Technical Artical

Discussions on Various Chopper Circuits for Power Factor Corrections


In general, for power factor correction circuits, whose input current waveform is given by nearly sinusoidal one, circuit is constructed by almost boost type choppers, so the output voltage control range is limited relatively to a narrow region. For alternative configurations, which can control over a wide range, the buck-boost converter including Cuk converter, Zeta converter, etc. can be mentioned for the power factor correction. Cuk converter type can control the output over a wide voltage range, and the input and output current flows are not interrupted where current is flowing continuously. By means of switch turning-on and off, however, it is required to transmit the total energy through capacitor, so that the capacity of converter is fairly reduced, as well as the requirement of double inductors of input and output circuits. Under such background, we had been considering and discussing for a novel power factor correction and its fundamental circuit for years. The first idea of fundamental circuit was presented(15) in 1988. However, it is found that this original circuit had been already presented by Landsman(6) in 1977 as canonical switching cell which is a basic circuit of various common dc-dc converters. In this paper, this circuit is termed CSC converter. After that, this circuit is introduced by Kassakian(11) in his book in 1991 with, own original idea. By our working group, however a novel power factor correction using such CSC converter had been presented and discussed. Under consideration of such converters, various buck-boost type converters are compared and discussed, with some procedures. An optimum dc-dc converter is pursuited as power factor correction.


Fig.1 shows various buck-boost type converters. Fig.2 shows the flowcharts of their power transmission.
In Fig.2, d is the on-duty cycle and d’ is the off-duty cycle. V, V and I, I are the input and output voltages, and the input and output currents, respectively. The V and V enclosed with circles represent the input and output voltages of the power supplies having respective values. The C and L enclosed with circles are the filter capacitor and inductor having respective values. This circle is termed as a port in this paper. Let us describe how to read this flowchart.
Firstly, in the well known buck-boost chopper in Fig.1(b), at turn on, VId is transmitted from V to L, and VI od is also simultaneously transmitted from C1 to L. On the output side, VoIod is also transmitted from C2 to V. During turn- off, VId’ is transmitted to C1, and VId’ is transmitted partly to Vo and partly to C2.
In the Cuk converter shown in Fig.1 (c), it is clear that the circuit operation is of duality with the above buck-boost converter. These symmetries are a manifestation of a general principle of circuit theory, which we call duality. Thus, current and voltage can be interchanged and each element can be replaced by its dual element, i.e., d for d’, C for L, etc. Thus, it can be seen that the appearance of the power transmission in the Cuk converter is of duality with the buck-boost chopper. 
By comparing the transmitted power, we can realize that power is transmitted alternately in a parallel path from V in the figures. As can be seen, the appearance of the power transmission of the CSC converter is identical to that of the Cuk converter, except that it is through single inductor for the CSC converter and through two inductors for the Cuk converter.
In the next place, we will examine Zeta converter and SEPIC converter. For Zeta converter in Fig.1(d), during turning on switch S, the power VId is transmitted from the input to L1. On the output side, the power VI0d which has been stored in the input capacitor, C1, and the power VId which has been stored in C2 during the off-period, are transmitted to L2 and output side, respectively. On the other hand, during turning off period d’, the power VId’ is transmitted to C1. During their period, it is assumed that as impedance of C1 receiving the power is small as compared to the internal impedance of the power supply and as the switching frequency is high sufficiently. As a result I  is flowing continuously and smoothly. On the output side, the power VoIid of L1 or VoIod of L2 are transmitted to C2 or Vo, respectively. Similarly, in SEPIC converter, during turning on and during turning off, analogous closed loops are completed in Fig.1(e).


Firstly, on the base of stray inductance in the circuit of Fig.1, the switching surge voltage characteristics are compared, where each inductance attached parenthesis represents the circuit stray inductance.
(a) CSC converter
In the figure, during turning-on, the input voltage applies across the primary stray inductance l1 and main inductance L, so the corresponding voltage applies and charges as follows,
As a result, this injected power for l1 is represented by
During turning-off period, this injected power is discharged into C as P2 and charges this capacitor. Charge and discharge power is identical each other,

Thus, the switching surge voltage on the base of stray inductance is completely absorbed by the main capacitor C, so that surge voltage does not generate entirely. On the other hand, for the secondary circuit stray inductance l2, during switching turning-off, by means of the discharge of stored energy, following voltage is applied,
As a result, the surge energy due to surge voltage is can be represented by
During turning-on period, this surge power is mostly transmitted toward the load as the output power P2’, even if it influences slightly toward primary circuit.
Thus, the power is transmitted toward the output and the surge voltage does not appeared.
(b) Buck-boost converter
As the stray inductance of the primary circuit, route V-C1 is closed loop due to capacitor, the influence due to switching does not happen. Due to the stray inductance l1 including switch S, as above procedure, the equation can be obtained during turned-on period, where l1 is charged like,
During turned-off period, this energy must be discharged, but there is no current path for discharge. As a result, extremely large surge voltage generates.
For the sake to indicate clearly such operation, such performance is represented by zigzag line like lightning flash, where there is no path for discharging place. These energies are shown by,

On the other hand, for the secondary stray capacitor l2 a similar equation to (3) is given as

This energy can be transmitted toward the load as

(c) Cuk converter
The primary stray inductance can be regarded as a part of the main input inductance, where L1 is much larger than l1, the influence of l1 is not considered.
For the center circuit loop, the input voltage is applied across the l2,

Thus, the stored energy during this period is

During turning-off period, there is no discharging path, then

This energy discharging path is indicated by zigzag line. The l3 in the output side loop is included in secondary main inductor, so the influence is included in this main inductance.
(d) Zeta converter
For l1 in the switch circuit, the stored energy is

this is charged identical to l1 in the primary circuit.
During turning-off period, as there is no discharging path, the similar a energy is discharged as a surge voltage. In the center circuit loop including C2 during the turning-off period, the following energy is charged by L1 toward l1, that is,

During turning-on period, the current in l2 through L1 is decaying through free wheel diode, where the energy is regenerated toward C2. As the voltage generation across the l2 is V+V, the value of such energy can be represented by

(e) SEPIC converter
For the l2 in the center switching loop, during on -period, the energy ?VI d is charged into l1, where I1 is the current flowing through l1, that is I1=Id’. During off-period, as these is no path to discharge, the zigzag line by lightning flash is represented as this operation. Finally, in the circulating loop including l2, during off-period, ?VI d’ is charged into l2, where I1 is circulating current during this period. During off-period, by the sum of the voltage V and V, P2 is discharged toward the output, where this procedure is developed like in (11).

In comparison among above results, all circuit has the zigzag line by lightning flash except CSC converter. As a result, we can say that CSC converter holds a dominant position compared to other converters. For Cuk converter, however, by means of making the area of S-C-D closed loop including the switch minimum, the stray inductance can be made reduced and the surge voltage fairly suppressed.


Fig.3 shows the voltage ripple model. Each circuit impedance is represented by  etc. In the power factor correction and the like, as the ripple characteristic in the input current is important, the ripple of the input current flowing through Z1 is to be resolved as ?I .
A. Comparison due to voltage ripple model
(a) CSC converter
The ripple current ?I for CSC converter is given by

If Zc is much less than Z1 and Z2, then

For the power factor correction, as the input current flow through utility network, the impedance Z1 is fairly large, and thus,

From this equation, it can be seen that Z2 should be selected by reduced value.
(b) Buck-boost converter
The ripple current ?I for buck-boost converter is

For CSC converter in (15), the current ripple ?v/ZL flowing through large impedance ZL, is necessarily suppressed. This ripple current may be divided into input impedance Z1 and output impedance Z 2. By means of suitable specification, the input impedance Z1 should be given by large value with compared to the output impedance. In such a way, ?I can be suppressed by much reduced value. As a result under such consideration, this converter is suitable as PFC circuit having large input impedance like utility network. In a case of buck-boost converter in (16), the current flow ?v/(Z1+Z2) through much reduced input and output impedance becomes much increased compared to that of CSC converter. The current is flowing and divided into Zc1 and Z1. Consequently, it is preferable that the input impedance should be fairly significant compared to Zc1. In such a way, ?I can be reduced. In (16), for fairly reduced impedance of input and output circuit, the outgoing ripple current ? v/(Z1+Z2) is large compared to that of CSC converter. This current is outgoing into input circuit by the ratio of Zc1/Z1. As a result, it can be seen that it is advantageous of specifying the reduced capacitor impedance. When thinking of large ?v/(Z1+Z2), however, we can say that the CSC converter is dominant relatively, compared to this buck-boost one.
(c) Cuk converter
In the figure, the applied voltage is appeared across Z1 according to the ratio of Z1 and L1. Thus,

(d) Zeta converter
From the voltage ripple model, the output impedance is fairly large compared to Z1 and Zc1 in the input side. Briefly,

e) SEPIC converter
The ripple voltage in parallel connection delivers separately toward input and output side according to their own impedance. On the input side, the input ripple voltage appears significantly because of large impedance Z1 compared to that of other converters.


In this paper, various buck-boost type converter was compared and discussed on the pursuit of ideal chopper circuit for power factor correction. The circuit principle are analyzed and discussed by using voltage model and the like. The surge generation mechanism is also discussed. By means of these analyses, it can be seen that CSC converter is most suitable for PFC circuit.

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