Designing the Boost Inductor of a CCM PFC Stage

In a boost converter running in continuous conduction mode, the duty cycle at each instant is d = 1 − v_in / V_out. The inductor sees v_in during the on-time, so the peak-to-peak ripple at that instant follows directly. Because v_in follows a rectified sine wave, the ripple changes throughout the line cycle.

Instantaneous ripple

ΔI_L(t) = v_in(t) · (1 − v_in(t) / V_out) / (f_s · L)

Largest possible ripple (at v_in = V_out / 2)

ΔI_L,max = V_out / (4 · f_s · L)

Peak line current

I_pk = √2 · P_out / (η · V_rms)

The ripple is zero at the zero crossing, rises to a maximum when the instantaneous input voltage equals half the output voltage, and falls again above that. With a 400 V output, the maximum sits at 200 V. At low line (90 V rms, 127 V peak) the input never reaches 200 V, so the largest ripple occurs at the peak of the sine. At high line (264 V rms, 373 V peak) the input passes through 200 V, so the absolute maximum ripple V_out / (4 f_s L) is reached twice per half cycle.

Designers usually fix the ripple as a fraction of the peak line current at low line and full load, where the current is largest. Values of 20 % to 40 % are common.

• Low ripple (around 20 %) means a large inductor, lower RMS current in the switch and capacitor, a smaller differential-mode EMI filter, and CCM over most of the load range.
• High ripple (40 % or more) means a smaller, cheaper inductor, but higher peak current, more core loss and an earlier transition to DCM at light load and high line, where the controller must handle mixed conduction modes.

1. 1Specifications: 1 kW output at 400 V, 90 to 264 V rms input, 65 kHz switching, 95 % efficiency assumed.
2. 2Peak line current at low line: I_pk = √2 · 1 000 / (0.95 · 90) ≈ 16.5 A. The input RMS current is about 11.7 A.
3. 3Target ripple: 30 % of 16.5 A ≈ 5.0 A peak-to-peak, at the peak of the 90 V line (v_in ≈ 127 V).
4. 4Inductance: L = 127 · (1 − 127/400) / (65 kHz · 5.0 A) ≈ 270 µH.
5. 5Peak inductor current: 16.5 A + 5.0 A / 2 ≈ 19 A. The inductor must still have at least the required inductance at this current, with margin for temperature.
6. 6High-line check: the maximum ripple is 400 / (4 · 65 kHz · 270 µH) ≈ 5.7 A peak-to-peak, while the peak line current is only about 5.6 A. Where v_in ≈ 200 V the instantaneous current is about 3 A, roughly half the ripple, so the converter sits on the CCM/DCM boundary there and is in DCM near the zero crossings at high line, which is normal and must be handled by the controller.

• Energy: the core must store ½ · L · I_pk² ≈ ½ · 270 µH · (19 A)² ≈ 49 mJ without saturating. Core size scales with this number.
• Inductance roll-off: powder cores (sendust, high-flux, MPP) lose permeability with DC bias. Specify the inductance at the peak current, not at zero bias, or the ripple will be much larger than designed at full load.
• Core loss: the AC flux swing follows the ripple, which changes over the line cycle. Average the loss over the cycle, or at least check it at the operating point with the largest ripple.
• Copper loss: the winding carries the low-frequency line current plus the high-frequency ripple. Use the RMS line current for DC loss and account for AC resistance for the ripple component.
• Temperature: permeability and saturation flux density both fall as the core heats up, so verify the inductance at the expected hot-spot temperature.

At power-up the PFC output capacitor charges through the inductor and the boost diode before the converter starts switching. Without help, that inrush can saturate the inductor and stress the diode. Most designs add a bypass diode from the rectified input directly to the output capacitor and a precharge resistor or NTC in the input path; the precharge guide and the inrush resistor calculator on this site cover that sizing.

Downstream, the PFC output usually feeds an isolated DC-DC stage such as an LLC converter. The double-line-frequency ripple on the PFC output capacitor becomes an input disturbance for that stage, so the two designs should be checked together.

All numbers in this guide come from the simple CCM boost equations above. They are a starting point; confirm the final inductor with the core manufacturer's DC-bias and loss data and with measurement.