A novel hysteresis PWM control strategy for synchronous buck converter is proposed. The proposed control strategy is based on amperesecond balance of the modulate capacitor, which not only offers faster transient response to meet the challenges of the power supply requirements of fast dynamic load changes, but also provides better stability and solves the compensation problem of error amplifier in the conversional voltage PWM control. Finally, the steadystate and dynamic operation of the control method is analyzed and verified by simulation and experimental results.
I. INTRODUCTION
Nowadays, DCDC switching converters have been increasingly used in a wide range of applications, such as LEDs, airspace industry, portable systems, and power factor correction
[1]

[6]
. The requirements of the transient response performance of the DCDC power switching converters are stringent. This performance is consistently expected to have a lower dynamic output voltage deviation and shorter settling time during load current transients. As one of the widely used converter topologies, buck converters have been investigated with different control strategies
[7]

[18]
. Voltage mode converter is a traditional PWM control buck converter that operates in continuous conduction mode (CCM), which requires a complicated compensation network to ensure stable operation challenged by complex poles in the loop gain transfer function
[7]
. This challenge not only increases the design difficulty of the control circuit, but also causes poor dynamic load performance. Many investigations have been carried out on this subject to avoid these difficulties. The current mode control is applied with voltage feedback to improve stability and dynamic performance
[8]
,
[9]
, which needs complex slope compensation and response speed limited by voltage loop controller. In
[10]

[12]
, timeoptimal digital and digital controllers are presented. These techniques significantly improve transient response, but suffer from complex implementation. In
[13]

[15]
, nonlinear slidingmode are presented to improve the dynamic response. However, the main drawback of sliding mode is variable frequency. Control strategies such as hysteresis control have received extensive attention. These strategies do not need compensation circuit and provide almost instantaneous load transient response
[16]

[18]
.
A novel hysteresis PWM control strategy based on amperesecond balance of the modulate capacitor is proposed. The proposed control strategy imports the inductor current information in the feedback loop of single output voltage as well as adds inductor current and output voltage as feedback variables. These variables improve capacitor charging and discharging rates effectively. Moreover, only a comparator is used with hysteresis, feedback resistors, and current sensor. Hence, the number of components will be obviously reduced in the control circuit. No error amplifier and complex compensating network is found. Hence, faster response was achieved when the load suddenly changes.
The operating principles of the proposed control strategy are introduced in Section II. The steadystate was analyzed. A smallsignal model is derived and analyzed to show the advantages of the proposed control strategy in Section III. The prototype board is tested. The simulation and experimental results are verified in Section IV. The conclusion is given in Section V.
II. OPERATING PRINCIPLES
The configuration of a buck converter with a synchronous rectifier that uses the proposed control strategy is shown in
Fig. 1
. The key waveforms of comparator
U
in one switching cycle are shown in
Fig. 2
. The control circuit consists of a comparator
U
with hysteresis and feedback resistors
R_{f}
and
R_{L}
. The output voltage and inductor current are returned to capacitor
C
for the triangular wave generator through resistor
R_{f}
and
R_{L}
, respectively. In addition, the output of the hysteresis comparator was connected with the noninverting input terminal through resistor
R_{2}
and then connected with
V_{ref}
through resistor
R_{1}
. Therefore, the upper and lower thresholds of hysteresis controlled buck converter were obtained when the output of comparator
U
changed.
Circuit diagram of the proposed converter.
Key waveforms of the comparator.
The working principle of the control circuit is as follows: When the output voltage becomes large (small), the charging current of capacitor
C
in the on mode period increases (decreases), and the discharging current of capacitor
C
in the off mode period decreases (increases). Hence, the on time duration of the pulse decreases (increases) and off time duration increases (decreases). Therefore, the switching duty was changed. Moreover, the output voltage can be regulated.
III. OPERATION ANALYSIS
 A. SteadyState Analysis
To simplify the analysis, all circuit elements are assumed to be ideal. In
Fig. 1
,
V_{f}
is the voltage across capacitor
C
.
V_{L}
and
V_{H}
are the threshold levels of comparator
U
.
V_{U}
is the output voltage of comparator
U
. The switching cycle starts at instant t=0.
 ( i ) state 1: 0˂t˂TON
When the output signal
V_{U}
is at a high level, the capacitor was charged through the feedback branch. The following equations are obtained:
Solving the above equations under the initial condition of
V_{f}
(0)
=
V_{L}
obtains the next equation as follows:
where
From Equation (2),
V_{f}
increases exponentially from
V_{L}
to
. Since
V_{f}
must be greater than
V_{H}
to invert the state of the comparator, the next constraint is obtained as follows:
Setting
V_{f}
=
V_{H}
and
t
=
T_{ON}
in Equation (2) obtains
T_{ON}
as follows:
If
V_{H}

V_{L}
˂˂

V_{H}
, the Equation (4) can be approximated as follows:
 ( ii ) state 2: TON˂t˂Ts
When output signal
V_{U}
is at a low level, the capacitor was discharged through the feedback branch. The following equations are obtained:
Solving the above equations under the initial condition of
V_{f}(T_{ON})
=
V_{H}
obtains the next equation as follows:
From Eq. (7),
V_{f}
decreases exponentially from V
_{H}
to
. Since
V_{f}
must be lower than
V_{L}
to invert the state of the comparator, the next constraint is obtained as follows:
From Equation (7),
T_{OFF}
is obtained by setting
V_{f}
=
V_{L}
and
t
=
T_{S}
as follows:
If
V_{H}

V_{L}
˂˂
V_{L}
 (
) Equation (9) can be approximated as follows:
Combining (4) and (9) obtains the duty ratio
D
=
T_{ON}
/(
T_{ON}
+
T_{OFF}
) as follows:
Frequency
f
s is as follows:
Combining (5), (10), and
D
=
T_{ON}
/(
T_{ON}
+
T_{OFF}
) obtains the output voltage as follows:
where
V_{H}
=
V_{ref}
+
V_{OH}
 B. Dynamic Analysis
The smallsignal circuit model is obtained by applying PWM switching modeling techniques. This application helps to further analyze the dynamic characteristics of the buck converter circuit.
Fig. 3
shows the smallsignal equivalent circuit of a buck converter with the proposed control strategy. In
Fig. 3
,
k_{i}
is the gain of the inductor current feedback circuit, and
k_{v}
is the gain of the output voltage feedback circuit.
R_{c}
is the seriesequivalent resistance of capacitor
C
. Based on
Figure 3
, the smallsignal transfer functions can be obtained.
Small signal equivalent circuit.
Combining (5) and (10) obtains the duty ratio
D
=
T_{ON}
/(
T_{ON}
+
T_{OFF}
) approximately as follows:
The small signal disturbance of (20) can be represented as follows:
From (20) and (21), the following formula can be obtained:
Combining (20) and (22) obtains the gain of the output voltage feedback and inductor current feedback circuit as follows:
Fig. 4
shows a control block diagram of the circuit proposed in this paper. In
Fig. 4
, the loop gain transfer function of the proposed controller is expressed as follows:
The closedloop transfer function can be obtained according to Mason’s rule.
Control block diagram of the buck converter employing the proposed control scheme.
“ControltoOutput” is as follows:
where
a
_{1}
=
C_{o}
(
R_{o}
+
R_{C}
) +
R_{C}C_{o}
(
k_{v}V_{i}
+ 1) +
“Input voltage susceptibility” is as follows:
If
G_{vv}G_{di}

G_{vi}G_{vd}
= 0, Equation (26) can be written as follows:
“Output impedance” is as follows:
Fig. 5
shows the results of the frequency response of the loop gain of output voltage feedback control transfer function. The feedback resistor
R_{f}
is taken as a parameter. The frequency response of the gain and phase shows that the control loop is steady and possesses good phase margin at different
R_{f}
. The smaller
R_{f}
has higher gain in all frequencies and better phase margin. In addition,
Fig. 6
shows the results of the frequency response of the loop gain of the inductor current feedback control transfer function, which takes the feedback resistor
R_{L}
as a parameter. The control loop is also seen as steady. The smaller
R_{L}
has higher gain in all frequencies, but the phase margin is kept unchanged.
Frequency response of the loop gain of output voltage feedback control with different R_{f}.
Frequency response of the loop gain of inductor current feedback control with different R_{L}.
The above analysis shows that taking
R_{f}
,
R_{L}
between the gain of open loop transfer function and phase margin is a tradeoff. Results show that good performance of proposed controller was achieved with
R_{f}
(=0.6kΩ) and
R_{L}
(=40kΩ).
The loop gain transfer function
T
(s) of the proposed controller is shown in
Fig. 7
. The frequency response of loop gain for the buck converter with feedback
T
(s) and without any feedback
G_{vd}
(s) is compared. The figure shows that feedback control increases the loop DC gain from 14 dB to 64.6 dB, which also has a larger cutoff frequency of 72.9 kHZ. The phase margin was increased to 35° and
T
(s) has 40 dB attenuation in middlehigh frequency. This margin is effective in highfrequency interference mitigation. Hence, both good stability and wide bandwidth are easily achieved if the feedback loop is added. Therefore, the dynamic characteristic is verified.
Frequency response of the loop gain T(s).
Fig. 8
describes the relationship of inductor current feedback resistor
R_{L}
output voltage feedback resistor
R_{f}
and output voltage
V_{o}
. This figure shows that feedback control parameters must be selected in a certain range to stabilize the output voltage.
Effect of R_{L} and R_{f} to Vo.
Fig. 9
(a) shows a Nyquist diagram of the transfer function. Point (1, 0
i
) is not surrounded by the Nyquist plot. In addition, no pole points of the open transfer function in the right half plane are found. The stability of the buck converter control system is obtained in terms of the Nyquist stability criterion.
Fig. 9
(b) shows the part of the amplification region at point (1,0
i
) of the Nyquist plot. Point (1,0
i
) is not be surrounded or passed through by the Nyquist plot.
(a) Nyquist diagram of loop gain transfer function. (b) Amplification region at point (1,0i).
IV. SIMULATION AND EXPERIMENTAL RESULTS
A simulation model based on
Fig. 1
was built in
PSIM
to verify the proposed control strategy, and a prototype was designed. The circuit parameters are shown in
Table I
. The conventional PWM controller is a TL5001 PWM controller. The regulator uses the PI compensation network, as shown in
Fig. 10
.
Traditional voltagemode controlled buck converter.
DESIGN PARAMETERS OF THE PROPOSED CONVERTER
DESIGN PARAMETERS OF THE PROPOSED CONVERTER
Fig. 11
shows the relation between the output current and the output voltage. The variations of the output voltage are extremely small, as seen in the figure. The simulation values of the output voltage are in good agreement with the experimental values.
Fig. 12
shows the relation between the input voltage and output voltage. The variation of the output voltage is also extremely small despite significant variation in the input voltage. No steadystate error is observed in the output voltage when changes of the input voltage and load current occur. The same observation is found even when the controller does not employ a highgain operational amplifier.
Relation of the output current and output voltage.
Relation of the input voltage and output voltage.
Fig. 13
shows the relation between the output current and switching frequency. The figure shows that the switching frequency remained at 120 kHz when the load current changed. Moreover, the drawback of variable frequency was solved compared with some control technologies.
Relation of the output current and switching frequency.
Fig. 14
shows the output voltage and inductor current waveforms during load transients. The load current initially decreased from 5 A to 2 A. The excess inductor current decreased slowly with a slope proportional to
V_{o}
. Operations were in the opposite direction when the load current increased from 2 A to 5 A. In addition, the output voltage drops with magnitude proportion and inductor current increased quickly with a slope proportional to
V_{i}

V_{o}
. Therefore,
V_{o}
quickly recovered. Moreover, the regulator was consistently stable during the load transients.
Waveforms of output voltage and inductor current during load transients.
Below is a comparative analysis of conventional and proposed controllers.
Fig. 15
shows the loop gain transfer function of the conventional and the proposed controllers. The proposed controller has higher gain in all frequency ranges, a higher cutoff frequency, and a higher phase margin than the conventional controller. This controller is simple to use in outer circuit design, which results in high closedloop gain and high closedloop bandwidth. Therefore, the proposed controller has a higher sensitivity to control signal and faster response than the conventional controller.
Bode diagram of loop gain function.
Fig. 16
shows the “output impedance” transfer function of the two. The output impedance of the circuit is mainly decided by the parasitic resistance of the output filter capacitor at high frequency ranges. Hence, both controllers have the same output impedance at high frequency ranges. In addition, the proposed controller has lower output impedance at medium and low frequency ranges. Therefore, the output voltage is less affected by changes in load current compared with the conventional controller. Consequently, better dynamic load performance is achieved.
Bode diagram of output impedance.
Fig. 17
shows the “input voltage susceptibility” transfer function of the two. The proposed controller has lower gain than the conventional controller at low and medium frequency ranges. Hence, the proposed controller has better antiinput voltage disturbance capability.
Bode diagram of inputtooutput function.
Figs. 18
(a) and
18
(b) show the simulated and experimental responses of the proposed and conventional controllers that undergo load current step changes of 5A to 2A and 2A to 5A, respectively. The proposed controller not only has a short response time, but also a small overshoot and undershoot. Hence, this controller has better dynamic response characteristics than the conventional controller.
(a) Simulated and experimental response to a 5 A to 2 A load current step change. (b) Simulated and experimental response to a 2 A to 5 A load current step change.
V. CONCLUSIONS
This paper proposed and analyzed a novel hysteresis PWM control strategy applied to a buck switching converter. The proposed control strategy based on amperesecond balance characteristics of the modulate capacitor uses the output feedback signal for capacitor charging and discharging to generate modulation voltage
V_{f}
. This technique is simple and solves the compensation problem of the error amplifier in conventional voltage PWM control. This strategy also achieves faster transient response and quasiswitching frequency to meet the challenges of power supply requirements for fast dynamic load changes. Finally, the steadystate and dynamic operation of the proposed control method are analyzed and verified by simulation and experimental results.
Acknowledgements
The authors would like to acknowledge the financial support of the Shanghai Talent Development Fund (Grant No. 2012024), the Innovation Program of Shanghai Municipal Education Commission (Grant No. 13ZZ132), and Shanghai Green Energy Grid Connected Technology Engineering Research Center (Grant No. 13DZ2251900).
BIO
JinBin Zhao (M’06) was born in China in 1972. He received his M.S. and Ph.D. in Electrical Engineering from Oita University, Oita, Japan, in 2002 and 2005, respectively. He worked as a researcher at the R&D Headquarters of Origin Electric Co., Ltd, Japan, from 2005 to 2011. He is currently a professor at the Shanghai University of Electric Power, Shanghai, China. His current research interests include control of power converters, softswitching power converters, inverters, distributed power systems, powerfactor correction, and electric drive systems. He currently holds three U.S. patents, ten Japanese patents, and five Chinese patents. He has published 60 technical papers in journals and conference proceedings. Dr. Zhao is a member of the Institute of Electrical Engineers of Japan and the Institute of Electronics Information and Communication Engineers of Japan as well as a senior member of the China Power Supply Society.
JianFeng Dai was born in China in 1989. He will receive his M.S. in Electrical Engineering from the Shanghai University of Electric Power, Shanghai, China, in 2015. His current research interests include modeling and control of DC–DC converter and inverter.
KeQing Qu was born in China in 1970. He received his Ph.D. in Electrical Engineering from Shanghai University, Shanghai, China, in 2004. He is currently an associate professor at the Shanghai University of Electric Power, Shanghai, China. He is also a master instructor. He studied in Germany as a visiting scholar with full funding by the national foundation from 2009 to 2010. His current research interests include power electronic conversion and new energy generation and its application to power systems. He holds one Chinese patent, one monograph, and more than 30 academic theses, 12 of which were included in the international Engineering Index.
Fen Li received her BS and Ph.D. degrees in Electrical Engineering from Huazhong University of Science and Technology, Wuhan, P.R. China, in 2005 and 2010, respectively. She has been an engineer in Hubei Meteorological Bureau, Wuhan, P.R. China, since 2010. Currently, she is a teacher at the Shanghai University of Electric Power, Shanghai, P.R. China. Her research interests are high power factor converters (power factor correction and PWM rectifier), gridconnected control of renewable energy power generation, solar resource evaluation and forecast, relationship of photovoltaic power and meteorological factors, and PV power prediction. To date, she has published 15 technical papers in journal and conference proceedings.
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