This paper presents a novel control strategy for passive output filter reduction using an active output filter. The proposed method achieves the dualfunction of regulating the output voltage ripple and output voltage variation during load transients. The novel control strategy allows traditional simple voltage controllers to be used, without requiring the expensive current sensors and complex controllers used in conventional approaches. The proposed method is verified with results from a 125W forward converter.
NOMENCLATURE

APArea product.

CAAOF capacitor [F].

COOutput capacitor [F].

CPPost regulator input capacitor [F].

dADuty ratio of AOF.

Small signal value ofdA.

DADC value ofdA.

ΔDA_OFFIdealDAvariation for forward SWOFF.

ΔDA_ONIdealDAvariation for forward SWON.

dFDuty ratio of forward converter.

Small signal value ofdF.

DFDC value ofdF.

fCBandwidth of feedback controller [Hz].

fCABandwidth of AOF controller [Hz].

fCFBandwidth of forward converter controller [Hz].

fCPBandwidth of post regulator controller [Hz].

fCrtCritical bandwidth [Hz].

FsASwitching frequency of AOF [Hz].

FsFSwitching frequency of forward converter [Hz].

FsPSwitching frequency of post regulator [Hz].

iACurrent from AOF [A].

Small signal value ofiA[A].

AverageiAduring switching period,TsA[A].

iCOCurrent intoCO[A].

iCACurrent intoCA[A].

iLFCurrent ofLF[A].

ILF_pkpkPeak to peak value of switching ripple ofiLF[A].

iOOutput current [A].

Small signal value ofiO[A].

IODC value ofiO[A].

IO_maxMaximumIO[A].

ΔIOIOvariation during a load transient [A].

iOFOutput current of separate model [A].

Small signal value ofiOF[A].

KCO_swOutput capacitor ratio for switching voltage ripple regulation.

KFF_DAAOF duty feedforward gain.

KAPArea product constant.

LAAOF inductor [H].

LFForward converter inductor [H].

LPPost regulator inductor [H].

nTransformer turn ratio.

PEftEffective power handled by AOF [W].

TsASwitching period of AOF [s].

TsFSwitching period of forward converter [s].

TvAClosed loop gain ofvA[s].

TvOClosed loop gain ofvO[s].

vAAOF capacitor voltage [V].

Small signal value ofvA[V].

VADC value ofvA[V].

VINDC value of input voltage [V].

vOOutput voltage [V].

Small signal value ofvO[V].

ΔVO_swOutput voltage switching ripple [V].

ΔVO_sw_maxOutput voltage regulation of switching ripple [V].

ΔVO_Tr_maxOutput voltage regulation of load transient [V].
I. INTRODUCTION
As power semiconductor technology matures, passive output filters (POF), such as LCfilters, accounts for a more significant part of the cost and volume of power converters. Therefore, reducing the POF is one of the most important issues in the design of power converters. However, this reduction is becoming increasingly difficult due to the demanding requirements of digital devices in terms of voltage regulations and efficiency
[1]

[3]
. Typically, voltage regulations are constraints on the output voltage ripple and on the output voltage fluctuations during load transients
[1]
,
[2]
. Highfrequency switching satisfies both of these regulations. However, the switching frequency is practically upperbounded due to a proportionally increasing power loss. Thus, a number of studies have been conducted to reduce the POF without highfrequency switching.
For voltage ripple regulation, a passive ripple filter (PRF), an active ripple filter (ARF), and an active output filter (AOF) have been introduced
[4]

[13]
. The PRF and the ARF show good performance with regard to reducing ripples. However, these methods are overly sensitive to parameter errors
[4]

[7]
, are ineffective owing to their dissipative schemes
[8]

[10]
, or require complex and expensive components
[11]

[13]
. In addition, they are not suitable for the voltage fluctuation regulation. For voltage fluctuation regulation during a load transient, enhancedcontrol methods and auxiliary converter methods are typical. Enhanced control methods, such as the V2 control method
[14]

[16]
, the sliding mode control method
[17]

[18]
, and the linearandnonlinear control method
[19]

[21]
, improve the load transient responses under identical hardware conditions. Nevertheless, the enhanced control methods have a limitation given the slewrates of their outputinductorcurrents. To overcome this slewrate limitation, auxiliary converter methods have been suggested
[22]

[25]
. Several approaches change the slewrate using a coupledinductor for the outputinductor
[22]

[23]
, while the AOF methods inject transient current directly into the output
[24]

[25]
. These methods are efficient because auxiliary converters handle only a small amount of power. As a result, the auxiliary converters can operate with highfrequency switching and small passive components. However, there are many problems with these devices, such as an expensive coupled inductor
[22]

[23]
and costly complex controller and current sensors
[24]
,
[25]
. In addition, these approaches are only for voltage fluctuation regulation. In brief, existing studies provide a singlefunction for one of the two voltage regulations. Unfortunately, single function methods are generally not sufficient for POF reduction. Although post regulators
[26]

[28]
have a dualfunction for both regulations, they show poor efficiency levels given their series structure.
The conventional AOFs
[11]
,
[24]
,
[25]
fundamentally share the same structure, indicating that this structure is able to operate for both functions. However, conventional studies have failed to achieve the dualfunction because they do not include a proper voltage control strategy or a stability analysis. Moreover, previous studies were not optimized for their own singlefunctions in spite of their costly current sensors and the complex control methods concealed in their digital controllers.
In this paper, a novel control strategy is proposed for a dualfunction AOF. The AOF has the potential for a wide bandwidth control loop given its highfrequency switching. To utilize this property, the main output voltage is controlled by the AOF rather than the main converter. As a result, the output voltage is tightly regulated naturally and a reduced output capacitor is sufficient for load transients. The main converter, on the other hand, controls the voltage of the AOF capacitor. Because there is no given regulation of the voltage, a wider voltage range is available and a small capacitor is sufficient. In addition, the output inductor of the main converter can be reduced because the inductance of the main output inductor is free from the switching voltage ripple due to the proposed method. The switching ripple current from the main converter is cancelled by the AOF and is absorbed into the AOF capacitor. To enhance the switching ripple current cancellation without a current control scheme, a duty feedforward control scheme is also proposed. Finally, it is demonstrated that the proposed dualfunction AOF achieves a truly reduced POF.
In Section II, the operation principle of the proposed control strategy is introduced. A small signal analysis and the controller design characteristics are described in Section III. In Section IV, the passive filter reduction process is analyzed and compared to the conventional methods, after which a design guideline for the AOF is described. Section V shows hardware verification results obtained through a 125W forward converter prototype. Finally, some conclusions are given in Section VI.
II. OPERATION PRINCIPLE
Fig. 1
shows the structure of the proposed system. The main converter is a forward converter and the AOF is a synchronous buck converter. This structure offers two benefits. First, because vA is not supplied externally, its voltage level is optimized for an efficient AOF
[25]
. Second, the switching voltage ripple is minimized because the current entering the output capacitor is continuous. In
Fig. 2
, the control strategies of the conventional AOFs and the proposed AOF are briefly described. The advantages and disadvantages are indicated in green and red, respectively. The conventional AOF for voltage ripple regulation
[11]

[13]
senses ripple current from the main converter and tracks the sensed current using a hysteresis controller, as shown in
Fig. 2
(a). The operation of the conventional AOF as a load transient assister
[24]
,
[25]
is described in
Fig. 2
(b). Under steady state conditions, vA is controlled by the hysteresis controller. In addition, during a load transient, the duty ratio is shown to be fully on/off by the load transient detector. With the proposed method, unlike conventional studies, the output voltage is controlled by the AOF while the voltage of the AOF capacitor is controlled by the main converter, as described in
Fig. 2
(c). Moreover, the proposed duty feedforward control scheme is utilized to effectively cancel the ripple current without the need for current sensors (see
Fig. 2
(d)). Detailed descriptions of these processes are given in Section IV.
Structure of the proposed system.
AOF control strategy and its advantages (green) and disadvantages (red) of, (a) the conventional AOF ripple filter, (b) the conventional AOF load transient assister, (c) the proposed method (w/o feedforward), (d) the proposed method (w/feedforward).
Fig. 3
shows the key waveforms of the proposed method.
Key waveforms of, (a) inductorcurrents under steady states, (b) currents into the output capacitor w/ and w/o the proposed method, (c) the output voltage, the AOF capacitor voltage, and the average inductorcurrents during a stepup (ΔI_{O}) load transient at t_{0}.
Under steady state conditions,
i_{A}
is controlled, and becomes a counter current of the switching ripple current from the forward converter, as shown in
Fig. 3
(a). As a result,
i_{CO}
follows the small switching ripple current of the AOF, as indicated in
Fig. 3
(b). Thus, a reduced
C_{O}
satisfies the requirement of Δ
V_{O_sw_max}
. In addition,
L_{F}
can be reduced because
I_{LF_pkpk}
does not affect
i_{CO}
. During a load transient event, the dynamic response is greatly improved because the output voltage is controlled by the AOF, which has a wide bandwidth controller according to its high switching frequency
[29]
.
Fig. 3
(c) shows the key waveforms during a stepup (Δ
I_{O}
) load transient at
t_{0}
. The output voltage,
v_{O}
, is tightly regulated, while the AOF voltage,
v_{A}
follows the slower dynamic response of the forward converter. As a result, the minimum
C_{O}
for load transients is also reduced. Finally, the minimum
C_{O}
for both voltage regulations is reduced. Although there are additional passive components,
C_{A}
and
L_{A}
, a small capacitor is sufficient for
C_{A}
due to the absence of tight voltage requirements on
v_{A}
. Moreover, the fast switching of the AOF enables a small
L_{A}
.
III. SMALL SIGNAL ANALYSIS OF THE AOF
 A. Small Signal Model
A small signal model of the AOF is derived in this section to guarantee the stability of the proposed method. An analysis is initially conducted of a separate unterminated model, as shown in
Fig. 4
, after which the results are combined for the sake of convenience, as shown in
Fig. 5
. The main parameters, including the equivalent series resistors (ESRs) are shown in
Fig. 4
. The transfer functions of the separated parts are arranged in
Table I
. Using the results of the partial analysis, a total small signal model of the power system is derived and shown in
Table II
.
Separate unterminated model for small signal analysis.
Structure of the openedloop small signal model.
TRANSFER FUNCTIONS OF THE SEPARATE UNTERMINATED MODEL
TRANSFER FUNCTIONS OF THE SEPARATE UNTERMINATED MODEL
TRANSFER FUNCTIONS OF THE COMBINED SYSTEM
TRANSFER FUNCTIONS OF THE COMBINED SYSTEM
 B. Controller Design
The corresponding closed loop gains of the proposed method are derived as follows:
The closedloop small signal diagrams are shown in
Fig. 6
.
H_{vO}
and
H_{vA}
are the voltage feedback controllers for
v_{O}
and
v_{A}
, and they determine the bandwidths of
T_{vO}
and
T_{vA}
, respectively. Unlike the conventional cases, the proposed control strategy shows unusual phenomena in the design of the controllers.
T
_{1}
shows a zero DC gain owing to the zero DC gain of
G_{vOdA}
. This phenomenon occurs due to the presence of a nonexternal voltage source. Fortunately, it disappears after the
v_{A}
control loop is closed. Therefore, only the highfrequency gain is considered in the
v_{O}
controller design. Finally,
T_{vO}
has an infinite DC gain and a wide bandwidth. During the
H_{vA}
design,
T
_{2}
shows two unnatural resonantpoints. Due to these resonances, there is no phase margin of
T
_{2}
. However, these resonant points are removed by the other parts of
T_{vA}
in Equ. (4). This procedure will be shown in detail in Section IV.
Diagram of the transfer function of the closedloopsystem with the proposed control strategy.
 C. Duty Feedforward
A traditional voltage feedback controller may not achieve switching ripple current cancellation due to the finite bandwidth of the feedback control loop. Thus, a duty feedforward control method is proposed. The proposed duty feedforward control achieves simultaneous ripple current cancellation with only one additional voltage sensing instance at the rectified point, as shown in
Fig. 7
. To cancel the ripple current of
i_{LF}
, the slew rate of <
i_{A}
> should be matched to the slew rate of
i_{LF}
, as follows.
where <
i_{A}
> refers to the average
i_{A}
during a switching period,
T_{sA}
. The slew rate of
i_{LF}
is shown below.
The variation of
d_{A}
to satisfy Equ. (5) during the forwardswitchon and switchoff times is derived as follows:
As a result,
i_{A}
is matched to the switching ripple current from the forward converter. This method is even valid when there are certain errors in the parameters, such as the transformer turn ratio, the input voltage, and the leakage inductor. In addition, the proposed feedforward scheme rarely affects the
H_{vO}
design because the feedforward scheme enhances the average model in the small signal analysis of the forward converter, as presented in Section III.
A
. Although the feedforward affects
v_{A}
, the voltage variation is attenuated as the gain of
T_{vA}
at
F_{sF}
. Finally, the proposed feedforward scheme does not affect the stability of the system.
Proposed system including the duty feed forward.
IV. CONVERTER DESIGN
As mentioned earlier, an AOF with highfrequency switching is possible because the power loss of an AOF is insignificant due to its low effective power as follow:
As a result, the power loss of the AOF is determined by
I_{LF_pkpk}
rather than by
I_{O}
. For example,
P_{Eft}
is only 5% of the rated power, under the condition of
I_{LF_pkpk}
=0.2
I_{O_max}
.
 A. Capacitor Reduction
The output voltage is determined by
i_{CO}
, as follows:
Through the cancellation of the switching ripple current, the switching voltage ripple is determined by the AOF as:
and the result should satisfy Δ
V_{O_sw}
≤Δ
V_{O_sw_max}
. From Equ. (14), the minimum output capacitance of the switching voltage ripple regulation,
C_{O_sw}
_{_min}
is determined as follows:
If the ESR of the output capacitor,
R_{CO}
is negligible, a comparison of the minimum output capacitances of the proposed system,
C_{O_sw_AOF}
_{_min}
and the conventional system,
C_{O_sw_SF}
_{_min}
proceeds as follows.
Fig. 8
shows an example of
K_{CO_sw}
versus the inductance ratio,
L_{A}
/
L_{F}
, and the frequency ratio,
F_{sA}
/
F_{sF}
, under the
D_{A}
=0.5 and
D_{F}
=0.25 conditions.
K_{CO_sw}
decreases dramatically when
F_{sA}
/
F_{sF}
increases even when
L_{A}
/
L_{F}
is 0.2.
Minimum output capacitance ratio.
According to
[29]
, the peak output voltage variation during a load transient is derived as follows.
where
f_{C}
is the bandwidth of the feedback controller and
f_{Crt}
is the critical bandwidth, which is determined as follows.
Thus, the minimum output capacitance,
C_{_Tr_AOF}
_{_min}
for a load transient when
f_{C}
<
f_{Crt}
is:
As is well known, the bandwidth of a feedback controller is proportional (1/10
^{th}
approximately) to the switching frequency. Therefore, the bandwidth of the proposed method is higher by as much as
F_{sA}
/
F_{sF}
when compared to the forward converter, and
C_{O_Tr_AOF}
_{_min}
is reduced.
Finally, the minimum output capacitance is determined with the following criterion:
The minimum AOF capacitance of the load transients,
C_{A_Tr}
_{_min}
is designed using the same equations for the
C_{O}
design, Eqs. (13)(21), while the maximum variation is set to ±20% rather than ±5%, as follows.
where Δ
V_{A_Tr}
_{_max}
= 0.2
V_{A}
.
Table III
shows the passive component results with a reference to the design margin.
PASSIVE COMPONENT INFORMATION
PASSIVE COMPONENT INFORMATION
 B. Inductor Reduction
First, the inductance of
L_{F}
is designed. The inductance of
L_{F}
for a conventional forward converter is greater than that of the other cases because the output capacitance is limited for practical reasons, such as a startup issue.
The startup issue is when an over current problem can occur for charging the output capacitor if its capacitance is large. Thus, this inductance is greater than the optimum value given for the voltage ripple. On the other hand,
L_{F}
in the proposed method is not affected by this issue. Therefore, its inductance can be reduced. The minimum inductance of the proposed method with the given specification,
L_{F}
is determined as follows:
In this paper, the inductance of
L_{F}
is designed for the peak value of
i_{LF}
to be less than 120% of
I_{O}
_{_max}
. In general, the core of an inductor is established using the following criterion
[30]
:
where
K_{AP}
is a constant value
[30]
, and the area product,
A_{P}
is a parameter which determines the core size. The minimum
A_{P}
 value of the output inductor
L_{F}
is reduced as shown below.
where:
An
A_{P}
comparison between the proposed method (
A_{P_AOF}
_{_min}
) and the postregulator method (
A_{P_PR}
_{_min}
), for additional inductors, is given below.
Fig. 9
shows the
A_{P}
values of the additional inductors,
L_{A}
and
L_{P}
, versus the switching frequency of the forward converter. The
A_{P}
value of
L_{A}
is less than 2% that of
L_{F}
, even in the worst case, while that of the
L_{P}
is 10~30% that of the main converter. The
A_{P}
result does not satisfy the ‘
I_{LF_pkpk}
<1.2
I_{O}
_{_max}
’ condition. The normalized total
A_{P}
value of the proposed method is shown in
Fig. 10
. The proposed method shows an
A_{P}
value which is reduced by half, even with the lower output inductance and lower switching frequency of the forward converter.
A_{P}ratio of additional inductors compared to L_{F} of, (a) the proposed method, (b) the post regulator method.
Total A_{P} of the proposed method.
To verify the analysis of the proposed method, a hardware prototype of a 125W forward converter with an AOF and a postregulator is built and tested. First, the passive parameters are determined following the criteria in Section III.
A
. The results are compared with a conventional singleforward converter (SF) and a forward converter with a postregulator (PR). Next, proper voltage controllers are designed based on the results in Section III.
B
. The target specifications are shown in
Table IV
.
PARAMETER VALUES OF THE CONVERTERS
PARAMETER VALUES OF THE CONVERTERS
 C. Controller Design
Fig. 11
shows the transfer functions
G_{vAdF}
and
G_{vOdA}
of the hardware. As mentioned in Section III,
G_{vOdA}
shows a zero DC gain due to the +20 dB/decade slope of the lowfrequency region. Thus, conventional voltage controllers with an integrator, such as a type3 compensator, cannot achieve an infinite DC gain for a zero steady state error. Fortunately, this problem will be corrected after the
v_{A}
control loop is closed. Thus, only the highfrequency characteristic is an issue. After the design of
H_{vO}
,
T
_{2}
is designed with a proper
H_{vA}
. Because
H_{vO}
was previously designed,
H_{vA}
is designed using the total
v_{A}
voltage loop,
T_{vA}
. Twopoletwozero with one integrator controllers are utilized for
H_{vO}
and
H_{vA}
. These results are shown in
Fig. 12
.
Bode plots of transfer functions of the proposed system (openedloop), (a) G_{vAdF}, (b) G_{vOdA}.
Bode plot of closedloopgains, (a) T_{vO}, (b) T_{vA}.
V. EXPERIMENTAL RESULTS
To verify the proposed method, a forward converter hardware prototype is built and tested. The parameters follow the results shown in Section IV. A typical forward converter and a forward converter with a postregulator are also built for comparison with the proposed method. The tests focus on three points: the voltage regulation, the volume, and the power efficiency.
Fig. 13
shows the key waveforms under the steady state with the proposed method. The output voltage ripple satisfies the switching voltage ripple regulation range, 50 mV. In addition,
Fig. 14
shows a 5 A stepup load transient response, which satisfies the voltage regulation, 250 mV. A comparison of the volumes between the proposed method and the conventional methods is briefly described in
Fig. 15
. The total volume of the inductors and capacitors of the proposed method is reduced by about 31.5% (20.9 ㎤) and by approximately 13.1% (8.7 ㎤) when compared to the conventional forward converter method and the postregulator method, respectively.
Fig. 16
shows the results of a power efficiency comparison. The efficiency of the proposed method is between those of the conventional forward converter method and the post regulator method. The proposed method shows only a 1% lower efficiency when compared to the conventional single forward converter case. The efficiency of the proposed method is 1~3% higher than that of the fast switching conventional single forward converter case and 2~8% higher than that of the postregulator case, which are conventional approaches for passive component reduction. As a result, the proposed method achieves a passive component reduction without significantly losing efficiency.
Key waveforms in a steady state.
Key waveforms during a stepup load transient.
Passive component volume comparison. (SF: a conventional single forward converter case, PR: a conventional postregulator case, AOF: the proposed method case).
Power efficiency comparion.
VI. CONCLUSION
In this paper, a novel POF reduction method is presented and analyzed. The proposed method reduces the POF while satisfying the output voltage regulations and demands for improved power efficiency. The proposed control strategy makes AOFs feasible for the voltage regulation of both the switching voltage ripple and voltage variations which arise during a load transient. A small signal analysis was done to ensure a stable and optimized system, and a design guideline was described. The volume of the POF is significantly reduced while the total efficiency is only slightly reduced. In addition, the results can be extended to other bucktype topologies such as buck converters and half/fullbridge converters, because operation algorithms and small signal models of these converters are practically the same. In addition, the proposed method can be extended to other PWMbasedconverters by a similar procedure.
BIO
Kyusik Choi received his B.S. and Ph.D. degrees in Electrical Engineering and Computer Science from Seoul National University, Seoul, Korea. His current research interests include multiple output converters, highefficiency under light load conditions, and active power filters. He is a Student Member of the IEEE and the Korean Institute of Power Electronics (KIPE).
BoHyung Cho received his B.S. and M.S. degrees from the California Institute of Technology, Pasadena, CA, USA; and his Ph.D. degree from Virginia Polytechnic Institute and State University (Virginia Tech), Blacksburg, VA, USA, all in Electrical Engineering. Prior to his research at Virginia Tech, he was a member of the Technical Staff with the Department of Power Conversion Electronics, TRW Defense and Space System Group, USA. From 1982 to 1995, he was a Professor in the Department of Electrical Engineering, Virginia Tech. In 1995, he joined the School of Electrical Engineering, Seoul National University, Seoul, Korea, where he is presently working as a Professor. His current research interests include power electronics, the modeling, analysis, and control of spacecraft power processing equipment, and distributed power systems. Dr. Cho is a member of Tau Beta Pi. He was a recipient of the 1989 Presidential Young Investigator Award from the National Science Foundation. He chaired the 2006 IEEE Power Electronics Specialists Conference.
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