Research Article  Open Access
Research on DualCarrier PulseTrainControlled Buck Converter
Abstract
In order to solve the lowfrequency oscillation of pulsetrain (PT) controlled switching converter operating in a continuous conduction mode (CCM), a dualcarrier pulsetrain (DCPT) control technique is proposed in this paper. With the CCM buck converter as an example, the operational principle, pulse control law, and output voltage ripple of the DCPTcontrolled converter are studied. The experimental results are provided to verify the theoretical analysis and simulation results. Compared with the PTcontrolled converter, the DCPTcontrolled CCM buck converter enjoys much better operating characteristics and smaller output voltage ripple.
1. Introduction
With the development of electronic technology, the steadystate performance and transient response of power supplies are very important in many electronic devices. However, for pulsewidth modulation (PWM) switching DCDC converters, with the disadvantages of slow transient response and complicated compensational network, it is hard to meet the requirements of modern electronic equipments [1–4].
In order to get a great transient response, a pulsetrain (PT) control technique for DCDC converter was proposed [5]. When the PTcontrolled switching converter operates in discontinuous conduction mode (DCM), the output voltage will increase during each highenergy pulse P_{H} and decrease during each lowenergy pulse P_{L}, which improves the transient characteristic of the converter. Qin and Xu [6] proposed a multiple pulsetrain (MPT) control technique by setting several duty cycle pulses to get better output characteristics. Qin and Xu [7] introduced a currentreferenced pulsetrain (CRPT) control technique to enlarge the load range and improve the voltage accuracy of the converter. Considering the spectrum of the switching converter, the bifrequency pulsetrain (BFPT) control technique was proposed [8]. However, all the control techniques mentioned above were used in DCM converters, which limited the applications.
Wang et al. [9] applied the PT control technique to a buck converter operating in the continuous conduction mode (CCM) and indicated that the lowfrequency oscillation existed at this time, which confused the pulse control law and enlarged the output voltage ripple. In order to solve this problem, several control techniques have been proposed. By limiting the valley value of the inductor current, the valley current mode PT (VCMPT) controlled buck converter eliminated the lowfrequency oscillation, but it limited the output power range at the same time [10]. By detecting the load current, the sliding current valley PT (SCVPT) controlled buck converter changed the valley value of the inductor current adaptively and improved the output power range of the converter [11]. However, load current, inductor current, and output voltage were detected at the same time for SCVPT control, which is quite complicated. Sha et al. [12] indicated that by limiting the peak value of the capacitor current within one switching cycle, the lowfrequency oscillation could be eliminated, although the control parameters were complicated to design. By controlling the leading edge of the pulse, the pulse phase shiftbased PT (PPSPT) control was proposed [13]. Although the PPSPTcontrolled buck converter could eliminate the lowfrequency oscillation, it weakened the transient characteristic. In [14], the PT control technique was applied to boost converter operated in the pseudo continuous conduction mode (PCCM). This converter enjoyed wide power range without lowfrequency oscillation, but the efficiency of the converter was poor due to the freewheeling phase. In addition, by improving the topology of the converter, the lowfrequency oscillation could be suppressed, but it was complicated to the integration of the switching converter [15–20].
In this paper, a dualcarrier pulsetrain (DCPT) control technique is proposed and studied in detail. In the DCPTcontrolled CCM buck converter, the capacitor current is limited to the preset valley current by a carrier signal at the beginning of each switching cycle. The output voltage will increase during one P_{H} switching cycle and decrease during each P_{L} switching cycle, which indicates that the lowfrequency oscillation did not exist in the DCPTcontrolled converter. The theoretical analysis, simulation, and experimental results verify that the DCPTcontrolled CCM buck converter enjoys small output ripple and fast transient response.
2. Operational Principle
For a buck converter, when the switch S is on, the inductor current will increase with a slope of ; when S is off, the inductor current will decrease with a slope of . Since the capacitor current reflects the ripple of the inductor current completely, the slope of the capacitor current is also or when the switch is on or off, respectively. If a control signal with a slope of is applied to the capacitor current, the capacitor current will move along with the trajectory of after the switch turns off.
Figure 1(a) shows the schematic diagram of the DCPTcontrolled buck converter. In the controller, a comparator is used to compare the output voltage of the switching converter with a reference value, a sense resistor connected to the output capacitor and its auxiliary circuit are employed to obtain the capacitor current, and two D/A converters are acquired to generate the carrier signals. Besides that, there is no extra compensational network in the controller, which indicates the DCPTcontrolled converter enjoys convenient design process and fast response. The main working waveforms including capacitor current i_{c}, control pulse control signal , and output voltage are shown in Figure 1(b). The carrier signals and generated by the controller have the same valley current I_{v} and slope V_{ref}/L. However, the frequency of or is different, which is f_{H} or f_{L}, respectively. Because the control pulse is generated by comparing the capacitor current with the carrier signal in the DCPT controller, the switching frequency of the converter is also f_{H} or f_{L} correspondingly.
(a)
(b)
The working principle of the DCPTcontrolled buck converter is as follows. The carrier signal is chosen between and . When decreases to the valley current I_{v}, the switch S turns on immediately, and the output voltage is compared with the reference voltage V_{ref}. If < V_{ref}, the carrier signal is selected as . When the capacitor current i_{c} > , the switch S turns off, which is recorded as a highenergy pulse P_{H}. Similarly, if ≥ V_{ref} at the time when decreases to I_{v}, the carrier signal will be selected. When i_{c} > , S turns off, which is recorded as the lowenergy pulse P_{L}. When the converter operates in a steady state, the DCPT controller will generate a pulse train, which consists of P_{H} and P_{L} to stabilize the output voltage.
3. SteadyState Analysis
3.1. Design of Control Parameters
In order to avoid lowfrequency oscillation, the output voltage should be increased during P_{H} and decreased during P_{L}. Based on this principle, the control parameters, the frequencies of the carrier signals, and the valley current can be designed properly.
Figure 2 shows the capacitor current waveform of the DCPTcontrolled buck converter within one switching cycle. For the switching converter with a low output voltage, the onstate voltage of the diode has a significant influence on the process of control law analysis. When the onstate voltage V_{D} of the diode is considered, the rising or falling slope of the capacitor current is (V_{in} − V_{o})/L or (V_{o} + V_{D})/L, respectively.
During t_{1} or t_{2}, the peak value of the capacitor current I_{p} can be expressed as
By combining equations (1) and (2), we have
Based on Figure 2 and equation (3), the area of the triangle ABC can be written as
The area of the quadrangle BCED within one switching period T is
Similarly, the areas of the triangle BOD and the triangle CFE can be expressed as
According to equation (6), the charge variation of the output capacitor during one switching cycle T can be calculated as
During the conduction time of the switch, I_{p} can be written as
By combining equations (7) and (8), it is available that
Therefore, the variation of the output voltage within one switching cycle can be calculated as
By choosing different T_{H} or T_{L}, the variation of the output voltage within P_{H} or P_{L} can be obtained as
Based on equation (11), the output voltage iterative equation of the DCPTcontrolled buck converter can be expressed as
According to the principle of the DCPT control technique, and should be guaranteed. Therefore, it is available that
The control parameter I_{v} can be determined by the preset input voltage range of the converter. Since the falling slope of the carrier signals and is /L, the peak value of the carrier signals can be calculated when the frequencies of the carrier signals f_{H} and f_{L} and the valley current I_{v} are determined. Based on the analysis above, the parameters of the researched the DCPTcontrolled buck converter are listed in Table 1.

From equation (12), it can be known that the output voltage variations and vary with the input voltage V_{in}. In order to achieve and , V_{in} would be limited within a valid range.
Assuming the output voltage variation is zero in one P_{H} switching cycle (), the lower boundary of the input voltage for the DCPTcontrolled buck converter will be calculated as
Similarly, assuming the output voltage variation is zero in one P_{L} switching cycle (), the upper boundary of the input voltage will be
Substituting the parameters of Table 1 into equation (14), the operating range of the input voltage can be calculated, which is [8.11 V, 19 V]. When the input voltage varies in this range, the output voltage will increase during each P_{H} and decrease during each P_{L}; thus, the lowfrequency oscillation can be avoided.
By using equation (12), the relationship between the output voltage variation and and the input voltage V_{in} can be obtained, as shown in Figure 3. It can be seen that, with the increasing input voltage, the variation of the output voltage increases and decreases.
3.2. Analysis of Pulse Control Law
According to the principle of charge balance, the variation of the output voltage is zero in a whole pulse train, that is,
By combining equations (12) and (16), it can be obtained that
Substituting the parameters shown in Table 1 into equation (17), the relationship between the pulse ratio μ_{H}/μ_{L} and the input voltage V_{in} can be obtained, as shown in Figure 4. It can be known that, the pulse ratio μ_{H}/μ_{L} decreases gradually with the increase of V_{in}, which is caused by the increase of and the decrease of . Therefore, the proportion of the highenergy pulse P_{H} in the pulse train gradually decreases with the increase in the input voltage.
According to equation (17), the typical pulse train of the DCPTcontrolled buck converter in the condition of different input voltages can be obtained, as listed in Table 2.

3.3. Analysis of the Output Voltage Ripple
To analyse the output voltage variation, the capacitor current i_{c} and output voltage of the DCPTcontrolled buck converter within one switching cycle are shown in Figure 5.
During [0, t_{on}], the capacitor current i_{c} (t) and the output voltage of the converter can be written as
By taking the derivation of equation (19), one obtains
Substituting the parameters listed in Table 1 into equation (20), it can be known that the output voltage rises to the maximum at the time t_{on}. Therefore, it is available that
For the DCPTcontrolled buck converter, the output voltage ripple is closely related to the pulse train. Taking the pulse train 2P_{H}1P_{L} as an example, the capacitor current i_{c} and the output voltage are shown in Figure 6(a). Obviously, the output voltage ripple of the converter is at this time.
(a)
(b)
In general, when the pulse train is nP_{H}1P_{L}, the output voltage ripple of the converter is
When the pulse train is 1P_{H}nP_{L}, the capacitor current i_{c} and the output voltage are shown in Figure 6(b). Apparently, the output voltage ripple on this condition is
By using equations (21)–(23), the output voltage ripple of the DCPTcontrolled buck converter can be calculated, as listed in Table 3. For the DCPTcontrolled buck converter, the output voltage ripple increases gradually with the increase of the input voltage.

4. Simulation and Experimental Results
4.1. Simulation Results
To verify the theoretical analysis, the simulation results are provided in Figure 7, which include carrier signal , control pulse , capacitor current i_{c,} and output voltage .
(a)
(b)
(c)
(d)
As shown in Figure 7(a), when the input voltage equals to 8.68 V, the pulse train is 2P_{H}1P_{L}, the pulse ratio is μ_{H}/μ_{L} = 2, and the output voltage ripple is 40 mV, which are consistent with the theoretical analysis. Similarly, as shown in Figures 7(b)–7(d), when the input voltage equals to 9.2 V, 10.83 V, or 12 V, the pulse train is 1P_{H}1P_{L}, 1P_{H}3P_{L}, or 1P_{H}5P_{L}, the pulse ratio is 1, 1/3, or 1/5, and the output voltage ripple is 40 mV, 55 mV, or 60 mV, respectively.
According to Figure 7, the following conclusion of the DCPTcontrolled buck converter can be obtained: as the input voltage V_{in} increases, μ_{H}/μ_{L} decreases gradually, i.e., the proportion of P_{H} in the pulse train decreases, which is consistent with the theoretical analysis in Section 3.2.
In addition, the value of the capacitor current at the beginning of each switching cycle is equal to the preset valley current I_{v} due to the traction of the carrier signals. Since the capacitor current reflects the ripple of the inductor current, the value of the inductor current is constant at the beginning of each switching cycle. Therefore, the variation of the output voltage is only influenced by the control pulse P_{H} or P_{L}, which indicates that the lowfrequency oscillation does not exist in the DCPTcontrolled buck converter.
4.2. Experimental Results
In order to verify and test the proposed technique, a prototype of the DCPTcontrolled buck converter is designed with the parameters in Table 1. In the prototype, the control scheme is achieved by an FPGA device, with a type of EP4CE15F17C8. An operational amplifier OPA228 and a 10 mΩ sense resistor connected with the output capacitor are employed to obtain the capacitor current. Two D/A DAC0808 converters are applied to generate the carrier signals, and an analogue multiplexer CD4051 is used to select the carrier signal between and . Besides, the type of the comparators in this prototype is LM393.
When the input voltage equals to 8.68 V, the experimental waveforms are shown in Figure 8(a). The pulse train is 2P_{H}1P_{L}, and the output voltage ripple is 40 mV approximately. Similarly, when the input voltage equals to 9.2 V, 10.83 V, or 12 V, the pulse train is 1P_{H}1P_{L}, 1P_{H}3P_{L}, or 1P_{H}5P_{L} and the output voltage ripple is 40 mV, 50 mV, or 60 mV, respectively.
(a)
(b)
(c)
(d)
According to the principle of DCPT control, the control pulse is generated by comparing the capacitor current with the carrier signals. It can be seen from Figure 8 that the combination of the carrier signals changes with the variation of the input voltage, which causes the variation of the pulse train. Based on the experimental results, it can be known that the DCPTcontrolled buck converter can operate in a steady state by adjusting the pulse train when the input voltage changes.
In order to study the transient response of the DCPT control method, the experimental transient waveforms are provided in Figure 9. When the load current increases from 2A to 3A, two highenergy pulses are generated successively by the controller to stabilize the output voltage, and this converter enjoys excellent transient response. Considering the parasitic parameters such as the onstate resistor of the MOSFET, when the load current increases, the input voltage of the inductor will decrease slightly, which causes the proportion of P_{H} in the pulse train to increase.
In order to verify the suppression effect on the lowfrequency oscillation, the comparative experimental results are provided in Figure 10. The control parameters of traditional PTcontrolled buck converter are as follows: D_{H} = 0.6, D_{L} = 0.3, and T = 25 μs.
(a)
(b)
As shown in Figure 10(a), the pulse train is 1P_{H}5P_{L} for the DCPTcontrolled CCM converter and the output voltage ripple is 60 mV. In contrast, the pulse train of the PTcontrolled buck converter is 4P_{H}4P_{L}, and the output voltage ripple is 120 mV, as shown in Figure 10(b). This phenomenon of successive several highenergy pulses followed by successive several lowenergy pulses indicates that the lowfrequency oscillation exists in the PTcontrolled CCM converter. The lowfrequency oscillation has not occurred in the DCPTcontrolled CCM buck converter. The proposed DCPT control technique enjoys much better output characteristics compared with the traditional PT control technique.
5. Conclusions
In this paper, a dualcarrier pulsetrain control technique is proposed. With the CCM buck converter as an example, the operational principle is analysed in detail. Based on the output voltage variation of the DCPTcontrolled buck converter within one switching cycle, the pulse control law and the output voltage ripple are analysed. The simulation and experimental results verify the theoretical analysis and indicate that there is no lowfrequency oscillation in the DCPTcontrolled CCM buck converter. Compared with the traditional PT control technique, the DCPTcontrolled buck converter enjoys better control characteristics and much smaller output voltage ripple.
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (51507155) and the Key Research Program of He’nan Higher Education (16A470014).
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Copyright
Copyright © 2019 Ming Qin and Shiwei Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.