SLYT838 January 2023 UCD3138

3 Peak current-mode control for DCM PFC

You can extend the same algorithm to discontinuous conduction mode (DCM) operation. Figure 3-1 shows the inductor current waveform in DCM. The inductor current drops to zero at the end of T_off and stays at zero for the rest of period T_dcm; therefore, T = T_on + T_off + T_dcm. The PWM waveform generator is the same as Figure 2-1, but the PWM off-time is T_off + T_dcm, not T_off, as shown in Figure 3-2.

Figure 3-1 A PFC inductor current waveform in DCM.

Figure 3-2 PWM waveform generation for the proposed method in DCM.

Rewriting Equation 4 to Equation 9 calculates the average current in DCM for one switching cycle:

Equation 9.

I_{a v g} = {(I}_{2} - \frac{V_{i n} * T_{o n}}{2 * L}) * \frac{T_{o n} + T_{o f f}}{T}

In steady state, inductor volt-second must be balanced in each switching cycle, resulting in Equation 10:

Equation 10.

V_{i n} * T_{o n} = (V_{o u t} - V_{i n}) * T_{o f f}

Solving for T_off and substituting Equation 9 results in Equation 11:

Equation 11.

I_{a v g} = {(I}_{2} - \frac{V_{i n} * T_{o n}}{2 * L}) * \frac{T_{o n} * V_{o u t}}{T (V_{o u t} - V_{i n})}

From Equation 6, Equation 12 is:

Equation 12.

\frac{I_{2} * R}{V_{R A M P}} = \frac{{T - T}_{o n}}{T}

Equation 13 calculates the peak value of the saw wave V_RAMP as:

Equation 13.

V_{R A M P} = (\frac{G_{v} * V_{i n} * T * (V_{o u t} - V_{i n})}{T_{o n} * V_{o u t}} + \frac{R * T_{o n} * V_{i n}}{2 * L}) * \frac{T}{T - T_{o n}}

Substituting Equation 13 into Equation 12 and solving for I₂ results in Equation 14:

Equation 14.

I_{2} = \frac{G_{v} * V_{i n} * T * (V_{o u t} - V_{i n})}{R * T_{o n} * V_{o u t}} + \frac{T_{o n} * V_{i n}}{2 * L}

Substituting I₂ into Equation 11 results in Equation 15:

Equation 15.

I_{a v g} = (\frac{G_{v} * V_{i n} * T * (V_{o u t} - V_{i n})}{R * T_{o n} * V_{o u t}} + \frac{T_{o n} * V_{i n}}{2 * L} - \frac{V_{i n} * T_{o n}}{2 * L}) * \frac{T_{o n} * V_{o u t}}{T (V_{o u t} - V_{i n})} = \frac{G_{v}}{R} * V_{i n}

In Equation 15, G_v is constant in steady state; therefore, I_avg is proportional to V_in and follows the shape of V_in. If V_in is a sine wave, I_avg will also be a sine wave, thus achieving a unity power factor.

Equation 9 through Equation 15 are valid for both CCM and DCM, so if the saw wave signal peak value is generated according to Equation 13, then it is possible to achieve a unity power factor for both CCM and DCM.

Equation 1 is a special case of Equation 13 where T = T_on + T_off. For applications in which light loads (PFC will be in DCM mode at light load), THD and the power factor are not important, use Equation 1 to simplify the implementation.