An improved hysteretic PWM control with feed-forward and feedback
LETTER
IEICE Electronics Express, Vol.10, No.10, 1–7
An improved hysteretic PWM control with feed-forward and feedback Jinbin Zhaoa) , Yongxiao Liu, Jianfeng Dai, and Ming Lin Electric power engineering, Shanghai University of Electric Power 2103, Ping liang Road, Yangpu, Shanghai, 200090, China a) [email protected]
Abstract: In this paper, an improved hysteretic PWM control with feed-forward and feedback for the buck converter is presented. The proposed control method is based on hysteretic control of capacitor C voltage, which not only offers faster transient response to meet the challenges of the power supply requirements of fast dynamic input and load changes, but also provides better stability and solves the compensation problem of the error amplifier in the conversional voltage PWM control. Finally, the steady-state operation of the control method is analyzed and verified by the simulation and experimental results. Keywords: hysteretic control, feed-forward, feedback, fast transient response Classification: Electron devices, circuits, and systems References [1] X. Wu and X. Wu, “Adaptive Hysteresis Window Control (AHWC) Technique for Hysteretic DC-DC Buck Converter with Constant Switching Frequency,” Proc. Power and Energy Engineering Conference Asia-Pacific, pp. 1–4, 2010. [2] M. Lin, T. Sato, and T. Nabeshima, “A Robust Hysteretic PWM Control Method for Switching Converters,” Proc. IEEE Telecommunications Energy Conference, pp. 1–6, 2009. [3] T. Nabeshima, T. Sato, K. Nishijima, and K. Onda, “Hysteretic PWM Control Method for All Types of DC-to-DC Converters,” Proc. IEEE Telecommunications Energy Conference, pp. 856–860, 2007. [4] Y. Zheng, H. Chen, and K. N. Leung, “A Fast-Response Pseudo PWM Buck Converter with PLL-Based Hysteresis Control,” Proc. IEEE Very Large Scale Integr. (VLSI) Syst., pp. 1167–1174, 2012. [5] J. Zhao, T. Sato, T. Nabeshima, and T. Nakano, “Characteristics of a Buck Converter with New Control Scheme Using a Triangle Waveform Modulated by Output Voltage,” Electronics and Communications in Japan (Part I: Communications), vol. 90, no. 7, pp. 52–59, July 2007.
c
IEICE 2013
DOI: 10.1587/elex.10.20120937 Received December 12, 2012 Accepted January 28, 2013 Published May 25, 2013
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IEICE Electronics Express, Vol.10, No.10, 1–7
1
Introduction
Recently, the switching converters have been widely applied to electronic equipments to regulate the output voltage against the changes of the input voltage and load current. However, for the popular PWM control buck converter operating in continuous conduction mode (CCM), a complicated compensation network is needed to ensure their stable operation due to the existence of the complex poles in the loop gain transfer function [1]. And a phase compensation technique is necessary in the feedback circuit to improve the system dynamic performance and compensate the effect of phase lag in the operational amplifier [2, 3]. It is known that hysteretic control has a fast transient response, the feedback delay of the control signal can be reduced to render fast response [4], and regulate the output voltage in response to step changes of loading current. It might take only one switching cycle to complete the same load transient response [2, 3, 5]. So far, the hysteretic control is considered as the simplest and fastest control method. It does not require the closed loop compensation network and results in low component count and small size in implementation, and it does not need massive external compensation components and has the advantage for on-chip applications. An improved hysteretic PWM control method using a triangle waveform modulated by output voltage feedback and input voltage feed-forward was proposed. The proposed control method only uses a comparator with hysteresis, a feedback resistor, and a feed-forward resistor. Thus, numbers of components in a control circuit are obviously reduced. In addition, due to the error amplifier is not be used, the stability of the converter will become better. Especially, when the input voltage is be changed, it has a smaller peak value and fast regulation speed than the referenced control method [5]. The operations of the control method are described in Section 2, The steady-state of the proposed converter is analyzed in Section 3, and the fast transient response and good regulation were verified by the experiment and PSIM simulation in Section 4.
c
IEICE 2013
DOI: 10.1587/elex.10.20120937 Received December 12, 2012 Accepted January 28, 2013 Published May 25, 2013
Fig. 1. Circuit diagram of the buck converter employing the proposed control method.
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IEICE Electronics Express, Vol.10, No.10, 1–7
2
Operating principles
The configuration of a buck converter with synchronous rectifier employing the proposed control method is shown in Fig. 1. The control circuit consists of a comparator U with hysteresis, a feedback resistor Rf and a feed-forward resistor R. The key and simulation waveforms of the comparator U in one switching cycle are shown in Fig. 2 (a) and (b), respectively. The output voltage is returned to the capacitor C for the triangular wave generator through Rf . V1 is connected to C through R and proportion control coefficient K. V1 is also returned to the comparator U through R2 and K. The control circuit operates as follows. When the output voltage or input voltage becomes large, the charging current of the capacitor C at on mode period increases and the discharging current of the capacitor C at off mode period decreases. Thus, the on time duration of the pulse decreases, and the off time duration increases. Also, while the input voltage Vi becomes large, the threshold voltage levels VH of the comparator U becomes large. Thus, the change of input voltage can directly have effect on the threshold voltage VH to rapidly regulate the duty cycle, not through the output voltage change caused by the input voltage. Therefore, switching duty was changed, and the output voltage can be regulated quickly.
(a)
(b)
Fig. 2. (a) Key waveforms of the comparator. (b) Simulation waveforms.
3
Steady state analysis
To simplify the analysis, all circuit elements are assumed to be ideal. In Fig. 1, Vf is the voltage across capacitor C, VL and VH are threshold levels of the comparator U , VU is the output voltage of the comparator U . The switching cycle starts at the instant t = 0: ( I ) State 1: 0 < t < TON When VU is high level, the following equation is obtained: i=C c
K × Vi − V f Vo − Vf dVf = + dt R Rf
(1)
IEICE 2013
DOI: 10.1587/elex.10.20120937 Received December 12, 2012 Accepted January 28, 2013 Published May 25, 2013
Solving the above equation under the initial condition of Vf (0) = VL , the
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IEICE Electronics Express, Vol.10, No.10, 1–7
next equation is obtained:
TON
Rp Rp KVi + Vo − VL R Rf = CRp ln Rp Rp KVi + Vo − VH R Rf
(2)
Rf R . Rf + R ( II ) State 2: TON < t < TS When VU is low level, the following equation is obtained: Where, Rp =
i=C
−Vf Vo − Vf dVf = + dt R Rf
(3)
Solving the above equation under the initial condition of Vf (TON ) = VH , we have: Rp VH − Vo Rf (4) TOF F = CRp ln Rp VL − Vo Rf Since, the switching frequency is fs = 1/Ts , the output voltage is obtained: Rf (R1 + R2 ) − (R + Rf )R1 Vi d ∗ (5) Vo = R2 Rf − RR1 Where, VH =
R2 R1 R2 Vref + KVi , VL = Vref , R1 + R2 R1 + R2 R1 + R2 R2 R Vref − VO R + R R + Rf 1 2 . d∗ = Rf R1 kVi − R + Rf R1 + R2
4
c
IEICE 2013
DOI: 10.1587/elex.10.20120937 Received December 12, 2012 Accepted January 28, 2013 Published May 25, 2013
Simulation and experimental results
To verify the proposed control method, The design parameters of the laboratory prototype are given in Table I. Fig. 3 (a) shows the relation of the output current and output voltage, Rf is 0.6 kΩ and Vref is 1.5 V. As can be seen from Fig. 3 (a), the variations of the output voltage are very small. The simulation value of output voltage are in good agreement with the experimental value. Fig. 3 (b) shows the relation of the input voltage and output voltage. We can find the variation of the output voltage is very small even when the input voltage varies significantly. Fig. 4 (a) and Fig. 4 (b) show the transient response of the proposed controller and the referenced controller undergoing 8 V to 5 V and 5 V to 8 V input voltage step change. As can be seen that the proposed controller has a smaller peak value and a fast transient recovery time than the referenced controller. Fig. 5 (a) and Fig. 5 (b) show the transient response of the proposed controller and the referenced controller undergoing 5 A to 2.5 A and 5 A to 4
IEICE Electronics Express, Vol.10, No.10, 1–7
2.5 A load current step change. It can be seen that steady-state error is improved to be very small and the employment of the proposed controller reduces the peak value of the output voltage.
Fig. 3. (a) Relation of the output current and output voltage. (b) Relation of the input voltage and output voltage.
(a)
(b) Fig. 4. (a) Transient response to a 8 V to 5 V input voltage step change. (b) Transient response to a 5 V to 8 V input voltage step change. c
IEICE 2013
DOI: 10.1587/elex.10.20120937 Received December 12, 2012 Accepted January 28, 2013 Published May 25, 2013
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IEICE Electronics Express, Vol.10, No.10, 1–7
(a)
(b)
c
IEICE 2013
DOI: 10.1587/elex.10.20120937 Received December 12, 2012 Accepted January 28, 2013 Published May 25, 2013
Fig. 5. (a) Transient response to a 5 A to 2.5 A load current step change. (b) Transient response to a 2.5 A to 5 A load current step change.
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IEICE Electronics Express, Vol.10, No.10, 1–7
Table I. Design parameters of the laboratory prototype.
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Conclusion
An improved hysteretic control method with voltage feed-forward and feedback has been proposed and analyzed in this paper. The proposed control method achieves good regulation and transient response in a buck converter for input voltage and load current transients to meet the increasing challenge of the fast transient recovery requirement of dc–dc converters.
Acknowledgments The authors would like to acknowledge the financial support of the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning and Shanghai PuJiang Program (project number: 12PJ1403900) and Leading Academic Discipline Project of Shanghai Municipal Education Commission (J51303).
c
IEICE 2013
DOI: 10.1587/elex.10.20120937 Received December 12, 2012 Accepted January 28, 2013 Published May 25, 2013
7
IEICE Electronics Express, Vol.10, No.10, 1–7
An improved hysteretic PWM control with feed-forward and feedback Jinbin Zhaoa) , Yongxiao Liu, Jianfeng Dai, and Ming Lin Electric power engineering, Shanghai University of Electric Power 2103, Ping liang Road, Yangpu, Shanghai, 200090, China a) [email protected]
Abstract: In this paper, an improved hysteretic PWM control with feed-forward and feedback for the buck converter is presented. The proposed control method is based on hysteretic control of capacitor C voltage, which not only offers faster transient response to meet the challenges of the power supply requirements of fast dynamic input and load changes, but also provides better stability and solves the compensation problem of the error amplifier in the conversional voltage PWM control. Finally, the steady-state operation of the control method is analyzed and verified by the simulation and experimental results. Keywords: hysteretic control, feed-forward, feedback, fast transient response Classification: Electron devices, circuits, and systems References [1] X. Wu and X. Wu, “Adaptive Hysteresis Window Control (AHWC) Technique for Hysteretic DC-DC Buck Converter with Constant Switching Frequency,” Proc. Power and Energy Engineering Conference Asia-Pacific, pp. 1–4, 2010. [2] M. Lin, T. Sato, and T. Nabeshima, “A Robust Hysteretic PWM Control Method for Switching Converters,” Proc. IEEE Telecommunications Energy Conference, pp. 1–6, 2009. [3] T. Nabeshima, T. Sato, K. Nishijima, and K. Onda, “Hysteretic PWM Control Method for All Types of DC-to-DC Converters,” Proc. IEEE Telecommunications Energy Conference, pp. 856–860, 2007. [4] Y. Zheng, H. Chen, and K. N. Leung, “A Fast-Response Pseudo PWM Buck Converter with PLL-Based Hysteresis Control,” Proc. IEEE Very Large Scale Integr. (VLSI) Syst., pp. 1167–1174, 2012. [5] J. Zhao, T. Sato, T. Nabeshima, and T. Nakano, “Characteristics of a Buck Converter with New Control Scheme Using a Triangle Waveform Modulated by Output Voltage,” Electronics and Communications in Japan (Part I: Communications), vol. 90, no. 7, pp. 52–59, July 2007.
c
IEICE 2013
DOI: 10.1587/elex.10.20120937 Received December 12, 2012 Accepted January 28, 2013 Published May 25, 2013
1
IEICE Electronics Express, Vol.10, No.10, 1–7
1
Introduction
Recently, the switching converters have been widely applied to electronic equipments to regulate the output voltage against the changes of the input voltage and load current. However, for the popular PWM control buck converter operating in continuous conduction mode (CCM), a complicated compensation network is needed to ensure their stable operation due to the existence of the complex poles in the loop gain transfer function [1]. And a phase compensation technique is necessary in the feedback circuit to improve the system dynamic performance and compensate the effect of phase lag in the operational amplifier [2, 3]. It is known that hysteretic control has a fast transient response, the feedback delay of the control signal can be reduced to render fast response [4], and regulate the output voltage in response to step changes of loading current. It might take only one switching cycle to complete the same load transient response [2, 3, 5]. So far, the hysteretic control is considered as the simplest and fastest control method. It does not require the closed loop compensation network and results in low component count and small size in implementation, and it does not need massive external compensation components and has the advantage for on-chip applications. An improved hysteretic PWM control method using a triangle waveform modulated by output voltage feedback and input voltage feed-forward was proposed. The proposed control method only uses a comparator with hysteresis, a feedback resistor, and a feed-forward resistor. Thus, numbers of components in a control circuit are obviously reduced. In addition, due to the error amplifier is not be used, the stability of the converter will become better. Especially, when the input voltage is be changed, it has a smaller peak value and fast regulation speed than the referenced control method [5]. The operations of the control method are described in Section 2, The steady-state of the proposed converter is analyzed in Section 3, and the fast transient response and good regulation were verified by the experiment and PSIM simulation in Section 4.
c
IEICE 2013
DOI: 10.1587/elex.10.20120937 Received December 12, 2012 Accepted January 28, 2013 Published May 25, 2013
Fig. 1. Circuit diagram of the buck converter employing the proposed control method.
2
IEICE Electronics Express, Vol.10, No.10, 1–7
2
Operating principles
The configuration of a buck converter with synchronous rectifier employing the proposed control method is shown in Fig. 1. The control circuit consists of a comparator U with hysteresis, a feedback resistor Rf and a feed-forward resistor R. The key and simulation waveforms of the comparator U in one switching cycle are shown in Fig. 2 (a) and (b), respectively. The output voltage is returned to the capacitor C for the triangular wave generator through Rf . V1 is connected to C through R and proportion control coefficient K. V1 is also returned to the comparator U through R2 and K. The control circuit operates as follows. When the output voltage or input voltage becomes large, the charging current of the capacitor C at on mode period increases and the discharging current of the capacitor C at off mode period decreases. Thus, the on time duration of the pulse decreases, and the off time duration increases. Also, while the input voltage Vi becomes large, the threshold voltage levels VH of the comparator U becomes large. Thus, the change of input voltage can directly have effect on the threshold voltage VH to rapidly regulate the duty cycle, not through the output voltage change caused by the input voltage. Therefore, switching duty was changed, and the output voltage can be regulated quickly.
(a)
(b)
Fig. 2. (a) Key waveforms of the comparator. (b) Simulation waveforms.
3
Steady state analysis
To simplify the analysis, all circuit elements are assumed to be ideal. In Fig. 1, Vf is the voltage across capacitor C, VL and VH are threshold levels of the comparator U , VU is the output voltage of the comparator U . The switching cycle starts at the instant t = 0: ( I ) State 1: 0 < t < TON When VU is high level, the following equation is obtained: i=C c
K × Vi − V f Vo − Vf dVf = + dt R Rf
(1)
IEICE 2013
DOI: 10.1587/elex.10.20120937 Received December 12, 2012 Accepted January 28, 2013 Published May 25, 2013
Solving the above equation under the initial condition of Vf (0) = VL , the
3
IEICE Electronics Express, Vol.10, No.10, 1–7
next equation is obtained:
TON
Rp Rp KVi + Vo − VL R Rf = CRp ln Rp Rp KVi + Vo − VH R Rf
(2)
Rf R . Rf + R ( II ) State 2: TON < t < TS When VU is low level, the following equation is obtained: Where, Rp =
i=C
−Vf Vo − Vf dVf = + dt R Rf
(3)
Solving the above equation under the initial condition of Vf (TON ) = VH , we have: Rp VH − Vo Rf (4) TOF F = CRp ln Rp VL − Vo Rf Since, the switching frequency is fs = 1/Ts , the output voltage is obtained: Rf (R1 + R2 ) − (R + Rf )R1 Vi d ∗ (5) Vo = R2 Rf − RR1 Where, VH =
R2 R1 R2 Vref + KVi , VL = Vref , R1 + R2 R1 + R2 R1 + R2 R2 R Vref − VO R + R R + Rf 1 2 . d∗ = Rf R1 kVi − R + Rf R1 + R2
4
c
IEICE 2013
DOI: 10.1587/elex.10.20120937 Received December 12, 2012 Accepted January 28, 2013 Published May 25, 2013
Simulation and experimental results
To verify the proposed control method, The design parameters of the laboratory prototype are given in Table I. Fig. 3 (a) shows the relation of the output current and output voltage, Rf is 0.6 kΩ and Vref is 1.5 V. As can be seen from Fig. 3 (a), the variations of the output voltage are very small. The simulation value of output voltage are in good agreement with the experimental value. Fig. 3 (b) shows the relation of the input voltage and output voltage. We can find the variation of the output voltage is very small even when the input voltage varies significantly. Fig. 4 (a) and Fig. 4 (b) show the transient response of the proposed controller and the referenced controller undergoing 8 V to 5 V and 5 V to 8 V input voltage step change. As can be seen that the proposed controller has a smaller peak value and a fast transient recovery time than the referenced controller. Fig. 5 (a) and Fig. 5 (b) show the transient response of the proposed controller and the referenced controller undergoing 5 A to 2.5 A and 5 A to 4
IEICE Electronics Express, Vol.10, No.10, 1–7
2.5 A load current step change. It can be seen that steady-state error is improved to be very small and the employment of the proposed controller reduces the peak value of the output voltage.
Fig. 3. (a) Relation of the output current and output voltage. (b) Relation of the input voltage and output voltage.
(a)
(b) Fig. 4. (a) Transient response to a 8 V to 5 V input voltage step change. (b) Transient response to a 5 V to 8 V input voltage step change. c
IEICE 2013
DOI: 10.1587/elex.10.20120937 Received December 12, 2012 Accepted January 28, 2013 Published May 25, 2013
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IEICE Electronics Express, Vol.10, No.10, 1–7
(a)
(b)
c
IEICE 2013
DOI: 10.1587/elex.10.20120937 Received December 12, 2012 Accepted January 28, 2013 Published May 25, 2013
Fig. 5. (a) Transient response to a 5 A to 2.5 A load current step change. (b) Transient response to a 2.5 A to 5 A load current step change.
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IEICE Electronics Express, Vol.10, No.10, 1–7
Table I. Design parameters of the laboratory prototype.
5
Conclusion
An improved hysteretic control method with voltage feed-forward and feedback has been proposed and analyzed in this paper. The proposed control method achieves good regulation and transient response in a buck converter for input voltage and load current transients to meet the increasing challenge of the fast transient recovery requirement of dc–dc converters.
Acknowledgments The authors would like to acknowledge the financial support of the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning and Shanghai PuJiang Program (project number: 12PJ1403900) and Leading Academic Discipline Project of Shanghai Municipal Education Commission (J51303).
c
IEICE 2013
DOI: 10.1587/elex.10.20120937 Received December 12, 2012 Accepted January 28, 2013 Published May 25, 2013
7
