White LED Power Supply Based on Buck Converter with Active Ripple Compensation

Zhide TANG, Guantao WANG, Xiaohui XIE College of Electrical Engineering, Chongqing University, Chongqing 400044, P.R. China

Abstract—Considering that the lifespan of electrolytic capacitors in power supply don’t match that of LED, we propose a Buck converter which uses active ripple compensation circuit to replace the traditional electrolytic capacitor filter. When the converter works on long duty ratio, the power loss in compensation circuit is small and ripple current and voltage are low. The operation principle of this new topology with peak current mode control (PCM) is discussed. The transfer function of PCM with slope compensation is established. The current loop stability with different slope compensation is discussed through frequency response analysis. Finally, simulation and experiment results of the power supply for LED verified correctness of the theory.

Keywords-LED lighting; electrolytic capacitor; active ripple compensation; sub-harmonic oscillation; slope compensation

I. INTRODUCTION Electrolytic capacitor filters have widely used in LED

lighting driving power supply. The life expectancy of LED is typically 100,000 hours and much longer than that of electrolytic capacitors, which is typically 10,000 hours in the LED lighting[1]. Limited by the temperature-dependent lifetime of electrolytic capacitor, the lifespan of power supply don’t match the lifespan of LED. When the mean time between failures of switch power supply is discussed, electrolytic capacitors are the weakest components [1][2]. The available operation time of an electrolytic capacitor is restricted by ambient temperature and the temperature rise caused by the ripple current and ESR. The electrolyte will be gradually exhausted when the electrolytic capacitors work in high temperature, so that the performances decline [2] [3] [4].

We propose in this paper an LED power supply based on buck converter with active ripple compensation. The scheme adopts active ripple compensation circuit to replace the traditional electrolytic capacitor filter. In order to reduce the loss in compensation circuit, this topology should work on long duty ratio and low ripple current state. On the other hand, PCM with slope compensation can accurately control the peak current of inductor and operate on long duty ratio, so that PCM and buck converter with active ripple compensation may compose better LED driving power.

II. CIRCUIT TOPOLOGY AND RIPPLE COMPENSATION

A. Circuit Topology Fig. 1 shows the circuit structure of the novel topology. It

consists of switching main circuit and linear auxiliary compensation circuit. The main circuit is the traditional buck

circuit without electrolytic capacitor and it consists of switch tube K inductance L and freewheel diode D. The transistor T, which is working on active state, is the auxiliary compensation circuits.

T

D

L K

iC

iL

LEDVd

io

Fig. 1 Topology of buck with active ripple compensation

Supposing the inductor current iL and the compensating current iC respectively are

rL Li I i= +

C C ci I i= + IL and IC are the DC component of inductor current and

compensating current, ir and ic are theirs AC component (ripple current), as in Fig. 2.

t/s

iC

i/A iL

0

IL iO

IC

II

Fig. 2.Scheme of inductance ripple current compensation

When rci i= − , the output is

O L C C OLi i i I I I= + = =+ The output iO is DC, as in Fig. 2 . IL and IC respectively are

( )G

1

2L PI I I= +

( )min G1

2C PI I I= −

Ip and I G are the peak point and valley point of inductor current.

943978-1-61284-459-6/11/$26.00 ©2011 IEEE

B. Ripple Current Detection and Compensation

The relationship of ripple current and voltage of the inductor is

( ) ( )1r LL

i t v t dt=

Fig. 3 shows the schematic of ripple current detection and compensation. Assuming that all the components are ideal, then

( ) ( )1 1 1

1( )o L ro ov t V v t dt V

RC

Li t

RC= − = −

K

A A2

vl

v2

Vd

vL vo1

T

vo2 T

iC

iL

io

Fig. 3 Ripple current detection and compensation

The output of operational amplifier A1 is 0V when the inductive current is peak point, the initial value is:

( )1 2 P GoVL

I IRC

= −

So that the output of A1 is:

( )1

12o P G rv

LI I i

RC= −−

The compensating current of transistor T is

( )T

C12 P G r

L

R RCi I I i= −−

Setting Tk L RR C= , if we choose component values makes k=1,

C ri i= − , so that the inductive current can be whole compensation by the compensating current.

C. Loss Calculation of Compensating Circuit The LED string takes some white LEDs in series, and VO is

the voltage drop through the string. The loss in the compensating circuit is

LOSS ( ) ( )1 DOd C d CV V I V IP = − = − 1 From Eq. (1), we can know that this topology should work

on long duty ratio and low ripple current state in order to reduce the loss.

III. PEAK CURRENT MODE CONTROL

A. Principle of Peak Current Mode Control Fig.4 shows the principle of PCM. This control architecture

consists of two loops: one is the peak current control loop and another is the output voltage [5].

The aim of the inner is to adjust the peak current in the output inductance according to the reference given by the voltage regulator.

Current sensor

Voltage sensor

Converter

Peak current Mode control

regulatorVoltage Q H S

Vref

VO

iL

R

Fig. 4 Principle of peak current mode control

B. Inductive Current Oscillation and Slope Compensation Fig. 5 shows the current loop schematic of PCM: VC is the

continuous-time control voltage (Vref) minus compensating voltage ramp (Vramp), RSiL is the sensed voltage of the inductive current. During a switching cycle, from t = kTS to t = (k+1)TS, the inductive current ramps up linearly until it reaches VC, and then ramps down.

Q R S Vc

K

L

RS

Vref

Vramp

Vei

iL

RSiL

H

Fig. 5 Structure of current loop in peak current mode control

Assuming that the perturbation of inductive current is iL(k) at t = kTS, as in Fig. 6 the solid lines are the initial steady-state waveforms, the dash-dot lines are the perturbed waveforms . This will result the perturbation iL(k+n) is:

( )( ) ( )nL Li k n i kaΔ Δ+ = − 2

Where ( )2 1 1M M Da D= = − , M1 is the sensed inductor current on-time slope, -M2 is the sensed inductor current off-time slope, n is positive integer. We can see from Eq. (2) that: for duty ratio D<50%, M2<M1, <1, the perturbation will damp after several cycle and the system can gradually stability; for duty ratio D>50%, M2>M1, >1, the inductor current will oscillate, as in Fig. 6(a).

944

VC

kTS

M1 -M2

(k+1)TS (a)

(k+2)TS

S ( )L kR iΔ

VC VC,RSiL

kTS

M1 -M2

(k+1)TS (b)

(k+2)TS

S ( )L kR iΔ

-MC

VC

kTS

CvΔ

S ( +1)L kR iΔM1 M2

(k+1)TS

-MC

ktΔ

VC,RSiL

(c)

VC,RSiL

Fig. 6 Perturbation of inductive current This problem is solved by slope compensation, as in Fig.

6(b). In this case: ( ) ( ) ( ) ( )2 1 1 1C CM M M M D D Dα β β= − + = − − +

MC is the compensation slope and 2CM Mβ = .We can see that if we choose rationally to enable <1, the perturbation will damp even if D>50%.

C. Current Loop Model and Stability Analysis The inductor current will be caused perturbation when the

control voltage was disturbed, as illustrated in Fig. 6 c

S

( 1) (1 ) ( 1)1

L Ci k kR

vαΔ Δ+ = + + 3

Combining Eq. (2) and Eq. (3), the whole disturbing current is:

S

( 1) ( ) (1 ) ( 1)1

L L Ci k i k kR

vα αΔ Δ Δ+ = − + + +

Taking the z-transform, we get:

S

1( ) ( ) (1 ) ( )L L C

Rzi z i z z zvα α= − + +

thus S

(1 )( ) ( )

1L C

zi z z

R zvα

α+

=+

4

From Eq. (4) , we can see that there is a pole zp=- . When >1 the current loop is unstable as the pole being outside of the

unit circle. If choose suitable slope compensation ( <1), the current loop can be stable.

The continuous-time representation of Eq. (4) can be found from the z-transform expression by using the substitution z=esTs, and multiplying by 1/sTs, The continuous-time representation of Eq. (4) is then:

S S

1( ) ( )

s1s

s

sT

L CsTs sT R

ee

i vαα

+=

+−

5

The term esTs in Eq. (5) can be approximated with a second-order Padé function[6] [7]:

2 2

2 2

6 126 12

ssT s s

s s

s f s fe

s f s f+ +≈− +

This leads to 2

S

2 2

12( ) 6

( )( ) 1 121

L sC

Cs

iR f

s f

i sG s

aa

v s s+= = − +

+

6

The frequency response of the transfer function Gic(s) with different is shown in Fig.7 for fs=100 kHz and D=85%; The compensation coefficient respectively is 0 0.25 0.5 0.75

1, corresponding is 5.76 1.75 0.74 0.27 0.

=0

=0.25

=0.5

=0.75

=1

Fig. 7 Bode diagram of Gic(s)

Fig.7 shows that Gic(s) is approximately 1 for low frequencies, as RSiL follows VC. With the increase of frequency, Gic(s) exhibits signi cant peaking at approximately half the switch frequency. When is smaller, as 0 0.25, The phase margin of Gic(s) is less 0º and the system will be unstable; when is 0.5 0.75 1, the phase margin is greater than 0º, the system is stable. With the increase of , the phase margin is increasing. So the slope compensation can avoid current oscillation.

IV. SIMULATION AND EXPERIMENT RESULTS A power supply based on Fig.3 and Fig. 4 has been

implemented. The load consists of a LED string using 3 LEDs in series. Its peak current rating is 700mA. The total voltage

945

across this LED string load is Vo=10.2V. We have the main circuit parameters as fellow: Vd=12V L=100uH R=10kC=0.01uF RT =1 . IC UC3843 is used as a PCM controller (D=85%, =0.75).

A. Simulation result The simulation of iL and iC are shown in Fig. 9. Fig. 9 (a)

and (b) are the waveforms without slope compensation, iL and iC take signi cant oscillation. Fig. 9 (c) and (d) are the waveforms with slope compensation of =0.75, the waveforms of iL and iC are stable. These results verify that frequency response of the Gic(s): when the converter is operated in long duty ratio, the proper slope compensation is very necessary in order to improve the stability.

i C/A

i L/A

i L/A

i C/A

(a) waveforms of iL ( =0)

(b) waveforms of iC ( =0)

(c) waveforms of iL ( =0.75)

(d) waveforms of iC ( =0.75)

Fig. 9 Waveforms of simulations

B. Experiment result

iC

iL

(a) waveforms of iL and iC

(b) waveform of iO Fig. 10 Waveforms of experiment results

Fig.10 shows the result of experiment. From Fig.10 (a), we can see that iL and iC are stable and iO is a constant DC current. The measurement results as fellow IL=600mAIC=120mA iO =720mA Vo=10.47V. So the output power and the loss power in the compensating circuit is 7.34W and 0.18W, the loss is small.

V. CONCLUSION A novel topology of buck circuit without electrolytic

capacitors has been presented. The new topology adopts active ripple compensate circuit to replace the traditional electrolytic capacitors filter. A prototype of LED power supply using the topology controlled by PCM with slope compensation has been implemented and tested. The experiment result proves that the inductive current can be full compensation by the compensating current and the LED driver provides a constant output current.

REFERENCES [1] Qin Y X, Chung H S H, Lin D Y, et al. “Current source ballast for high

power lighting emitting diodes without electrolytic capacitor”, 34th Annual Conference of IEEE Industrial Electronics, 2008, Nov, Orlando. pp.1968–1973.

[2] Sunfeng Yan, Youren Wang, Jiang Cui, et al. Research on failure prediction method of electrolytic capacitor used in power conversion circuit. Journal of Electronic Measurement and Instrument, Vol 24, pp.29–33, Jan , 2010 (In Chinese).

[3] Hao Ma, Linguo Wang. “Fault diagnosis and failure prediction of aluminum electrolytic capacitors in power electronic converters”, 31st IEEE Annual Conference of Industrial Electronics Society, 2005, Nov, Raleigh, USA. pp. 842-847.

[4] A RIZ, D FODOR, O KLUG, et al . “Inner gas pressure measurement based life-span estimation of electrolytic capacitors”, 13th Power Electronics and Motion Control Conference, 2008, Sept, Poznan. Pp.2096- 2101.

[5] Charif Karimi, et al. “High frequency modeling of peak current mode control of DC-DC converters”, 2009 International Conference On Power Engineering, Energy and Electrical Drives. 2009, March, Lisbon. Pp.146-151.

[6] Ridley Raymond B. A new continuous-time model for current-mode control. Power Electronics IEEE Transactions, Vol 6, pp271-280. Apr 1991.

[7] B Bryant, M K Kazimierczuk. Modeling the closed-current loop of PWM boost DC-DC converters operating in CCM with peak current-mode control . IEEE Transactions on Circuits and Systems I:Regular Papers, Vol 52, pp2404-2412 . Nov 2005.

946