## 1

Cbulk

Vout

Vout

Rearranging the terms of this equation, one can obtain: Vout*^Vout = 1 *<> * i 2 * sin 2(mt) - 1] (eq. 82)

Cbulk

Noting that = 2* Vout*dVou and that dt dt cos(2mt) = 1-2*sin2(mt), one can deduct the square of the output voltage from the precedent equation:

where <Vout> is the average output voltage.

Dividing the terms of the precedent equations by the square of the average output voltage, it becomes:

Vout

< Vout > + 6Vout = /1 — " *< Pin > *sin(2mt)

Where SVout is the instantaneous output voltage ripple. Equation (85) can be rearranged as follows:

1 n *< Pin > *sin(2mt) i Cbulk*m*< Vout > 2

one can simplify this equation considering that the output voltage ripple is small compared to the average output voltage

(fortunately, it is generally true). This leads to say that the term I / 1 —1—< Pin >—sin(2mt) - 1 I is nearly zero or in other yV Cbulk*m*< Vout > 2 J

words, that I —-1-— I is small compared to 1. Thus, one can write that:

11 - n*< Pin > *sin(2mt) _ 1 _ 1 * n < Pin > *sin(2mt) (eq. 87)

Cbulk*m*< Vout > 2 ~ 2 Cbulk*m*< Vout > 2

Substitution of equation (86) into equation (87), leads to the simplified ripple expression that one can generally find in the literature:

2*Cbulk*m*< Vout > The maximum ripple is obtained when (sin(2rot) = -1) and minimum when (sin(2mt) = 1). Thus, the peak-to-peak ripple that is the difference of these two values is:

And:

Vout = < Vout > - (5Vout)pk-pk * sin(2wt) (eq. 90)

### Conclusion

Compared to traditional switch mode power supplies, one faces an additional difficulty when trying to predict the currents and voltages within a PFC stage: the sinusoid modulation. This is particularly true in critical conduction mode where the switching ripple cannot be neglected. As proposed in this paper, one can overcome this difficulty by:

• First calculating their value within a switching period,

• Then the switching period being considered as very small compared to the AC line cycle, integrating the result over the sinusoid period.

The proposed theoretical analysis helps predict the stress faced by the main elements of the PFC stages: coil, MOSFET, diode and bulk capacitor, with the goal of easing the selection of the power components and therefore, the PFC implementation. Nevertheless, as always, it cannot replace the bench work and the reliability tests necessary to ensure the application proper operation.

Switching Frequency:

MC33260 like Current Sense Resistor (Rs = R5) Dissipation:

MC33262 like Current Sense Resistor (Rs = R7) Dissipation:

Capacitor Low Frequency Ripple: rç*< Pin >

Cbulk* m *< Vout > RMS Capacitor Current:

Switching Frequency:

Capacitor Low Frequency Ripple: rç*< Pin >

I Vac: AC line rms voltage I VacLL: Vac lowest level m: AC line angular frequency <Pin>: Average input power I <Pin>max: Maximum pin level