Abstract— The purpose of this paper is to present a new digital control boundary current mode buck-boost dc-dc converter. This buck boost dc-dc converter is intended for use as the low power converters, such as solar and wind power generation. The buck-boost dc-dc converter is widely used in the energy management field, because it has capability to obtain the wide input range characteristic. Moreover, the circuit configuration is very simple. However, it also has the disadvantage likely to be unstable system. On the other hand, the dc-dc converter that operates in a boundary current mode has the some advantages. This paper presents a consideration of the prediction error of the zero-cross point. In the proposed method, the current zero point of the inductor is predicted using the equations based on the nonlinear analysis of the output voltage and input voltage. The simulation results show that the zero-cross point detection error is attributed to the resolution error of the A-D converter and DPWM. Index Terms-- Buck-boost dc-dc converter, Digital control, Boundary current mode, Nonlinear equation.

I. INTRODUCTION In recent years, the power supply system plays an

important role in renewable energy systems. In the renewable system, the input voltage of the power supply fluctuates. Therefore, the dc-dc converter which has a wide range input voltage is required. Since it has capability to obtain the wide input range characteristic, the buck-boost dc-dc converter is widely used. The buck boost dc-dc converter is useful for low power applications. Especially, the dc-dc converter that operates in a boundary current mode has the some advantages. It is expected to have a high efficiency has also a low switching noise. Recently, the digital control has been attracting attentions are to speeding up of the processing speed of the CPU and reducing the cost. While a digital control has negative elements for response such as the processing time of digital control circuit and A-D conversion time, it is possible that the addition of the monitoring function and the complex processing is easy to implement. Therefore, the digital control realizes simultaneously of high reliability and high conversion efficiency [1]-[5].

In the conventional reactor current zero-crossing point detection method using the A-D converter, there is a

This work is supported in part by the Grant-in-Aid for Scientific Research (No.21360134) of JSPS (Japan Society for the Promotion of Science) and the Ministry of Education, Science, Sports and Culture.

delay time when the sampling frequency of A-D converter is low. Hence, it is necessary to use the high sampling frequency A-D converter. However, this causes the high cost system. In another approach, the zero-cross point is predicted by calculating the slope of reactor current. In this method, a large error can exist because it is calculated by linear equations. In addition, the sensing resistor of reactor current causes a large power loss [6]-[8].

This paper presents a new digital control boundary current mode buck-boost dc-dc converter without a current detector. In the proposed method, the reactor current zero-crossing point is predicted using the equation based on the nonlinear analysis of the output voltage and input voltage. The proposed method needs no sensing resistor of reactor current. Therefore, the proposed method is excellent in the power efficiency compared to conventional one.

II. OPERATION PRINCIPAL AND CIRCUIT CONFIGURATION Figure 1 shows a basic circuit diagram of conventional

buck-boost digital control dc-dc converter. Figure 2 shows the basic circuit diagram of proposed buck-boost digital control dc-dc converter. Ei is the input voltage, eo is the output voltage, R is the load resistance, Tr is the switch, D is the diode, L is the inductor, C is the capacitor and iL is the current of inductor. In the conventional method, the inductor current, input voltage and output voltage are detected. On the other hand the proposed method, it is necessary to detect only the input voltage and output voltages, as shown in Fig.2. The output voltage is sent to the calculation circuit to predict the zero point of the inductor current. Moreover, the output voltage is also sent to the PID control circuit to determine the pulse width of the driving signal. Figure 3 shows the configuration of the proposed digital control circuit. The output voltage and input voltage is sampled. Then, it is sent to the A-D converter through the anti-aliasing filter. The output voltage is converted to the digital value Neo. The digital value Neo is sent to the P-I-D control part and an arithmetic processing part where the off-time of Tr is predicted. The on-time of the drive signal for main switch Tr is determined based on the Neo. Then off-time of the drive signal for Tr is determined based on the on-time of main switch and digital value of the output voltage, Neo.

A New Digital Control Boundary Current Mode Buck-Boost DC-DC Converter

Fujio Kurokawa and Kota Ueno Nagasaki University, 1-14 Bunkyo-machi, Nagasaki, 852-8521 Japan

978-1-4673-1301-8/12/$31.00 ©2012 IEEE

2012International Symposium on Power Electronics,Electrical Drives, Automation and Motion

1301

The drive signal for a main switch Tr is generated by the DPWM signal generator using clock pulse (CLK).

Figure 4 shows the sample timing chart. Firstly, the output voltage is sampled. As shown in Fig.4, the delay time from the calculation is considered. The delay time includes one or two switching cycle. The output voltage is converted to digital value by A-D converter and sent to the calculation is circuit to predict the zero point of the reactor current is also sent to the PID control circuit. Then, the pulse width is determined by the PID controller. The off time of the switch is calculated based on the output voltage eo, input voltage Ei and the on time of switch.

The operation of proposed digital control is as follows. An operational state I (Tr:ON,D:OFF) and operational state II (Tr:OFF,D:ON) of the circuit operation. Equation (1) is the expression of the inductor current iL1 in the operation state I. Equation (2) denotes the expression of the inductor current iL2 in the operation state II. Inductor current zero cross point is predicted numerical analysis. In the proposed method, Newton method is used. Firstly, the peak value of inductor current is determined by Eq (1). To predict the zero crossing point, the left side of Eq (2) (iL(t)) is assumed to be equal to 0. Then, Q1, Q2, Q3, B3, B4, is numerically calculated to satisfy the equation. As a result, the boundary current mode is realized by detecting the output voltage and input voltage. Here, A1, B3, B4, Z1, Z2, Q1, Q2 and Q3 are the circuit parameter in Fig.2.

( ) ( ) ( ){ }11121 --exp ttAtZZtiL += (1)

{ })-(exp)}]-(sin{)(

)-(cos{)([)(

232423

2421

ttBttBtQttBtQQti L

+

+=

(2)

Equations (3) through (9) are obtained from the equivalent circuit of operating state I (Tr:ON,D:OFF).

LrA 1

1 =

(3)

( ) ( )112 titA L= (4)

LEA i

*

3 =

(5)

11 LTri rrrr ++= (6)

Trii VEE -* = (7)

1

31 A

AZ =

(8)

( ) ( )1

31212 -

AAtAtZ =

(9)

In this case, ri is the internal resistance of power supply, rTr is the on-resistance of the transistor, rL1 is the winding resistance and effective series resistance of the inductor core losses, VTr is the voltage drop on period. Equations (10) through (21) are obtained from the equivalent circuit of operating state II (Tr:OFF,D:ON).

21

3aB =

(10)

24DB =

(11)

221 4a-aD = (12)

( ) ( )c

c

c rRLRr

Lr

rRCa

+++

+= 2

11

(13)

���

����

�++=

crRrR

LCa 2

21

(14)

( )c

D

rRLCEa

+= -3

(15)

( ) ( ){ } ( ) ( )22241- ti

rRLCCRrLteE

Lta L

c

coD +

+++=

(16)

( ) ( )225 tita L= (17)

22 LD rrr += (18)

2

31 a

aQ =

(19)

( ) ( )2

32522 -

aatatQ =

(20)

( ) ( ) ( )42

3331

4

253

4

2423 -

BaBaaa

BtaB

BtatQ ++=

(21)

Fig. 1. Conventional digital control buck-boost dc-dc converter.

Fig. 2. Boundary current mode digital control

buck-boost dc-dc converter.

C R

D

Digital PIDControl circuit

DPWMGenerator

L

n : 1

A-DConverter

eo

rT

Ei

SG

oi

C R

D

eo

rToi

Ei

SG

Digital PIDControl circuit

Zero CrossCalculation

DPWMGenerator

L

n : 1

NTon

NToff

A-DConverter

A-DConverter

eo

Ei

1302

Fig. 3. Configuration of proposed digital control circuit.

Fig. 4. Operating principle of proposed method.

III. PERFORMANCE CHARACTERISTICS Figures 5 through 7 show the simulation results. The

output target value is 5V, the inductor L is 20�H and the capacitor C is 470�F. The number of bits of the A-D converter is 10. In this case, ri is the internal resistance of power supply, rTr is the on-resistance of the transistor, rL1 is the winding resistance and effective series resistance of the inductor core losses, rD is the forward resistance of the diode, rL2 is the winding resistance and effective series resistance of the inductor core losses, rC is the effective series resistance. Figure 5 shows inductor current waveform, case one ri =0.1�, rTr =0.1�, rL1 =0.35�, rD =0.1�, rL2 =0.35�, rC =0.027�. In proposed method, the bias value NB is fixed to 141. The proportional coefficient KP is equal to 5, integral coefficient KI is equal to 0.025 and the differential coefficient KD is equal to 3. The simulator used here is the PSIM. The switching frequency is variable.

Figure 5 shows the simulation results of inductor current waveforms. Figures 5(a) and 5(b) show results in case of R=5� and R=10�, respectively. As it can be seen in the Figs. 5 (a) and (b), the boundary inductor current mode is maintained by the zero cross point predictive calculation. In the conventional voltage control method, under the light load condition, the buck-boost converter operates in the discontinuous mode. However, in this predictive

digital control, the boundary inductor current

(a) R=5�

(b) R=10�

Fig.5. Inductor current. mode is maintained. As shown in Fig. 5, under the light load condition, the current boundary mode is maintained even when the load changes.

A. Characteristics against change of resolution. Figure 6 shows the inductor current waveform when the

resolution of A-D converter and DPWM are changed. The circuit parameters are R=5� and Io=1.0A. Figures 6(a) through (c) show the inductor current waveform. The switching frequency of converter is 100kHz. Figure 6(a) shows inductor current waveform in case that the number of bits of A-D converter and DPWM are 8 bits. The resolution of DPWM is 40ns. In this case, the dead time of the simulation is 44ns. Fig. 6(b) shows the waveform in the condition that the number of bits of A-D converter and DPWM are 10 bits. Therefore, the resolution of DPWM is 10ns. In this case, the dead time of the simulation is 11ns. Similarly, in Fig. 6(c), the number of bits of A-D converter and DPWM are 12 bits. The resolution of DPWM is 2ns. In this case, the dead time of the simulation is 2.9ns. In those simulation results, it is assumed that the prediction calculation cause one switching cycle delay. It is confirmed that the calculation error is decreased by increasing the number of bits. The decreased calculation error makes the dead time smaller. The simulation results show that the zero-cross point detection error is attributed to resolutions of the A-D converter and DPWM.

eo Ei

A-D Converter

Anti-Aliasing Filter

Zero Cross Calculation

NEOPID Control

DPWMSignal

Generator

CLK

To Drive Circuit

Digital Signal Processor

A-D Converter

Anti-AliasingFilter

NEI

NTon

NToff

NTon

SG

iL

PID Control

t1 t2 t

t

: Sampling Points of Ei and eo

t0

Zero Cross Calculation

Ton Toff

1.0

2.5

2.0

L(A

)i

0.5

0 5.0 10.0t (�s)

15.0

1.5

3.0

20.0

1.0

2.5

2.0

L(A

)i

0.5

0 5.0 10.0t (�s)

15.0

1.5

20.0

3.0

1303

(b) Q=8 bits.

(c) Q=10 bits.

(d) Q=12 bits.

Fig. 6. Enlarged Inductor current.

Fig. 7. Trajectory of switching frequency against change of io.

Figure 7 shows the switching frequency according to the

load current. From this figure, it is seen that the switching frequency is increased when the output current is decreased. When the load current is 1A, the switching frequency is 100kHz, while the switching frequency is 330 kHz when the load current is 0.1A. Figure 7 shows the trajectory of switching frequency against the change of output current io. As it can be seen, the boundary current mode is maintained by the variable switching frequency.

B. Transient response Figure 8 shows the simulation results of averaged output

voltage. The voltage ripple is small so it is neglected. In this case, the capacitor is 2000�F. The proportional coefficient KP is equal to 5, integral coefficient KI is equal to 0.05 and the differential coefficient KD is equal to 3. Figure 8(a) shows the transient response when the step change in load is occurred. As shown in Fig. 8(a), the undershoot and convergence time Tst are 212mV and 3.84ms, respectively. Figure 8(b) shows the transient response of the input voltage step change. As it can be seen, the undershoot and the convergence time Tst are 128mV and 3.41ms, respectively. The undershoots is suppressed within 5% of the desired output voltage.

(a) Step change of R.

(b) Step change of Ei.

Fig. 8. Transient response characteristics.

L(A

)i 0.02

0 20.0t (ns)

40.0 60.0 80.0

44ns

0.04

100.0

L(A

)i 0.02

0 20.0t (ns)

40.0 60.0 80.0

11ns

0.04

100.0

L(A

)i 0.02

0 20.0t (ns)

40.0 60.0 80.0

2.9ns

0.04

100.0

f s(k

Hz)

Io (A)

0 0.2 0.4 0.6 0.8 1.0 1.2

100

200

300

400

o(v)

e

5.0

5.4

t (ms)

5.2

4.8

4.6

1%

Convergence time:3.84ms

Undershoot:212mv

0 2.0 6.0 10.0 14.0 18.0

o(v)

e

5.0

0 2.0

5.4

t (ms)

5.2

4.8

4.6

1%

Convergence time:3.41ms

Undershoot:128mv

6.0 10.0 14.0 18.0

1304

IV. CONCLUSIONS The boundary inductor current mode is maintained by

applying the proposed digital control method. In the proposed digital control method, the zero cross point of inductor current is predicted by the calculation using the output voltage and input voltage. The switching frequency is variable so that the inductor current boundary mode in maintained. As a result, the boundary current mode is realized by detecting the output voltage and input voltage. It is also confirmed that the zero-cross point detection error is attributed to the prediction error and resolution error of the A-D converter and DPWM by the simulation results.

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