Switch-Mode Power Magnetics, Gapped Ferrite Buck/Flyback Inductors & Reluctance
Gapped Ferrite Core Inductor Reluctance, AL & Isat Formula
Calculate Total Series Magnetic Reluctance R_tot (MA/Wb), Gapped Inductance Factor AL (nH/turn²), Winding Inductance L (uH), and Hard-Saturation Peak Current Isat (A).
Paradox of power magnetics: grinding a 0.8 mm air gap into a ferrite core LOWERS inductance—so the inductor can store 15x MORE DC energy without saturating!
Ungapped MnZn power ferrite (`mu_r ≈ 2,200`, `B_sat ≈ 0.38` T at `100 °C`) has tiny Core Magnetic Reluctance `R_core = l_e / (mu_0 * mu_r * A_e)` (`mu_0 = 4*PI()*10^-7` H/m)—so even half an amp of DC buck/flyback bias drives `B = (N * I) / (A_e * R_core)` past `0.38` T, collapsing permeability to air and blowing the MOSFET! Grinding a non-magnetic Air Gap `l_g` (mm, where `mu_r,air = 1`!) adds Series Gap Reluctance `R_gap = l_g / (mu_0 * A_e)` that dominates `R_tot = R_core + R_gap` (`>93%` of magnetic energy `(1/2)*B^2/mu_0` now resides safely inside the non-saturating air gap!), stabilizing Inductance Factor `A_L = 10^9 / R_tot` (`nH/turn²`), Winding Inductance `L = (N^2 * A_L) / 1,000` (`uH`), and boosting Peak Saturation Current `I_sat = (B_sat * A_e * R_tot) / N` (`A`) by an order of magnitude!
Verify on an ETD34 Gapped Buck/Flyback Choke—Effective_Core_Path `l_e` = 78.0 mm (B2), Ground_Center-Leg_Air_Gap `l_g` = 0.80 mm (B3), Effective_Cross-Section `A_e` = 120.0 mm² (B4), Ferrite_Relative_Permeability `mu_r` = 2,200 (B5), Copper_Turns `N` = 36 (B6), and `100 °C` Ferrite_Saturation_Flux `B_sat` = 0.38 T (B7): Total Reluctance hits `5.540` MA/Wb (E2), Gapped `A_L` equals `180.50` nH/turn² (E3), Winding Inductance equals `233.92` uH (E4), and Hard Saturation Current reaches `7.02` A (E5)!
| SMPS Gapped Ferrite KPI (le=78 mm, lg=0.80 mm, Ae=120 mm², mur=2,200, N=36, Bsat=0.38 T) | Formula | Verified Output |
|---|---|---|
| Total Reluctance R_tot (MA/Wb) | (le_m/(mu0*mur*Ae_m2) + lg_m/(mu0*Ae_m2))/1e6 | 5.540 MA/Wb (0.368 @ ungapped 0.02 mm) |
| Gapped AL Value (nH/turn²) | 1,000,000,000 / R_tot_A_Wb | 180.50 nH/N² (2,719.28 @ ungapped) |
| Winding Inductance L (uH) | ((Turns_N ^ 2) * AL_nH) / 1000 | 233.92 uH (3,524.19 uH @ ungapped) |
| Peak Saturation Current Isat (A) | (Bsat_T * Ae_m2 * R_tot_A_Wb) / Turns_N | 7.02 A (0.47 A saturates instantly @ 0.02 mm!) |
Magnetic Circuit Series Reluctance, AL Factor & Bsat Saturation Current Formula
Validate `Core_Path l_e > 5` mm, `Air_Gap l_g >= 0` mm, `Core_Area A_e > 5` mm², `Relative_Perm mu_r >= 50`, `Turns N >= 1`, and `B_sat` in `(0.10, 2.20]` T!
=LET(le_m, B2 / 1000, lg_m, B3 / 1000, ae_m, B4 * 0.000001, mr_p, B5, nt_c, B6, bs_t, B7, mz_p, 4 * PI() * 0.0000001, rt_w, (le_m / (mz_p * mr_p * ae_m)) + (lg_m / (mz_p * ae_m)), IF(OR(B2 <= 5, B3 < 0, B4 <= 5, mr_p < 50, nt_c < 1, bs_t <= 0.1, bs_t > 2.2), "Invalid Magnetics Input", ROUND((bs_t * ae_m * rt_w) / nt_c, 2)))Ungapped Mating-Surface Residual 0.02 mm Saturation Trap Check (Set Air Gap lg B3 = 0.02 mm)
Omit the center-leg spacer leaving only `0.02` mm (`20` um) mirror-lapped mating contact (`B3 = 0.02`): Reluctance E2 plunges `15x` to `0.368` MA/Wb (`A_L = 2,719.28` nH/N² in E3, `L = 3,524.19` uH in E4), and Saturation Current E5 collapses from `7.02` A down to `0.47` A—saturating on the very first PWM switching pulse!
=IF(ISTEXT(E5), E5, LET(le_m, B2 / 1000, lg_m, B3 / 1000, ae_m, B4 * 0.000001, mz_p, 4 * PI() * 0.0000001, rt_w, (le_m / (mz_p * B5 * ae_m)) + (lg_m / (mz_p * ae_m)), ROUND(((B6 ^ 2) * (1000000000 / rt_w)) / 1000, 2)))Try the example
Use the original values or change them to test your understanding.