PFC Inductance & Efficiency Calculation

Calculate the inductance:

01Minimum AC input voltage Vac_min, default = 90

02PFC output voltage Vbus, default = 400 V

Output power Pout, range 150~2000W; enter a specific value for calculation

Input power Pin=1.05*Pout

Minimum switching frequency; at high power the operating frequency can be lowered appropriately

Current ripple; default is 2.0 below 400W and 0.2 above 400W

PFC inductance: L_pfc=(Vac_min^2 (Vbus-1.4*Vac_min))/(Δ_ripple⋅P_in⋅Vbus⋅f_min ),

2Calculate the currents

Maximum input RMS current: I_in_rms_max = 1.05*Pout/Vac_in Peak input current: Iin_pk=1.4*I_in_rms_max Maximum average input current: I_in_avg = 2*Iin_pk/3.14 The ripple current is calculated by: Δ_ripple⋅I_(in_pk )= Δ_ripple⋅I_(in_pk ) Inductor peak current: I_L_pk = Iin_pk*(1+0.5*Δ_ripple)

Inductor RMS current: I_L_rms ≈ I_in_rms_max

The MOSFET current approximately equals the inductor current, because the on-time is far longer than the off-time

3Calculate the AP value and select the core or toroid.

Ku is the window factor; for toroidal inductors

Kj is the current density

The PFC inductance L is obtained from the calculation above.

The peak inductor current is obtained from the calculation above.

Bmax is the peak flux density. For 100~400W output we use a PC95 core with dBmax=0.3;

for 400~3000W, use a HighFlux toroid with Bmax=1.35

The inductor AP value is calculated as follows:

AP = Ae*Aw=L*I_L_pk*I_L_rms*10^4/(Ku*Bmax*J), unit cm^4

Calculate turns, wire diameter and DC resistance

Minimum turns N>=Lpfc*Imax/(Ae*Bmax),

Ae is the core cross-sectional area; Bmax is 0.3 for PC40, 0.9 for NPS, 1.2 for NPN; Imax is the maximum current.

Verify the actual flux swing: dBmax =Lpfc*dImax/(N*Ae), where dBmax is the flux change and dImax is the inductor ripple current.

Calculate the required copper wire cross-section S=I_L_rms/J from the preset current density J.

Select the actual wire diameter (below 400W, use multiple parallel wires to reduce skin effect) and compute the real cross-section S.

Calculate the winding DC resistance from the mean turn length MLT, turns N and cross-section S:

5Calculate the inductor losses

Copper loss formula: ; the AC/DC resistance ratio Fr defaults to 1.2

Core loss formula: Pcore= K*fs^a*Bac^b*Ve

fs is the frequency, B is the flux density change, Ve is the effective core volume

fs in kHz, Bac in mT, Ve in cm3, Pcore in mW

K, a, b are constants; refer to the manufacturer datasheet (derived from loss curves):

For Sendust toroids (black or blue): Magnetics u60 has K=2.5×10^-4, a=1.28, β=1.78 (cost-effective with DC bias) NBTM u75 has K=2.6×10^-4, a=1.20, β=2.0 (cost-effective with DC bias) For HighFlux toroids (green): NBTM u60 has K=1.5×10^-4, a=1.28, β=2.0 (chosen when the DC current is very large) For PC95 or similar transformer cores: most manufacturers are K=2.4×10^-6, a=1.22, b=2.55 (low price, low loss; first choice in critical mode)

6Main physical parameters of common PFC inductor toroid cores (Ae, Ve, Ap, AL, Bmax, mean turn length MLT) are listed in Table 1

Toroid Model	Material	Loss/cm3 50kH0.1T	Main Dimensions (mm)	Saturation Flux Bmax(T)	AL Value (nH/n^2)	Core Area Ae (cm^2)	Window Area Ae (cm^2)	AP Value cm^4	Core Volume Ve (cm^3)	Length per Turn MLT (m)
PQ2625	PC95	20mW	26*25, W=19	0.35	5200	1.18	0.8	0.94	6.53	0.065
PQ3225	PC95	200mW	32*25, W=22	0.35	5500	1.61	1.17	1.89	9.76	0.079
KH130060A	HighFlux	200mW	34*19 T=11	1.5	61	0.67	2.92	1.95	5.48	0.041
KH130060A-2P	HighFlux	200mW	34*19 T=22	1.5	122	1.35	2.92	3.9	11.0	0.065
KH158060A	HighFlux	200mW	41*22 T=18	1.5	122	1.5	3.80	5.70	15.0	0.063
KH158060A-2P	HighFlux	200mW	41*22 T=36	1.5	244	3.0	3.80	11.4	30.0	0.103

7Loss Calculation Table for Conventional PFC Switches and Freewheeling Diodes at 150~2000W (Table 2)

L=（(Vac_min^2)*(Vpfc-1.4*Vac_min))/(Δ_ripple*1.05*Pout*Vpfc*fs ),

I_L_rms = 1.05*Pout/Vac_min I_L_pk = Iin_pk*(1+0.5*Δ_ripple), Iin_pk=1.4*I_L_rms_ AP = L*I_L_pk*I_L_rms*10^4/(Ku*Bmax*J)，J=600 For PQ-series cores N= L*I_L_pk/(Ae*Bmax*0.8*100); for KH toroids N=(1000*L/AL)^0.5, with L in uH and Ae in cm^2. S >= Irms/6, unit is mm^2 Rdc = 0.01*2.1*ML*N/S, unit is (Ω) If Δ_ripple <1.0, Bac = 10*L*Δ_ripple*I_L_pk/(N*Ae), unit mT; if Δ_ripple>1.0, then Bac = 10*L*I_L_pk/(N*Ae), unit mT Pcu=I_rms^2×R_dc×1.2 Pcore= K*fs^a*Bac^b*Ve; for PQ cores K=1.6×10^-9, a=1.22, b=2.55; for KH toroids K=1.5×10^-7, a=1.28, β=2.0

Note: Bac must be in mT and Ve in cm^3 here

PFC switch conduction loss Ppfc_on = I_L_rms^2*Rds_on PFC switch switching loss Ppfc_rs_ff = 0.5*Vpfc*Ipeak*(tr+tf)*fs+0.5*Coss*Vpfc*Vpfc*fs PFC diode loss: Ppfc_dio = 0.5*I_L_rms*1.2 PFC circuit efficiency: Eff_pfc = Pout/(Pout+Pcu+Pcore+Ppfc_on+Ppfc_rsff+Ppfc_dio)

Item	Pout	200W	300W	400W	600W	800W	1200W	1500W	2000W
AC Input Voltage	Vac_min	90	90	90	90	90	90	90	90
PFC Output Voltage	Vpfc	400	400	400	400	400	400	400	400
PFC Full-Load Frequency	Fs	60k	60k	60k	60k	60k	60k	60k	60k
Recommended Inductor Material		Ferrite	Ferrite	Ferrite	HighFlux	HighFlux	HighFlux	HighFlux	HighFlux
Recommended Inductor Spec		PQ2625	PQ3225	PQ3225	KH130060A	KH130060A	KH158060A-H	KH158060A-H	KH158060A-H-2P
Inductor Core Area	Ae	1.18	1.61	1.61	0.67	0.67	1.5	1.5	3.0
Inductor Window Area	Aw	0.8	1.17	1.17	2.92	2.92	3.8	3.8	3.8
Inductor Core Volume	Ve	6.53	9.76	9.76	5.48	5.48	15	15	30
Inductor Window Factor	Ku	0.55	0.55	0.55	0.35	0.35	0.35	0.35	0.35
Maximum Flux	Bmax(T)	0.3T	0.3T	0.3T	1.35T	1.35T	1.35T	1.35T	1.35T
Inductor AL Value	AL	5200	5500	5500	61	61	122	122	244
Inductor Length per Turn	ML	0.065	0.079	0.079	0.041	0.041	0.063	0.063	0.103
Inductor Ripple Factor	Δ_ripple	2	2	2	0.3	0.3	0.3	0.3	0.3
Inductance	L (μH)	220.18	146.79	110.09	489.29	366.96	244.64	195.71	146.79
Inductor Maximum Current	I_L_pk	6.53	9.8	13.07	11.27	15.03	22.54	28.17	37.57
Inductor RMS Current	I_L_rms	2.33	3.5	4.67	7	9.33	14	17.5	23.33
Inductor Minimum AP	AP_min	0.339	0.5086	0.6781	1.3615	1.8154	2.7231	3.4039	4.5385
Inductor Minimum Turns	N	51	37	37	90	78	45	40	25
Copper Wire Area	S(mm²)	0.3889	0.5833	0.7778	1.1667	1.5556	2.3333	2.9167	3.8889
Maximum Flux Swing	Bac(mT)	0.179	0.1052	0.0789	0.0664	0.0432	0.0255	0.0181	0.0139
Winding DC Resistance	Rdc(mΩ	239.03	241.48	241.48	274.34	316.55	245.08	275.71	220.57
Inductor Copper Loss	Pcu	1.1695	1.5469	2.0625	3.9055	4.513	6.0011	6.6679	9.0846
Inductor Core Loss	Pcore	1.7924	2.7496	2.7496	11.681	15.5518	25.5167	32.2945	41.337
Switch Model		ZN65C1R120	SRC60R090BS	ZN65C1R075	ZN65C1R075	SRC60R090BS	SRC60R068BS	SRC60R040BST	SRC60R030BS
Switch On-Resistance	Rds_on	0.12	0.09	0.075	0.075	0.09	0.068	0.04	0.03
Switch Rise Time	tr	7ns	28ns	7ns	7ns	28ns	6ns	22ns	30ns
Switch Fall Time	tf	10ns	7ns	10ns	10ns	7ns	4ns	13ns	12ns
Switch Output Capacitance	Coss	47pF	136pF	47pF	47pF	136pF	171pF	137pF	136pF
Switch Conduction Loss	Ppfc_on	0.6533	1.1025	1.6333	3.675	7.84	13.328	12.25	16.3333
Switch Switching Loss	Ppfc_rsff	1.5584	4.7688	2.8912	2.5247	6.964	3.5256	12.4911	19.5864
Freewheeling Diode Loss	Ppfc_dio	1.398	2.1	2.802	4.2	5.598	8.4	10.5	13.998
PFC Circuit Efficiency @AC90V Full Load	Eff_pfc	96.82%	96.07%	97.05%	95.85%	95.19%	95.48%	95.29%	95.22%