# Research on Dual-Carrier Pulse-Train-Controlled Buck Converter

Authors: Ming Qin; Shiwei Li
Journal: Journal of Control Science and Engineering
 (2019)

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## Abstract

In order to solve the low-frequency oscillation of pulse-train- (PT-) controlled switching converter operating in a continuous conduction mode (CCM), a dual-carrier pulse-train (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 DCPT-controlled converter are studied. The experimental results are provided to verify the theoretical analysis and simulation results. Compared with the PT-controlled converter, the DCPT-controlled CCM buck converter enjoys much better operating characteristics and smaller output voltage ripple.


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## Body

## 1. Introduction

With the development of electronic technology, the steady-state performance and transient response of power supplies are very important in many electronic devices. However, for pulse-width modulation (PWM) switching DC-DC 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 pulse-train (PT) control technique for DC-DC converter was proposed [5]. When the PT-controlled switching converter operates in discontinuous conduction mode (DCM), the output voltage will increase during each high-energy pulse PH and decrease during each low-energy pulse PL, which improves the transient characteristic of the converter. Qin and Xu [6] proposed a multiple pulse-train (MPT) control technique by setting several duty cycle pulses to get better output characteristics. Qin and Xu [7] introduced a current-referenced pulse-train (CRPT) control technique to enlarge the load range and improve the voltage accuracy of the converter. Considering the spectrum of the switching converter, the bi-frequency pulse-train (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 low-frequency 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 (VCM-PT) controlled buck converter eliminated the low-frequency oscillation, but it limited the output power range at the same time [10]. By detecting the load current, the sliding current valley PT (SCV-PT) 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 SCV-PT 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 low-frequency oscillation could be eliminated, although the control parameters were complicated to design. By controlling the leading edge of the pulse, the pulse phase shift-based PT (PPS-PT) control was proposed [13]. Although the PPS-PT-controlled buck converter could eliminate the low-frequency 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 low-frequency oscillation, but the efficiency of the converter was poor due to the freewheeling phase. In addition, by improving the topology of the converter, the low-frequency oscillation could be suppressed, but it was complicated to the integration of the switching converter [15–20].In this paper, a dual-carrier pulse-train (DCPT) control technique is proposed and studied in detail. In the DCPT-controlled 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 onePH switching cycle and decrease during each PL switching cycle, which indicates that the low-frequency oscillation did not exist in the DCPT-controlled converter. The theoretical analysis, simulation, and experimental results verify that the DCPT-controlled CCM buck converter enjoys small output ripple and fast transient response.


## 2. Operational Principle

For a buck converter, when the switchS is on, the inductor current will increase with a slope of Vin−Vo/L; when S is off, the inductor current will decrease with a slope of Vo/L. Since the capacitor current reflects the ripple of the inductor current completely, the slope of the capacitor current is also Vin−Vo/L or Vo/L when the switch is on or off, respectively. If a control signal vsaw with a slope of Vo/L is applied to the capacitor current, the capacitor current will move along with the trajectory of vsaw after the switch turns off.Figure1(a) shows the schematic diagram of the DCPT-controlled 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 DCPT-controlled converter enjoys convenient design process and fast response. The main working waveforms including capacitor current ic, control pulse control signal vp, and output voltage vo are shown in Figure 1(b). The carrier signals vsaw,H and vsaw,L generated by the controller have the same valley current Iv and slope Vref/L. However, the frequency of vsaw,H or vsaw,L is different, which is fH or fL, 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 fH or fL correspondingly.Figure 1
Working principle diagram of the DCPT-controlled buck converter. (a) Schematic diagram. (b) Working waveforms.
(a)
(b)The working principle of the DCPT-controlled buck converter is as follows. The carrier signalvsaw is chosen between vsaw,H and vsaw,L. When vsaw decreases to the valley current Iv, the switch S turns on immediately, and the output voltage is compared with the reference voltage Vref. If vo < Vref, the carrier signal vsaw,H is selected as vsaw. When the capacitor current ic > vsaw,H, the switch S turns off, which is recorded as a high-energy pulse PH. Similarly, if vo ≥ Vref at the time when vsaw decreases to Iv, the carrier signal vsaw,L will be selected. When ic > vsaw,L, S turns off, which is recorded as the low-energy pulse PL. When the converter operates in a steady state, the DCPT controller will generate a pulse train, which consists of PH and PL to stabilize the output voltage.


## 3. Steady-State Analysis

### 3.1. Design of Control Parameters

In order to avoid low-frequency oscillation, the output voltage should be increased duringPH and decreased during PL. Based on this principle, the control parameters, the frequencies of the carrier signals, and the valley current can be designed properly.Figure2 shows the capacitor current waveform of the DCPT-controlled buck converter within one switching cycle. For the switching converter with a low output voltage, the on-state voltage of the diode has a significant influence on the process of control law analysis. When the on-state voltage VD of the diode is considered, the rising or falling slope of the capacitor current is (Vin − Vo)/L or (Vo + VD)/L, respectively.Figure 2
Capacitor current of the DCPT-controlled buck converter.Duringt1 or t2, the peak value of the capacitor current Ip can be expressed as(1)Ip=Vin−VoLt1,(2)Ip=Vo+VDLt2.By combining equations (1) and (2), we have(3)t1+t2=LIpVin+VDVin−VoVo+VD.Based on Figure2 and equation (3), the area of the triangle ABC can be written as(4)SΔABC=12t1+t2Ip=Vin+VDLIp22Vin−VoVo+VD.The area of the quadrangleBCED within one switching period T is(5)SBCED=−12t1+t2+TIv=−Vin+VDLIvIp2Vin−VoVo+VD−12IvT.Similarly, the areas of the triangleBOD and the triangle CFE can be expressed as(6)SΔBOD+SΔCFE=SOFED−SBCED=−12IvT+Vin+VDLIvIp2Vin−VoVo+VD.According to equation (6), the charge variation of the output capacitor during one switching cycle T can be calculated as(7)Δq=SΔABC−SΔBOD+SΔCFE=Vin+VDLIp22Vin−VoVo+VD+12IvT−Vin+VDLIvIp2Vin−VoVo+VD.During the conduction time of the switch,Ip can be written as(8)Ip=Iv+Vin−VoLDT=Iv+Vin−VoVo+VDLVin+VDT.By combining equations (7) and (8), it is available that(9)Δq=IvT+Vin−VoVo+VD2LVin+VDT2.Therefore, the variation of the output voltage within one switching cycle can be calculated as(10)Δvo=ΔqC=IvCT+Vin−VoVo+VD2LCVin+VDT2.By choosing differentTH or TL, the variation of the output voltage within PH or PL can be obtained as(11)ΔvoH=IvCTH+Vin−VoVo+VD2LCVin+VDTH2,ΔvoL=IvCTL+Vin−VoVo+VD2LCVin+VDTL2.Based on equation (11), the output voltage iterative equation of the DCPT-controlled buck converter can be expressed as(12)vo,n+1=vo,n+IvCTH+Vin−VoVo+VD2LCVin+VDTH2,vo,n<Vref,vo,n+IvCTL+Vin−VoVo+VD2LCVin+VDTL2,vo,n≥Vref.According to the principle of the DCPT control technique,ΔvoH>0 and ΔvoL<0 should be guaranteed. Therefore, it is available that(13)−Vin−VoVo+VD2LCVin+VDTH<Iv<−Vin−VoVo+VD2LVin+VDTL.The control parameterIv can be determined by the preset input voltage range of the converter. Since the falling slope of the carrier signals vsaw,H and vsaw,L is Vref/L, the peak value of the carrier signals can be calculated when the frequencies of the carrier signals fH and fL and the valley current Iv are determined. Based on the analysis above, the parameters of the researched the DCPT-controlled buck converter are listed in Table 1.Table 1
Parameters of the DCPT-controlled buck converter.
Parameters
Value
Rated input voltage,Vin
12 V
Reference voltage,Vref
5 V
Inductor,L
100μH
Capacitor,C
560μF
Equivalent series resistance,RE
30 mΩ
FrequencyfL of carrier, vsaw,L
40 kHz
FrequencyfH of carrier, vsaw,H
20 kHz
Valley current,Iv
−0.5 AFrom equation (12), it can be known that the output voltage variations ΔvoH and ΔvoL vary with the input voltage Vin. In order to achieve ΔvoH>0 and ΔvoL<0, Vin would be limited within a valid range.Assuming the output voltage variation is zero in onePH switching cycle (ΔvoH=0), the lower boundary of the input voltage for the DCPT-controlled buck converter will be calculated as(14)Vin,min=Vo+VD2THVo+VDT−2LIv−VD.Similarly, assuming the output voltage variation is zero in onePL switching cycle (ΔvoL=0), the upper boundary of the input voltage will be(15)Vin,max=Vo+VD2TLVo+VDT−2LIv−VD.Substituting the parameters of Table1 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 PH and decrease during each PL; thus, the low-frequency oscillation can be avoided.By using equation (12), the relationship between the output voltage variation ΔvoH>0 and −ΔvoL<0 and the input voltage Vin can be obtained, as shown in Figure 3. It can be seen that, with the increasing input voltage, the variation of the output voltage ΔvoH>0 increases and −ΔvoL<0 decreases.Figure 3
Output voltage variation versus input voltage of the DCPT-controlled buck converter.


### 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,(16)μHΔvoH+μLΔvoL=0.By combining equations (12) and (16), it can be obtained that(17)μHμL=−Vin−VoVo+VDTL2−2LIvTLVin+VDVin−VoVo+VDTH2−2LIvTHVin+VD.Substituting the parameters shown in Table1 into equation (17), the relationship between the pulse ratio μH/μL and the input voltage Vin can be obtained, as shown in Figure 4. It can be known that, the pulse ratio μH/μL decreases gradually with the increase of Vin, which is caused by the increase of ΔvoH>0 and the decrease of −ΔvoL<0. Therefore, the proportion of the high-energy pulse PH in the pulse train gradually decreases with the increase in the input voltage.Figure 4
Pulse ratio versus input voltage of the DCPT-controlled buck converter.According to equation (17), the typical pulse train of the DCPT-controlled buck converter in the condition of different input voltages can be obtained, as listed in Table 2.Table 2
Pulse train of the DCPT-controlled buck converter at different voltages.
V
in (V)
μ
H/μL
Pulse train
8.49
3
3PH-1PL
8.68
2
2PH-1PL
9.2
1
1PH-1PL
10.83
1/3
1PH-3PL
12
1/5
1PH-5PL


### 3.3. Analysis of the Output Voltage Ripple

To analyse the output voltage variation, the capacitor currentic and output voltage vo of the DCPT-controlled buck converter within one switching cycle are shown in Figure 5.Figure 5
Capacitor current and output voltage of the DCPT-controlled buck converter.During [0,ton], the capacitor current ic (t) and the output voltage of the converter can be written as(18)ict=Iv+Vin−VoLt,(19)vot=1C∫0tictdt+ictREIvCt+Vin−Vo2LCt2+Vin−VoLREt.By taking the derivation of equation (19), one obtains(20)dvotdt=IvC+Vin−Vo2LCt+Vin−VoLCRE.Substituting the parameters listed in Table1 into equation (20), it can be known that the output voltage rises to the maximum at the time ton. Therefore, it is available that(21)ΔvppH=IvCton+Vin−Vo2LCton2+Vin−VoLREton.For the DCPT-controlled buck converter, the output voltage ripple is closely related to the pulse train. Taking the pulse train 2PH-1PL as an example, the capacitor current ic and the output voltage vo are shown in Figure 6(a). Obviously, the output voltage ripple of the converter is Δvo=ΔvppH+ΔvoH at this time.Figure 6
Output voltage ripple of the DCPT-controlled buck converter. (a) The case of 2PH-1PL. (b) The case of 1PH-3PL.
(a)
(b)In general, when the pulse train isnPH-1PL, the output voltage ripple of the converter is(22)Δvo=n−1ΔvppH+ΔvoH.When the pulse train is 1PH-nPL, the capacitor current ic and the output voltage vo are shown in Figure 6(b). Apparently, the output voltage ripple on this condition is(23)Δvo=ΔvppH.By using equations (21)–(23), the output voltage ripple Δvo of the DCPT-controlled buck converter can be calculated, as listed in Table 3. For the DCPT-controlled buck converter, the output voltage ripple increases gradually with the increase of the input voltage.Table 3
The output voltage ripple of the DCPT-controlled buck converter.
V
in (V)
Δ
v
o
H (mV)
Δ
v
pp
H (mV)
Δ
v
o (mV)
8.49
3.3
34.3
40.9
8.68
4.9
36.3
41.2
9.2
8.9
41.5
41.5
10.83
19.1
52.2
52.2
12
24.8
57.7
57.7


## 3.1. Design of Control Parameters

In order to avoid low-frequency oscillation, the output voltage should be increased duringPH and decreased during PL. Based on this principle, the control parameters, the frequencies of the carrier signals, and the valley current can be designed properly.Figure2 shows the capacitor current waveform of the DCPT-controlled buck converter within one switching cycle. For the switching converter with a low output voltage, the on-state voltage of the diode has a significant influence on the process of control law analysis. When the on-state voltage VD of the diode is considered, the rising or falling slope of the capacitor current is (Vin − Vo)/L or (Vo + VD)/L, respectively.Figure 2
Capacitor current of the DCPT-controlled buck converter.Duringt1 or t2, the peak value of the capacitor current Ip can be expressed as(1)Ip=Vin−VoLt1,(2)Ip=Vo+VDLt2.By combining equations (1) and (2), we have(3)t1+t2=LIpVin+VDVin−VoVo+VD.Based on Figure2 and equation (3), the area of the triangle ABC can be written as(4)SΔABC=12t1+t2Ip=Vin+VDLIp22Vin−VoVo+VD.The area of the quadrangleBCED within one switching period T is(5)SBCED=−12t1+t2+TIv=−Vin+VDLIvIp2Vin−VoVo+VD−12IvT.Similarly, the areas of the triangleBOD and the triangle CFE can be expressed as(6)SΔBOD+SΔCFE=SOFED−SBCED=−12IvT+Vin+VDLIvIp2Vin−VoVo+VD.According to equation (6), the charge variation of the output capacitor during one switching cycle T can be calculated as(7)Δq=SΔABC−SΔBOD+SΔCFE=Vin+VDLIp22Vin−VoVo+VD+12IvT−Vin+VDLIvIp2Vin−VoVo+VD.During the conduction time of the switch,Ip can be written as(8)Ip=Iv+Vin−VoLDT=Iv+Vin−VoVo+VDLVin+VDT.By combining equations (7) and (8), it is available that(9)Δq=IvT+Vin−VoVo+VD2LVin+VDT2.Therefore, the variation of the output voltage within one switching cycle can be calculated as(10)Δvo=ΔqC=IvCT+Vin−VoVo+VD2LCVin+VDT2.By choosing differentTH or TL, the variation of the output voltage within PH or PL can be obtained as(11)ΔvoH=IvCTH+Vin−VoVo+VD2LCVin+VDTH2,ΔvoL=IvCTL+Vin−VoVo+VD2LCVin+VDTL2.Based on equation (11), the output voltage iterative equation of the DCPT-controlled buck converter can be expressed as(12)vo,n+1=vo,n+IvCTH+Vin−VoVo+VD2LCVin+VDTH2,vo,n<Vref,vo,n+IvCTL+Vin−VoVo+VD2LCVin+VDTL2,vo,n≥Vref.According to the principle of the DCPT control technique,ΔvoH>0 and ΔvoL<0 should be guaranteed. Therefore, it is available that(13)−Vin−VoVo+VD2LCVin+VDTH<Iv<−Vin−VoVo+VD2LVin+VDTL.The control parameterIv can be determined by the preset input voltage range of the converter. Since the falling slope of the carrier signals vsaw,H and vsaw,L is Vref/L, the peak value of the carrier signals can be calculated when the frequencies of the carrier signals fH and fL and the valley current Iv are determined. Based on the analysis above, the parameters of the researched the DCPT-controlled buck converter are listed in Table 1.Table 1
Parameters of the DCPT-controlled buck converter.
Parameters
Value
Rated input voltage,Vin
12 V
Reference voltage,Vref
5 V
Inductor,L
100μH
Capacitor,C
560μF
Equivalent series resistance,RE
30 mΩ
FrequencyfL of carrier, vsaw,L
40 kHz
FrequencyfH of carrier, vsaw,H
20 kHz
Valley current,Iv
−0.5 AFrom equation (12), it can be known that the output voltage variations ΔvoH and ΔvoL vary with the input voltage Vin. In order to achieve ΔvoH>0 and ΔvoL<0, Vin would be limited within a valid range.Assuming the output voltage variation is zero in onePH switching cycle (ΔvoH=0), the lower boundary of the input voltage for the DCPT-controlled buck converter will be calculated as(14)Vin,min=Vo+VD2THVo+VDT−2LIv−VD.Similarly, assuming the output voltage variation is zero in onePL switching cycle (ΔvoL=0), the upper boundary of the input voltage will be(15)Vin,max=Vo+VD2TLVo+VDT−2LIv−VD.Substituting the parameters of Table1 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 PH and decrease during each PL; thus, the low-frequency oscillation can be avoided.By using equation (12), the relationship between the output voltage variation ΔvoH>0 and −ΔvoL<0 and the input voltage Vin can be obtained, as shown in Figure 3. It can be seen that, with the increasing input voltage, the variation of the output voltage ΔvoH>0 increases and −ΔvoL<0 decreases.Figure 3
Output voltage variation versus input voltage of the DCPT-controlled buck converter.


## 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,(16)μHΔvoH+μLΔvoL=0.By combining equations (12) and (16), it can be obtained that(17)μHμL=−Vin−VoVo+VDTL2−2LIvTLVin+VDVin−VoVo+VDTH2−2LIvTHVin+VD.Substituting the parameters shown in Table1 into equation (17), the relationship between the pulse ratio μH/μL and the input voltage Vin can be obtained, as shown in Figure 4. It can be known that, the pulse ratio μH/μL decreases gradually with the increase of Vin, which is caused by the increase of ΔvoH>0 and the decrease of −ΔvoL<0. Therefore, the proportion of the high-energy pulse PH in the pulse train gradually decreases with the increase in the input voltage.Figure 4
Pulse ratio versus input voltage of the DCPT-controlled buck converter.According to equation (17), the typical pulse train of the DCPT-controlled buck converter in the condition of different input voltages can be obtained, as listed in Table 2.Table 2
Pulse train of the DCPT-controlled buck converter at different voltages.
V
in (V)
μ
H/μL
Pulse train
8.49
3
3PH-1PL
8.68
2
2PH-1PL
9.2
1
1PH-1PL
10.83
1/3
1PH-3PL
12
1/5
1PH-5PL


## 3.3. Analysis of the Output Voltage Ripple

To analyse the output voltage variation, the capacitor currentic and output voltage vo of the DCPT-controlled buck converter within one switching cycle are shown in Figure 5.Figure 5
Capacitor current and output voltage of the DCPT-controlled buck converter.During [0,ton], the capacitor current ic (t) and the output voltage of the converter can be written as(18)ict=Iv+Vin−VoLt,(19)vot=1C∫0tictdt+ictREIvCt+Vin−Vo2LCt2+Vin−VoLREt.By taking the derivation of equation (19), one obtains(20)dvotdt=IvC+Vin−Vo2LCt+Vin−VoLCRE.Substituting the parameters listed in Table1 into equation (20), it can be known that the output voltage rises to the maximum at the time ton. Therefore, it is available that(21)ΔvppH=IvCton+Vin−Vo2LCton2+Vin−VoLREton.For the DCPT-controlled buck converter, the output voltage ripple is closely related to the pulse train. Taking the pulse train 2PH-1PL as an example, the capacitor current ic and the output voltage vo are shown in Figure 6(a). Obviously, the output voltage ripple of the converter is Δvo=ΔvppH+ΔvoH at this time.Figure 6
Output voltage ripple of the DCPT-controlled buck converter. (a) The case of 2PH-1PL. (b) The case of 1PH-3PL.
(a)
(b)In general, when the pulse train isnPH-1PL, the output voltage ripple of the converter is(22)Δvo=n−1ΔvppH+ΔvoH.When the pulse train is 1PH-nPL, the capacitor current ic and the output voltage vo are shown in Figure 6(b). Apparently, the output voltage ripple on this condition is(23)Δvo=ΔvppH.By using equations (21)–(23), the output voltage ripple Δvo of the DCPT-controlled buck converter can be calculated, as listed in Table 3. For the DCPT-controlled buck converter, the output voltage ripple increases gradually with the increase of the input voltage.Table 3
The output voltage ripple of the DCPT-controlled buck converter.
V
in (V)
Δ
v
o
H (mV)
Δ
v
pp
H (mV)
Δ
v
o (mV)
8.49
3.3
34.3
40.9
8.68
4.9
36.3
41.2
9.2
8.9
41.5
41.5
10.83
19.1
52.2
52.2
12
24.8
57.7
57.7


## 4. Simulation and Experimental Results

### 4.1. Simulation Results

To verify the theoretical analysis, the simulation results are provided in Figure7, which include carrier signal vsaw, control pulse vp, capacitor current ic, and output voltage vo.Figure 7
Simulation waveforms of the DCPT-controlled buck converter. (a)Vin = 8.68 V. (b) Vin = 9.2 V. (c) Vin = 10.83 V. (d) Vin = 12 V.
(a)
(b)
(c)
(d)As shown in Figure7(a), when the input voltage equals to 8.68 V, the pulse train is 2PH-1PL, the pulse ratio is μH/μL = 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 1PH-1PL, 1PH-3PL, or 1PH-5PL, 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 Figure7, the following conclusion of the DCPT-controlled buck converter can be obtained: as the input voltage Vin increases, μH/μL decreases gradually, i.e., the proportion of PH 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 currentIv 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 PH or PL, which indicates that the low-frequency oscillation does not exist in the DCPT-controlled buck converter.


### 4.2. Experimental Results

In order to verify and test the proposed technique, a prototype of the DCPT-controlled buck converter is designed with the parameters in Table1. 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 vsaw,H and vsaw,L. 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 Figure8(a). The pulse train is 2PH-1PL, 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 1PH-1PL, 1PH-3PL, or 1PH-5PL and the output voltage ripple is 40 mV, 50 mV, or 60 mV, respectively.Figure 8
Experimental waveforms of the DCPT-controlled buck converter. (a)Vin = 8.68 V. (b) Vin = 9.2 V. (c) Vin = 10.83 V. (d) Vin = 12 V.
(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 Figure8 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 DCPT-controlled 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 Figure9. When the load current increases from 2A to 3A, two high-energy 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 on-state resistor of the MOSFET, when the load current increases, the input voltage of the inductor will decrease slightly, which causes the proportion of PH in the pulse train to increase.Figure 9
Experimental transient waveforms of the DCPT-controlled buck converter while load changes.In order to verify the suppression effect on the low-frequency oscillation, the comparative experimental results are provided in Figure10. The control parameters of traditional PT-controlled buck converter are as follows: DH = 0.6, DL = 0.3, and T = 25 μs.Figure 10
Experimental waveforms.(a) DCPT-controlled buck converter. (b) PT-controlled buck converter.
(a)
(b)As shown in Figure10(a), the pulse train is 1PH-5PL for the DCPT-controlled CCM converter and the output voltage ripple is 60 mV. In contrast, the pulse train of the PT-controlled buck converter is 4PH-4PL, and the output voltage ripple is 120 mV, as shown in Figure 10(b). This phenomenon of successive several high-energy pulses followed by successive several low-energy pulses indicates that the low-frequency oscillation exists in the PT-controlled CCM converter. The low-frequency oscillation has not occurred in the DCPT-controlled CCM buck converter. The proposed DCPT control technique enjoys much better output characteristics compared with the traditional PT control technique.


## 4.1. Simulation Results

To verify the theoretical analysis, the simulation results are provided in Figure7, which include carrier signal vsaw, control pulse vp, capacitor current ic, and output voltage vo.Figure 7
Simulation waveforms of the DCPT-controlled buck converter. (a)Vin = 8.68 V. (b) Vin = 9.2 V. (c) Vin = 10.83 V. (d) Vin = 12 V.
(a)
(b)
(c)
(d)As shown in Figure7(a), when the input voltage equals to 8.68 V, the pulse train is 2PH-1PL, the pulse ratio is μH/μL = 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 1PH-1PL, 1PH-3PL, or 1PH-5PL, 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 Figure7, the following conclusion of the DCPT-controlled buck converter can be obtained: as the input voltage Vin increases, μH/μL decreases gradually, i.e., the proportion of PH 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 currentIv 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 PH or PL, which indicates that the low-frequency oscillation does not exist in the DCPT-controlled buck converter.


## 4.2. Experimental Results

In order to verify and test the proposed technique, a prototype of the DCPT-controlled buck converter is designed with the parameters in Table1. 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 vsaw,H and vsaw,L. 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 Figure8(a). The pulse train is 2PH-1PL, 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 1PH-1PL, 1PH-3PL, or 1PH-5PL and the output voltage ripple is 40 mV, 50 mV, or 60 mV, respectively.Figure 8
Experimental waveforms of the DCPT-controlled buck converter. (a)Vin = 8.68 V. (b) Vin = 9.2 V. (c) Vin = 10.83 V. (d) Vin = 12 V.
(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 Figure8 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 DCPT-controlled 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 Figure9. When the load current increases from 2A to 3A, two high-energy 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 on-state resistor of the MOSFET, when the load current increases, the input voltage of the inductor will decrease slightly, which causes the proportion of PH in the pulse train to increase.Figure 9
Experimental transient waveforms of the DCPT-controlled buck converter while load changes.In order to verify the suppression effect on the low-frequency oscillation, the comparative experimental results are provided in Figure10. The control parameters of traditional PT-controlled buck converter are as follows: DH = 0.6, DL = 0.3, and T = 25 μs.Figure 10
Experimental waveforms.(a) DCPT-controlled buck converter. (b) PT-controlled buck converter.
(a)
(b)As shown in Figure10(a), the pulse train is 1PH-5PL for the DCPT-controlled CCM converter and the output voltage ripple is 60 mV. In contrast, the pulse train of the PT-controlled buck converter is 4PH-4PL, and the output voltage ripple is 120 mV, as shown in Figure 10(b). This phenomenon of successive several high-energy pulses followed by successive several low-energy pulses indicates that the low-frequency oscillation exists in the PT-controlled CCM converter. The low-frequency oscillation has not occurred in the DCPT-controlled 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 dual-carrier pulse-train 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 DCPT-controlled 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 low-frequency oscillation in the DCPT-controlled CCM buck converter. Compared with the traditional PT control technique, the DCPT-controlled buck converter enjoys better control characteristics and much smaller output voltage ripple.



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*Source: 7514621-2019-09-10.xml*