
k
=2,
C
=200
μF
. In addition, the primary leakage inductance of the transformer is
L_{e}
=0.02
L_{M}
, that is
η
=0.98. Considering Eqs. (4), (6) and (49),
L_{sC}
=367.4
μH
and
L
_{sK,min}
=LsK=727.6
μH
are obtained.
Take the magnetizing inductances of the transformers as
L_{M}
=986
μH
,
L_{M}
=727
μH
,
L_{M}
=555
μH
and
L_{M}
=329
μH
, separately. Then the secondary selfinductances are, in order,
L_{s}
=246.5
μH
,
L_{s}
=181.75
μH
,
L_{s}
=138.75
μH
and
L_{s}
=82.25
μH
, which correspond to CISMCCM, CriticalInductance State, IISMCCM and IISMDCM, respectively. In addition, the simulation waveforms of the output voltage, the transformer secondary winding and output currents are illustrated in
Fig. 7
(a), (b), (c) and (d), using the PSIM simulator.
Secondary inductor current and output voltage waveforms of Flyback converter in different modes. (a) CISMCCM. (b) Critical inductance state. (c) IISMCCM mode. (d) IISMDCM mode.
Fig. 7
(a) shows that when the system operates in CISMCCM and the switch disconnects,
i_{s}
is always greater than 0.8A. Therefore, the secondary wingding inductor charges the capacitor, and the capacitor voltage goes up, and does not go down until the next period. The descend range of the capacitor voltage is only decided by the capacitor. As a result, the OVR in the operation area and the inductance are totally unrelated, and the ripple voltage is smaller.
From
Fig. 7
(b), it is known that when
L_{s}
equals
L_{sK}
, the converter operates in the Critical Inductance State, which ensures the Minimum OVR.
From
Fig. 7
(c), it is known that when the system is in IISMCCM operation, the switch disconnects, and when
i_{s}
decreases to less than 0.8A, the capacitor voltage starts to decrease. Compared with the former, the descend range of the capacitor voltage has an increase and it is relevant to the capacitor and the inductance.
Fig. 7
(d) shows that when the converter is in IISMDCM, the switch blocks and
i_{s}
decreases to less than 0.8A. Just like the converter in IISMCCM operation, the capacitor voltage starts to decrease. The difference is that the capacitor voltage needs to experience two descend periods, i.e.,
i_{s}
<0.8A and
i_{s}
=0. It can be seen that the OVR is the best among all of the situations discussed above.
The voltage controlled Flyback converter circuit diagram, as shown in
Fig. 8
, is set up. The system components are as shown in the figure. It is worth noting that the sawtooth signal varies from 0 to 7V. The experimental waveforms are shown in
Fig. 9
(a), (b), (c) and (d). At the top of every diagram are the output voltages
u_{O}
(deep blue). The middle waveforms are the secondary windings current
i_{s}
(light blue) and the output current
I_{O}
(black). At the bottom are the duty cycles (green). Obviously, the system operation modes fall in different regions with varied secondary selfinductances resulting from a distinct Magnetizing inductance
L_{M}
. Owing to the parasitic parameters of the electric component, the experimental waveforms show small differences when compared with the theoretical analysis.
The circuit diagram of voltage controlled Flyback converter.
The experimental waveforms of Flyback converter in different operation modes. (a) CISMCCM. (b) Critical inductance state. (c)IISMCCM. (d)IISMDCM.
In sum, the Flyback converter operates in three different modes: CISMCCM, IISMCCM and IISMDCM. Meanwhile, the OVR in the CISMCCM is the smallest among the three operation modes.
L_{sK}
is the minimum secondary selfinductance that ensures the smallest OVR.
VIII. CONCLUSIONS
1) The paper divided the operation modes of an intrinsic safety Flyback converter into three types, namely, CISMCCM, IISMCCM and IISMDCM. The expressions of the critical inductance among the three modes are
L_{sC}
= R(1
d
)
^{2}
/2
f
and
L_{sK}
=
R
(1
d
)
^{2}
/2
df
.
2) The critical secondary selfinductance
L_{sK}
is the minimum one that ensures that the OVR is smallest in the whole operation region, as well as the optimal parameter for the intrinsic safety Flyback converter.
3) After figuring out the OVRs in all kinds of operation modes and combining them with the critical inductances
L_{sC}
and
L_{sK}
, they have a guiding significance for the design of the intrinsic safety system.
4) The IISMDCM mode is not suitable for the intrinsic safety Flyback converter with a light resistance in high power, since the peak magnetizing current of the primary winding is
k
times the secondary selfinductance.
5) This research helps the smaller secondary selfinductance and capacitance to meet the performance indexes in a given working scope. Meanwhile, it is constructive in terms of the miniaturization and integration design of the converter. In particular, the proposed method helps in designing the Flyback converter to meet the intrinsic safety characteristics, which are suitable for dangerous situation applications.
BIO
Wei Hu was born in Ningxiang, China, in 1980. He received his B.S. and M.S. degrees in the College of Electrical and Information Engineering, Hunan University, Changsha, China, in 2003 and 2006, respectively. He is currently working toward his Ph.D. degree. Since 2006, he has been with Guangzhou University, Guangzhou, China, where he is presently an Experimentalist in the Lab Center. His current research interests include the modeling and nonlinear control of power converters, and stability analysis of DCDC converters.
Fangying Zhang was born in Hubei, China, in 1981. She received her B.S. degree in Electronics and Information Engineering from the Hubei University of Technology, Wuhan, China, in 2003, and her M.S. degree in Geodetic Survey from Wuhan University, Wuhan, China, in 2006. She is presently an Experimentalist in the Lab Center of Guangzhou University, Guangzhou, China. Her current research interests include the modeling and nonlinear control of power converters, and stability analysis of DCDC converters.
Yawu Xu was born in Hubei, China, in 1967. He received his B.S. and M.S. degrees, in 2003 and 2006, respectively. He is presently working toward his Ph.D. degree. His current research interests include the modeling and nonlinear control of power converters, and stability analysis of DCDC converters.
Xinbing Chen was born in Henan, China, in 1978. His current research interests include the modeling and nonlinear control of power converters, and stability analysis of DCDC converters.
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