The Discontinuous Conduction Mode Sepic and ´ Cuk Power

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SIMONETTI et al.: SEPIC AND ĆUK POWER FACTOR PREREGULATORS 633 Therefore, can be obtained considering the specified maximum current ripple: and (24) (25) ( normally is a percentage of the fundamental input current .) H. The Design of the Intermediate Capacitor In conventional Sepic and Ćuk converters, the capacitor voltage is assumed to be constant. When operating as a PFP, the capacitor voltage is under the following two conflicting constraints: 1) to present a nearly constant value within a switching period and 2) to follow the input voltage profile within a line period. Its value has a significant influence in the input current waveform. The resonant frequency of , , and must be much greater than the line frequency to avoid input current oscillations at every line half cycle. Also, the resonant frequency between and must be lower than the switching frequency to assure almost constant voltage in a switching period. A good initial approximation for is given by [9] where (26) (27) An isolated Ćuk converter presents an additional resonance caused by the transformer magnetizing inductance that might constitute a major problem [10]. In the Sepic converter, the magnetizing inductance is usually used as the inductor . I. Small-Signal Model A small-signal model can be easily obtained using the CIECA approach [11]. The following small-signal perturbations will be applied to both input and output average currents: where the caret means steady-state value and means the introduced perturbation (small-signal value). Applying the perturbations in (10) and performing the small-signal approximation ( ) results in (28) Fig. 6. Small-signal model equivalent circuit. where Repeating the procedure for (13) results in where (29) (30) (31) The equivalent electric circuit described by (28) and (30) is shown in Fig. 6. From the equivalent circuit, the transfer function for the particular application can be found. The equivalent small-signal impedance of the load is a function of the type of load the PFP is feeding. 1) Constant Impedance Load: The small-signal impedance is the actual load impedance: (32) 2) Constant Power Load: A PFP usually feeds a dc–dc converter [(switch-mode power supply (SMPS)]. An SMPS presents the following small-signal input impedance [12]: (33) 3) Constant Current Load: The load acts as a current source (e.g., a linear regulator). The small-signal impedance is (34) III. DESIGN EXAMPLE AND SIMULATION A Sepic PFP was designed with the following characteristics: t V; V; kHz s W Authorized licensed use limited to: ELETTRONICA E INFORMATICA PADOVA. Downloaded on April 12, 2009 at 16:08 from IEEE Xplore. Restrictions apply.
634 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 5, OCTOBER 1997 (a) (b) (c) (d) Fig. 7. Simulation results. (a) Input current. (b) Inductor currents. (c) Output voltage. (d) Intermediate capacitor (gI) voltage. The ratio is (35) The critical conduction parameter (boundary between discontinuous and continuous conduction operation) is (36) To assure DCM operation, the following is chosen: From (18), the nominal duty cycle is found: and, using (21), The current ripple is (37) (38) H (39) A (40) and, from (24) and (25), mH H (41) Considering a resonant frequency of 2500 [Hz] the intermediate capacitor is given by F (42) Through simulation, was chosen to be 0.39 F. Simulation results are shown in Fig. 7. Fig. 7(a) shows the input current; Fig. 7(b) shows the current in inductors and for a few switching periods; Fig. 7(c) shows the output voltage and Fig. 7(d) shows capacitor voltage. The importance of a correct choice of capacitor is shown in Fig. 8. Fig. 8(a) shows the input current using F; a low-frequency oscillation ( kHz) can be observed in the current signal. On the other hand, Fig. 8(b) shows the capacitor voltage for F. In this case, the capacitor voltage cannot be considered constant in a switching period, and its peak value is much higher than that shown in Fig. 7(d). Authorized licensed use limited to: ELETTRONICA E INFORMATICA PADOVA. Downloaded on April 12, 2009 at 16:08 from IEEE Xplore. Restrictions apply.
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The Discontinuous Conduction Mode Sepic and ´ Cuk Power

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