Analysis and Measurement of DCM Power Factor Correctors Kin-Siu Fung, Wing-Hung Ki and Philip K.T. Mok

Integrated Power Electronics Laboratory Department of Electrical & Electronic Engineering

The Hong Kong University of Science and Technology Clear Water Bay, Hong Kong, China

Fax: (852) 2358-1485, Web site: http://www.ee.ust.hk/'ipel/

Abstmct- Analysis of active power factor correctors op- erating in discontinuous conduction mode is presented. In- put currents are modeled as series of triangular .pulses with appropriate duty ratios, from which the power fac- tors are computed for three common corrector topologies - the pulse width modulated (PWM) boost, the PWM fly- back and the hysteretic boost correctors. Power spectrums are also examined and the harmonic distortions of the dis- continuous input currents are computed. Circuit simula- tions and experimental results are presented in verifying the theoretical analysis.

Index Terms- discontinuous conducting current, power factor, power factor corrector, harmonic distortion.

I. INTRODUCTION

The power line supplies electrical energy for our daily consumption. Various appliances tapped to the line are not resistive, thus reducing the power factor seen by the line and contaminating the quality of the energy source. High power factor can easily be achieved by active power factor correctors (PFCs) based on switch mode power con- verter topologies operating in either continuous or discon- tinuous conduction mode (CCM or DCM). For CCM cor- rectors, the input current is shaped to be sinusoidal super- imposed with high frequency ripples, and the power factor could approach unity for small ripple amplitude. To main- tain CCM operation, very often a large inductor has to be used. The situation get worse for low power applications, and DCM control fits better. Moreover, DCM control usually reduces the circuit complexity, which translates to lower production cost and could gain a foothold in the consumer market.

A generic pulse-width modulated (PWM) PFC imple- mentation is shown in Fig. 1. Either a boost or a flyback converter is usually employed, while the buck topology is rarely considered since part of the input voltage must be lower than the output voltage, introducing serious distor- tion to the input current. In Fig. 1, the peak inductor cur- rent is forced to align with the feed-forward rectified line voltage waveform to achieve a zero displacement angle. Hysteretic (or variable frequency) controller in Fig. 2 can also be used, whereas the RS flip-flop is set by the negative zero-crossing of the inductor current. A simpler strategy is to use fixed duty ratio in a PWM implementation [l], such that conventional voltage- or current-programming PWM controller can be used.

t This work is in part supported by the Hong Kong Research Grant Council CERG HKVST 765/96E.

'. - . . . . . . . . . - - . . . . . . - - - - - - - - - - - - - - - - - I

Fig. 2. Hysteretic controller for discontinuous PFCs.

DCM power factor corrector plays an important role in low power processing, yet its harmonic components intro- duce significant EM1 (electromagnetic interference) prob- lems. Prior research in power factor computation mainly focuses on either CCM correctors, or DCM correctors with filtered input current. Detail analysis is essential in deter- mining the various harmonic magnitudes, thus command- ing the design of the preceding EM1 filter. In this article, three DCM correctors are analysed. Firstly, average and apparent power are obtained to calculate the power factor. Secondly, harmonic distortion is examined by computing the power spectrum. Finally, these theoretical analysis are verified by circuit simulations and experimental mea- surement.

11. MODELING OF DCM INPUT CURRENT

Each converter has specific portions of the inductor cur- rent serving as the input current. For a boost converter, the input current is the same as the inductor current, while for a flyback converter, the input current is the

0-7803-5421-4/99/$10.00 Q 1999 IEEE 709

switch current. The discontinuous inductor current is now shaped as a chain of triangular pulses enclosed in a sinu- soidal envelope, Fig.3, with the following assumptions.

1. Output voltage V, is constant with negligible ripple; 2 . Input voltage Vp sin wi t is constant over one switch-

ing period Ts, i.e., ws >> wi, where wi and ws are the line and switching frequencies in radls;

3. Time constants of the converter are much larger than

PWM Boost

Tk Tk+l

PWM Hysteretic Flyback Boost 4

the switching period; (a) (bl 4. There are 4N switching cycles in a line period Ti; 5. Cusp and quadratic distortions of the input current Fig. 4. The kth input current pulses of PWM flyback and hysteretic

boost P F C s . are ignored [4].

For PWM control, the ICth inductor current pulse in each of the three time intervals of T i is

F1)r I kT1 W I T

Fig. 3. The inductor current and the k t h current pulse in PWM control.

where D l k , D 2 k and D 3 k are the duty ratios in s 1 , s 2 and S3 of the kth current pulse, m l k and m 2 k are the slopes of the inductor current during S 1 and S 2 and are

spectively. Therefore, the discontinuous conducting input current is formulated by the sum of these current pulses from one to 4N.

The corresponding duty ratios for the PWM boost cor- rector can be solved as [ 5 ] ,

to Ip s i n w i ( k - l + D l k ) T . and I , s i n w i ( k - l + D i b ) T . , re- DlbTa DakTa

Similar current model and parameters can be derived for the PWM flyback converter shown in Fig.4a where the input current consists of only the S1 portions. For the hysteretic boost PFC in Fig.4b, Ts is replaced by variable periods T k . The third state S 3 does not exist and kTs is replaced by r k = E,"=, T j .

TABLE I COEFFICIENTS OF GENERALIZED Z R M ~ AND Pavg.

111. COMPUTATION OF POWER FACTORS To compute the power factor with sinusoidal voltage

source, the root-mean-square (RMS) input current IRMS and the average input power P a v g are needed. Generalized expressions of these two parameters can be derived from the kth input current pulses of Fig.3, Fig.4a & b.

}1'2 ( 6 )

2 N

I R M S = z p (& Ab sin2 wi(Tk-1 + tlk) k=l 2 N

pavs = v , I ~ ~ ~ { s k s i n 2 w w i ( r r - l + t l * )

The corresponding coefficients A k ' S through T k - 1 ' ~ are listed in Table I, where t l k and t 2 k are the time inter- vals in S1 and S2, respectively. The power factor prior to filtering can be calculated from the ratio between the average and apparent power P a v g / ( V R M S I R M S ) -

A . Analytic solutions of power factors The above expressions may not be solved in compact

analytic forms, but duty ratio D l k can be approximated as constant D 1 = & in eqn. (3), and D a k as the peak of

710

S I I I U L P T l O W OF HlSlERETlt CONTROL I I T W B P N O ~ B P W D COWTROLLEP S l l l U L P T l O N OF WISTCRETIC CONTROL I I T W BPNO.BPND tONTROLLER

L, mH 1 1 ~ ~ ~ 1 lPavgl PF

a.) Rectified input voltage and output voltage.

PWM PWM Hysteretic Boost Flyback Boost

1.1 1.8 2.9 0.340 0.303 0.408 0.174 0.138 0.250 0.722 0.642 0.866

b.) Input current and a zoom in view.

Fig. 5. The simulation results of the hysteretic boost PFC.

eqn. (4), D2 = &. Simplified results are thus obtained for the PWM boost and flyback PFCs [4]:

PFboost M (8) 2

P F f l y b a c k 2 f i (9)

Observed that the input currents are non-zero during S1 and S2 for the PWM boost corrector and during S1 for the PWM flyback corrector, while the power factors are pro- portional to the square root of the duty ratios correspond- ing to the conducting periods d m and a. These approximations, although not very accurate, provide in- sights between the power factors and the duty ratios of conduction. Recall for the hysteretic boost corrector op- erating in CCM [6], the power factor is q,*, where a is the ratio of lower to upper boundaries of the induc- tor current. When the corrector operates at the bound- ary of CCM and DCM, i.e., a = 0, the power factor be- comes d / 2 , which is consistent with eqn. (8), since now D1 +D2 = 1.

Thus, all the expressions are closely related to &/2 and it is reasonable to suggest that the maximum power factor (prior to EM1 filter) of DCM correctors is limited by this value.

B. Numerical computation

For numerical computation, a criteria for the input cur- rent to be at the boundary of CCM and DCM when k = N ( D ~ N = 0 ) is imposed, such that the value of the inductor can be fixed. The power factor corrector is designed for an

TABLE I1 CALCULATION OF POWER FACTORS AND RELATED PARAMETERS.

electronic ballast of a 40W fluorescent lamp system with the following parameters:

0 P0=40W, efficiency q = go%, Vo = 380V;

Circuit parameters and computed power factors are shown in Table I1 for V, = 2 2 O a V . The normalized RMS current and average power are defined as 1 1 ~ ~ ~ 1 = IRMS / I p and I Pavg I = Pavg / ( VpIp) such that the compar- isons are independent of current and power levels. Ob- serve that power factor decreases its the conducting duty ratios decrease and the maximum value of DCM correctors is limited by &/2, as suggested in the previous section.

fs = lOOk Hz, fi = 50 Hz.

IV. CIRCUIT SIMULATION

The current waveforms of the three converters are simu- lated using HSPICE with conditions stated in section III- B. The PWM controller is replaced by a gate drive signal

711

0.0

1 0.8- 1 0.75

Fig. 6. The variation of power factor with different inductance and input voltages, Star line: Circuit simulations, Dash line: Theoretical calculation.

0.8

-OB-\ - ;O.=-\

-... 5 OJ- '.. ',

0.65. .-. ~

with constant duty ratio given by eqn. (3) and a band- band controller in Fig. 2 is employed in the hysteretic control.

Typical simulation waveforms of the rectified input volt- age, output voltage and rectified input current of the hys- teretic boost PFC are shown in Fig.5a and b. Although the input current consists of triangular pulses, the current peaks track the sinusoidal line voltage waveform and unity displacement factor is achieved.

Besides imposing the CCM-DCM boundary criteria at k = N , a lower inductance can be used to drive the PFC in deeper discontinuous conduction mode. The power factor therefore decreases as the inductance is reduced, Fig. 6a. Note that an input voltage of 12ovRMs is used. Another parameter affecting the discontinuity of the input current is the peak input to output voltage ratio. Different supply voltages are available around the world, e.g. 22ovRMS in Hong Kong and 12ovRMS in USA. Such changes affect the power factors for different places with the same PFC de- sign. This variation is simulated by HSPICE and plotted in Fig. 6b along with theoretical computation.

V. POWER SPECTRUM ANALYSIS Power factor is closely related to total harmonic dis-

tortion (THD) and affects the degree of electromagnetic interference (EMI), and international standards such as IEC-1000 and IEEE519 [7], [8] set limits to individual harmonic amplitudes. Harmonic components can be eval- uated by taking the fast Fourier transform (FFT) of the DCM current waveforms for the three correctors men- tioned. The computed power spectrums with sinusoidal input of 22ovRMS are shown in Fig. 7.

200 300 400

TABLE 111 HARMONIC MAGNITUDE OF THE THREE CORRECTORS WITH 220K,.

~~ ~~

-12.55dB -10.66dB -18.61dB - 12.54dB -25.57dB -16.01dB

1 Freuuencv. k Hz 11 PWM Boost I PWM Flvback I

500 600

I 100 11 -5.50dB I -2.66dB I

-35.60dB -16.86dB -39.44dB -19.10dB

Peak Harmonic ~

- 17.03dB

Hysteretic Boost PFC

As predicted, the PWM correctors give rise to high or- der harmonics at the multiples of the switching frequency, while the hysteretic boost corrector demonstrates wide frequency range harmonics. The harmonic magnitudes are summarized in Table I11 and the corresponding THDs and power factors (with unity displacement factor) are tabulated in Table IV.

VI. MEASUREMENTS Two prototypes of power factor correctors are con-

structed and their performance are measured. A PWM boost corrector is designed using ML4812 from Micro Lin-

712

0.2 0.4 0.6 0.8 1 1.2 frequency, MHz

V R M ~ P F

01 I ! I

PWM boost Hysteretic boost

120 220 120 220 0.8395 0.7572 0.8497 0.8369

-201 I I I I f I I I I 1 I -I

PFcal THD, %

-401 ......I ........ 1.. ,..I .. . . . . . I ....... I ........ I , .,,.I .. . . . . . I... ...I .... .I. (b) ..I...... 4

0.8230 0.7216 0.8660 0.8660

64.55 85.92 61.99 65.34

... frequency, MHZ

PWM PWM Boost Flyback

THD, % 95.91 118.03 PF. ~ 5 1 = 0 0.7217 0.6464

01 I 1

Hysteretic Boost

57.70 0.8661

-201 Lr. 4

-""O 0.2 0.4 0.6 0.8 1 1.2 frequency, MHz

Fig. 7. Power spectrums from the Fourier transform analysis of the three PFC' topologies, a.) PWM boost, b.) PWM flyback and c.) Hysteretic boost.

TABLE IV TOTAL HARMONIC DISTORTION AND THE CORRESPONDING POWER

FACTOR WITH ZERO DISPLACEMENT ANGLE

ear [9], and the other is a hysteretic boost converter using MC33262 from Motorola [lo]. The experimental setup is shown in Fig. 8 for measuring both power factors with and without an EM1 filter. The measured DCM current wave- forms for both correctors are shown in Fig. 9 for a sinu- soidal input voltage of 22OvRMS. Triangular pulses with peaks following a sinusoidal voltage envelope is obtained, but 'dead-angles' are observed at the zero-crossings of the line voltage, which increases the harmonic content and degrades the power factor. The power factors of the two correctors with input voltages of 12ovRMS and 22ovRMS are listed in Table V. Comparing the calculated values Peal with those measured, the power factors are reduced for the hysteretic boost PFC, but those of the PWM boost PFC are increased. The reason is that the middle portion of the input current of the PWM boost corrector enters the CCM region which increases the power factor.

HPBSBlE

Fig. 8. The equipment setup for power factor and power spectrum measurement.

TABLE V MEASURED POWER FACTORS AND THDS FOR TWO INPUT VOLTAGE

The DCM input currents of the two correctors are fed to the power spectrum analyzer and harmonic components are obtained and shown in Fig. 10a and b. The results correlate well with theoretical computation as previously shown in Fig. 7a and c, validating our analysis. Total harmonic distortion are measured and listed in Table V for comparison.

VII. CONCLUSION

The discontinuous current waveforms of three common power factor correctors with high frequency switching r i p ples are analysed. With appropriate approximations, it can be shown that the power factor of a corrector (prior to the addition of an EM1 filter) is proportional to the square root of the sum of duty ratios with non-zero in- put current. An important observation follows: for PWM corrector, the power factor of a boost corrector is better than that of a flyback corrector, which is the reverse of the case with filtered input currents [l]. In fact, if the high frequency currents are filtered (perform averaging math- ematically) for computing the power factor, the flyback corrector performs better. Now, by calculating the power spectrum of the un-filtered DCM current, the amplitudes of individual harmonics can be pinpointed, such that an optimal EM1 filter can be designed to meet a particular harmonic standard such as IEC-1000. The variation of power factor with respected to the changes of inductance and valley-to-peak voltage ratio are investigated. Both circuit simulations and measurement of correctors verify the accuracy.of the analysis.

713

a.) PWM boost PFC. b.) Hysteretic Boost PFC.

Fig. 9. The measured input current waveforms of PWM boost and hysteretic boost PFC with 22ovRMs input voltage.

0 0

-1 0 -1 0

-20 -20

-30 -30

0 4 0 e -40

-50 -50

-60 -60

-70

-80 0.2 0.4 0.6 0.8 1.2 0.2 0.4 0.6 0.8 1 1.2

Frequency, MHz Frequency, MHz

a.) PWM boost. b.) Hysteretic boost.

Fig. 10. Measurement of the power spectrums of the two PFCs with 22ovRMs input.

ACKNOWLEDGMENT [9] M.K. Nalbant, ‘Power Factor Calculations and Measurements’,

[lo] Motorola, ‘Power Factor Controller MC34262/MC33262’, Ana- IEEE APEC ’90 Conf. Rec., March, 1990.

log/Interference ICs-vol. I , pp.7.39-7.52, 1995. The authors would like to thank Micro Linear and her

Hong Kong distributor Memec Asia Pacific Ltd. for pro- viding technical support and samples of controller IC.

REFERENCES C.K. Tse, ‘Zero-Order Switching Networks and Their Appli- cations to Power Factor Correction in Switching Converters’, IEEE %ns. on Circuit and Systems-I, Vol. 44, No. 8, pp. 667-675, August, 1997. D. Maksimovic, ‘Design of the Clamped-Current High-Power- Factor Boost Rectifier’, IEEE h n s . on Industry Application, Vol. 31, No. 5, pp.986-992, September, 1995. A. Abramovitz & S.B. Yaakov, ‘Current Spectra Translation in Single Phase Rectifiers: Implications to Active Power Factor Corrections’, IEEE h n s . on Circuit and System - I, Vol. 44,

K.S. Fung, ‘Analysis and Measurement of DCM Power Factor Correctors’, M.Phi1. Thesis, Hong Kong University of Science and Technology, August, 1998. C. Zhou, R.B. Ridley & F.C. Lee, ‘Design and Analysis of a Hysteretic Boost Power Factor Correction Circuit’, IEEE PESC ’90 Conf. Rec., pp.800-807, June, 1990. D.S. Chen & J.S. Lai, ‘A Study of Power Correction Boost Con- verter operating at CCM-DCM Mode’, Proceedings of IEEE Southeastcon ’93, April, 1993. T.S. Key & J.S. Lai, ‘Comparison of Standards and Power Sup- ply Design Options for Limiting Harmonic Distortion in Power Systems’, IEEE %ns. on Industry Applications, Vol. 29, pp. 688-695, July, 1993. T. Williams, EMC for Product Designers, Newnes, 1996.

NO. 8, pp.771-775, August, 1997.

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