The Discontinuous Conduction Mode Sepic and ´ Cuk Power

SIMONETTI et al.: SEPIC AND ĆUK POWER FACTOR PREREGULATORS 631
(a) (b)
(c) (d)
Fig. 3. A Sepic DCM–PFP. (a) First stage of operation. (b) Second stage. (c) Third stage. (d) Inductor currents.
loop is not necessary. Second, input–output isolation is easily
implemented. Finally, the input current ripple is defined at
the design stage by the correct choice of magnetic component
values. The converters work with zero-current turn-on in the
switch and zero-current turn-off in the output diode, but with
high rms current and voltage stresses, which limits their
application range. Also, it is necessary to consider inherent
problems caused by an isolation transformer (e.g., leakage
inductance) if one is used.
In the following sections, the operating stages are presented
for both converters as DCM–PFP’s, along with the design
equations and a small-signal model. Some design examples,
simulations, and experimental results complete the analysis.
In this paper, DCM means that each switching period presents
a time interval in which neither the switch nor the output diode
is conducting (freewheeling stage).
II. ANALYSIS OF OPERATION
A Sepic PFP with input–output isolation is shown in
Fig. 1(a), and a similar Ćuk PFP is shown in Fig. 1(b). In
the analysis, the output stage is referred to the primary side of
the transformer, and the resulting Sepic and Ćuk topologies are
shown in Fig. 2(a) and (b), respectively. Because of space, in
the following figures, only the Sepic operation is considered,
but a similar development can be made for the Ćuk converter.
Equations for both converters are identical, provided that, for
the Sepic converter,
and for the Ćuk converter,
(1)
(2)
For the Sepic converter, the capacitor voltage is equal
to the input voltage, whereas, for the Ćuk converter, it is the
sum of input and (referred) output voltage.
A. First Stage of Operation
This stage is shown in Fig. 3(a). The inductor currents are
defined as
and can be seen in Fig. 3(d). This stage is defined by the ON
time of the switch ( ).
B. Second Stage of Operation
The second stage is shown in Fig. 3(b), and and
are given by
This stage finishes when and lasts
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(3)
(4)
(5)