True Bridgeless PFC Converter Achieves Over 98% Efficiency, 0.999 Power Factor

Jul 1, 2010 12:00 PM
Dr. Slobodan Cuk, President, TESLAco, Irvine, CA

FLUX (VOLT-SECOND) BALANCE OF TWO INDUCTORS

The volt-second (flux balance) on inductor L requires that for the steady-state, the positive and negative areas of the voltage waveform in Figure 5a must be balanced so that:

VgDTS = (V + VCr - Vg) (1-D)TS (5)

where:

Vg = input voltage

D = Duty ratio

TS = Switching period in seconds

VCr = DC voltage on the resonant capacitor Cr

Unlike the PWM inductor L, which was flux balanced over the entire switching period TS, the resonant inductor Lr must be fully flux balanced during the ON-time interval only as seen in Figure 5b. Thus applying the steady-state criteria for the resonant inductor Lr results in:

VCr = 0 (6)

as the resonant inductor must be flux-balanced and cannot support any net dc voltage.

Therefore, the dc voltage, VCr, of the resonant capacitor Cr must be zero so that the volt-second balance is satisfied on the resonant inductor Lr.

DC CONVERSION RATIO

Using Equation (6) in Equation (5), the dc conversion ratio is obtained as:

V/Vg = 1/(1-D) (7)

Note that the dc conversion ratio given by Equation (7) is the same as for well-known boost converter. Furthermore, despite the resonant circuit consisting of resonant capacitor Cr and resonant inductor Lr, and corresponding sinusoidal and co-sinusoidal time domain waveforms of resonant current and resonant capacitor voltage, the dc conversion ratio does not depend on either one of them and their values or the switching period TS, but only depends on the operating duty ratio, D, as in conventional dc-dc converters.

The simple dc conversion ratio dependent on duty ratio only, as in square-wave PWM switching, is obtained. Hence, the regular duty ratio control can be employed to use this converter as a basis for PFC control, as in boost and other conventional converters.

The resonant inductor current, ir, during entire switching period is shown in Figure 6a, while the resonant capacitor voltage is shown in Figure 6b, which displays the linear charging of the resonant capacitor Cr during the OFF-time interval. Note also the continuity of the capacitor voltage at the transition between two switching intervals.

Next, we analyze the converter operation with respect to the converter in Figure 7a in which input voltage source is negative polarity dc voltage and having the switch states as in Figure 7b. The linear switched networks for ON-time interval are shown in Figure 7c and linear switched network for OFF-time interval is shown in Figure 7d.

We now use the two linear switched networks in Figure 7c and Figure 7d to construct the time domain of the current in the PWM inductor L and in the resonant inductor L. The voltage waveform on inductor L is shown in Figure 8a to be just as in conventional PWM square-wave switching converters, while the resonant capacitor VCr voltage is illustrated in Figure 8b only for ON-time resonant interval and its complete time domain waveform in Figure 9b.

The Volt-second (flux balance) on inductor L requires that for the steady-state, the positive and negative areas of the voltage waveforms in Figure 8a must be balanced so that:

VgDTS = (VCr - Vg)(1-D)TS (8)

Unlike the PWM inductor, which was flux balanced over the entire period TS, the resonant inductor must be fully flux-balanced during the ON-time interval only as per resonant circuit model of Fig. 10b and Fig. 10c.

The resonant circuit model of Figure Figure 10b is formed by the loop consisting of five components, two capacitors Cr and C and resonant inductor Lr, switch S and current rectifier CR2. However, since the output capacitor C is much larger than the resonant capacitor Cr, their series connection is effectively equal to Cr.

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