UDK 621.3:(53+54+621+66), ISSN 0352-9045 Informacije MIDEM 22(1992)1 , Ljubljana 
UNITY POWER FACTOR CORRECTION CIRCUIT BASED ON 
BOOST-BUCK DC-TO-DC CONVERTER WITH COUPLED 
INDUCTANCE 
Miro Milanovic, Franc Mihalič, Karel Jezernik, Danilo Zadravec, 
Alenka Planinc, Uroš Milutinovic 
KEYWORDS: power electronics, power factor correction, DC-TO-DC converters, coupled inductance, single phase circuits 
ABSTRACT: The Unity power factor correction circuits are nowadays becoming one of the most important requirements for all power electronic 
rectifiers (equipment). The idea of using coupled inductance in a single phase diode rectifier power factor correction circuits and the influence of 
the coupling factor on the current rip ple will be discussed in this paper. 
VEZJE ZA KOREKCIJO FAKTORJA MOČI ZASNOVANO NA 
BOOST-BUCK ENOSMERNEM PRESMERNIKU SSKLOPLJENO 
INDUKTIVNOST JO 
KLJUčNE BESEDE: močnos!na elektronika, korekcija faktorja moči, enosmerniki presmerniki, sklopljena induktivnost, enofazna vezja 
POVZETEK: Vezja za korekcijo faktorja moči postajajo vse pomembnejši sestavni del vseh naprav močnostne elektronike. V članku bo obdelano 
vezje za Korekcijo faktorja moči z uporabo sklopljenih induktivnosti, prav tako bo raziskan vpliv faktorja skJopljenosti na valovitost toka. 
INTRODUCTION 
Switch-mode power supplies, DC-AC converters for 
motor drive, (5, 8) require an AC-DC bridge rectifier, 
with a large filter capacitor. The capacitor is needed to 
give the specified output voltage ripple and to provide 
energy storage. Since the capacitor draws line current 
only when the output voltage is below the line voltage, 
the line current pulsates. This pulsating current causes 
a low power factor. Power supplies with such rectifica-
tion have less than 0.65 power factor (Fig. 1). 
•. or.aoot 
/ 
/ 
/ 
/' 
,/ 
'''OC~t::-:-, --------------:,.oc::+-~-' 
Fig. 1,' Input current waveform 
15 
Using the Fourier analYSiS, the line current can be 
expressed in terms of its fundamental frequency compo-
nent iS1 (shown by the dashed line in Fig.1) plus the other 
harmonic components. If Vs is assumed to be purely 
sinusoidal, only iS1 contributes to the ave rage power flow 
(2). In terms of the rms voltage Vs and the rms current 
IS1 of the fundamental frequency component of is, the 
ave rage power P, flowing through the rectifier, is: 
P = Vs Is1 COS c!l1 (1 ) 
where c!l1 is the phase shift between iS1 and Vs. The 
magnitude of the apparent power S is: 
S = Vs Is 
and the power factor is defined as: 
P IS1 
PF = -S = - cos c!l1 
Is 
(2) 
(3) 
From eq. (3), it can be noted that a large distortion in the 
line current will result in a small value of the current ratio 
IS1/1s, and hence, a small value of PF, even if cos c!l1 is 
close to unity. 
The unity power factor, ie. the current ratio IS1/1s and cos 
c!l1 are close to unity, can be achieved by the introduction 
of a high power factor correction circuits (HPFCC) (7). 
Informacije MIDEM 22(1992)1, str. 15-20 
The choice of power electronic converters is bas ed on 
the following considerations: 
- ln general, for HPFC circuits, electrical isolation be-
tween the utility input and the output of the circuit is 
not strictly required 
ln most applications, it is acceptable and in many 
case s desirable to stabilize the DC voltage Vd slightly 
higher than the maximum peak of the AC input 
voltage. 
Cost, power loss and size of the current shaping 
circuits should be as small as possible. 
From the set of diHerent available HPFC circuits for 
power factor correction, the boost-buck converter is 
chosen to be discussed. 
THE PROPOSED CIRCUIT 
The proposed circuit for current shaping shown in Fig. 2 
consists of a boost converter connected to the line, and 
a buck converter connected to the output capacitor. 
The boost part of the circuit, appropriately controlIed, 
forces the input current to be sinusoidal and in phase 
with the input voltage (5). Relatively high amount of input 
current ripple is caused by the switching frequency and 
depends on the value of the used inductance. It will be 
shown that the current ripple can be significantly redu-
ced using the effect of inductance coupling. Filtering of 
the input current ripple is accomplished by the buck part 
BOOST CONVERTER: 
IVd 
220 V N SWl 
Fig. 2: Boost-buck with coupled inductance 
Gate 
Drive 
16 
M. Milanovič, F. Mihalič, K. Jezernik, et al.: 
Vezje za korekcijo faktorja moči zasnovano na ... 
of the circuit. The coupled inductance for zero current 
ripple in DC-DC converters was introduce by Cuk and 
Middlebrook (3,4). 
Before describing how the current ripple can be reduced 
by inductance coupling, the state space equations of 
cascade boost-buck converter will be reviewed. 
For the two switch states (ON, OFF), the circuit opera-
tion shown in Fig.11 can be described by a set of linear 
time-invariant differential equations: 
during dTs (4) 
and 
x = A2X + b2Vg during (1-d)Ts (5) 
where: 
T 
X = (iu iL2 uc, UC2); Vg = Vin 
o O Lm 
L1 L2 - L~, L1L2 - L~ 
O O L1 L1 
A1= 
1 1 
L1L2 - L~ L1L2 - L~ 
-
C2 
1 O 
C1 RLC 1 1 
O 
C2 
O O 
BUCK CONVERTER: 
RL: 
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ J 
+ Vel,rel 
M. Milanovič, F. Mihalič, K. Jezernik, et al.: 
Vezje za korekcijo faktorja moči zasnovano na ... 
o 
o 
O O L2 Lm -
L1L2 - L~ L1L2 - L~ 
O O Lm L1 
A2= 1 O 
L1L2- L~ L1L2 - L~ 
1 O 
C, RLC, 
O 1 O O 
C2 
The operation of the boost-buck converter with coupled 
inductance is based on a very simple principle. During 
the ON time input current flow only through the induc-
tance L 1 (Fig. 3a). 
The slope of the inductance current diL1/dt depends on 
the input line voltage. By introducing the opposite volt-
age source VOPP (Fig. 3b), this slope can be reduced 
(Fig. 4). 
Voltage VOPP is due to the introduction of a buck 
converter and a coupled inductance between L1 and L2 
(Fig. 5). 
The slope of the inductance current can be determined 
from equation (4). 
(6) 
After making the following substitutions: 
Lm = k-/L1L2 
Fig. 5 
17 
Informacije MIDEM 22(1992)1, str. 15-20 
1 
L r--
I 
V. 
ln I 
I 
-1 __ 
1 
L 
LI 
r--
I + 
Vopp I V. ln 
I 
-1 __ 
Fig.3a,b 
i 
L 
di L 1 
= V. 
dl LI 
ln 
-- diu 1 = (VIII-VoPP) 
dl LI 
l 
Fig. 4 
Informacije MIDEM 22(1992)1, str. 15-20 
Vo = Ve1 
Ve2 = d Vo 
1 
Vo =-- Vin 
1 - d 
Fig. 6 
(buck-converter) 
(boost-converter) 
and rearranging, the final equation is obtained: 
dil1 I _ 1 Vin - k Vin 
dt ON - L1 1 - k2 
(7) 
Generally. it is desired that the slope dil1/dt decreases 
as the coupled factor k increases. By the well-known 
theorems of mathematical analysis, it will hold true when 
k satisfies the following inequality: 
JL(dil1 I J = - --.L k2Vin - 2kVin
2
+ Vin s:; O (8) 
dk dt ON L 1 (1 _ k2) 
Since the denominator of inequality (8) is always greater 
than O, the inequality is equivalent to: 
(9) 
The discriminant of the quadratic inequality (9) is equal 
to 4(vrn - Vrn). Therefore, all val~s of k sat~fy (9) if 
- - . 2 . 
Vin s:; Vin, If Vin> Vin, the equallty k Vin - 2kvin + Vin = O 
has two real solutions 
k
1
,2 = ~n ± -Vr-(~-in-J2-_-1- (10) 
Vin Vin 
Inequality (9) is satisfied by all k in the range 
[ O, ~n _ ~(~n)2 _ 1 ] Vin Vin 
18 
M. Milanovič, F. Mihalič, K. Jezernik, et al.: 
Vezje za korekcijo faktorja moči zasnovano na ... 
and is not satisfied by k in the range 
Using notation (12): 
Vin .~ 'A = =-, kmax = 'A - 'lA? _ 1 
Vin 
(12) 
the range of solutions of (9) (0,1) is further restricted to 
lo, krnax I. If k Il lo, krnax 1, the theorem as well as the 
experiment show that the slope of the current increases 
uncontrollably. 
SMALL SIGNAL ANALYSIS 
ln order to shape the input current of the boost-buck 
converter,it must operate under the current-mode 
control (Fig. 7). 
PI Error 
\, Contl'oller 
Fig. 7 
Current 
Il10cie 
control 
S.ri teh 
control 
signal 
Once iL1ref and il are available, there are various me-
thods to implement the current mode control of the 
boost-buck converter. In this section, the constant fre-
quency control is described in details. 
The transfer function iold can be obtained by the follo-
wing procedure (1,2), The description of the ave rage 
state-space model is given below: 
~I L2 Lm ( ) 
dl = 2
Vin + 2VinVC2-VC1 (13) 
ON L1L2 Lm L1L2 - Lm 
~I dt (14) 
The average state-space model is obtained as the sum 
of equations (13) and (14), after they are multiplied by d 
and (1-d) respectively, 
diLl I l2 Lm) (1 5) dON-OFF = --  (v," - VCI + Vcld)+ --2 (Vc,d + VC2 
t l,l2- L;;, L,L2- L;;, 
By introducing small signal perturbations in (15): 
iL1 = 1L1 + k. 1 
Vin = Vin +Vln 
Ve1 = Ve1 + Ve1 
Vc2 + VC2 + Vc2 
d=D+d 
(16) 
M. Milanovič, F. Mihalič, K. Jezernik, et al.: 
Vezje za korekcijo faktorja moči zasnovano na ... 
and considering that Vin= 0, Vc1= ° andvc2= 0, AC and 
DC components of (15) can be separated as follows: 
(17) 
(18) 
The transfer function il1/ d can be obtained by applying 
Laplace Transformations on eq. (18) and considering 
Vc1 = Vo. 
After substituting Lm = k--JL1 L2 and n = --JL1/L2 
upper equation, the transfer function becomes: 
'" 
Gid = iu (s) = Vo 1 - kn .1 
d(S) L1 1 - k2 S 
(19) 
in the 
(20) 
Fig. 8 shows the Bode plots of the transfer function 
expressed by (20). 
ln order to obtain the voltage transfer function, the 
following procedure can be used: the inductance current 
flows through the 'rest' of the filter (Fig.9) 
For the circuit shown in Fig.9 system of equations (21) 
can be obtained: 
~.~~---------------------c.~ 
Fig.10a,b,c,d 
Informacije MIDEM 22(1992)1, str. 15-20 
.11 ~ ______ l.-_______ -.L._----''--' 
lO • ItO -",tk. 
Fig.B 
C 2 
J:;jo Q 
Fig. 9 
I 
1.«-::' ±:\"'::--__ +-_______________ .;-;;.-:=_ 
k=O.S 
... ...: 
AA. tJ." J. kcO.7 
v Y v 'V"V 
o .• _ ......... 
19 
Informacije MIDEM 22(1992)1, str. 15-20 
T. , 
Fig. 11 
(21 ) 
The transfer function can be determined by using (21). 
(22) 
The transfer function vo(s)/iref(s) is needed for the volt-
age control design. 
G _ '0'o(S) _ GVi Gid 
v - lrel(S) - 1 + Gid (23) 
By dividing the control problem into two parts, it is 
possible to shape the inductance current (line current) 
and control the output voltage. 
SIMULATION RESULTS 
Fig.10 a,b,c and d show the simulation results for half a 
line period (10ms) and a part of the line current. The 
current ripple is reduced by factor 7.S. It is very important 
to note that the sampling frequency is the same in all 
cases. 
20 
M. Milanovič, F. Mihalič, K. Jezernik, et al.: 
Vezje za korekcijo faktorja moči zasnovano na ... 
The same ripple can be achieved if the sampling fre-
quency is increased by a factor equal to the reduction 
factor of the line current ripple (Fig.11). With coupled 
inductance, the power loss increases by 2 folds while 
with the increase of sampling frequency, it increases by 
factor 7.S. The sensitivity of the system to the compo-
nent value variations was checked by simulation. If the 
component value varies for 10%, the performance is 
quite satisfactory. 
CONCLUSION 
The goal of current ripple reduction with the coupled 
inductance lie s behind reduction of power loss. In 
comparison with current ripple reduction by increasing 
the switching frequency (Fig.2), the proposed circuit 
proves to be far superior. By using the Cuk and Middle-
brook optimal topology of DC-DC converter circuit for 
active waveshaping interface Š3C, even a better result 
can be achieved since only one switching element would 
be needed. 
REFERENCES 
(1) N. Mohan et al. Sinusoidalline Current Rectilication with a 100 
kHz B-sit Step up Converter. PESC 1984. 
(2) N. Mohan. T. Undeland W. Robins. Power Electronics Conver-
ters, Applications and Design; John Wiley & Sons, New York 1989. 
(3) S. CUk. Switching DC to DC Converter with zero input or output 
Current Ripple. Proceedings of IEEE Industry Applications Society 
Annual Meeting, October 1978. Toronto. 
(4) S. CUk. R.D. Middlebrook. Coupled Inductor and Other Exten-
sions of a New Optimum Topology Switching DC to DC Converter. 
IEEE Industry Applications Society Annual Meeting 1977. 
(5.) C. Zhou. R.B. Ridley, F.C. Lee, Design and Analysis of an Ac-
tive Unity Power Factor Correction Circuit. Proceedings VPEC, Bla-
cksburg VA.1988. 
(6) M. Kazerani et al, Programable input power factor correction me-
thods for single phase diode rectifier circuits APEC. LA 1990. 
(7) R. White. M. Sayani, High Power Factor AC-DC converters. Pro-
fessional Education Seminars Workbook, APEC '90, L. A., CA, 
March 11-16, 1990, pp. 1-52. 
(8) F. Mihalič. M. Milanovic and K. Jezernik, Unity Power Factor 
Rectification for an AC Motor Drive, IEEE Melecon '91, Ljubljana 
1991. SLO. Proceedings Volu me II. pp. 1421-1424. 
Miro Milanovi6, Franc Mihalič, Karel Jezernik, Oanilo 
Zadravec, Alenka Planinc, Uroš Milutinovi6* 
University of Maribor Faculty of Technical Sciences 
Smetanova 17 
62000 Maribor, Slovenia 
*Faculty of Education 
Koroška cesta 160 
62000 Maribor, Slovenia