Power Inductor Design Calculator

Magnetic circuit and flux

The equations are derived here from Ampère's law and flux linkage: $\mathcal R_c=l_e/(\mu_0\mu_r A_e)$, $\mathcal R_g=g/(\mu_0 A_e)$ and $L=N^2/(\mathcal R_c+\mathcal R_g)$. The total series air gap excludes fringing. In target mode, $g=\mu_0 A_eN^2/L_{target}-l_e/\mu_r$; a negative required gap is infeasible. The published IIT Kharagpur tutorial provides independent circuit benchmarks.

Peak absolute current is $I_{DC}+\Delta I/2$ for the nonnegative mean-current input. Peak local flux is $LI_{pk}/(NA_{min})$; the loss excursion uses $\Delta B=L\Delta I/(NA_e)$. Stored energy is $LI_{pk}^2/2$. Its ideal gap fraction is $\mathcal R_g/(\mathcal R_c+\mathcal R_g)$. The selected allowable flux is a design input, not a measured saturation knee.

Copper loss

Annealed copper uses $\rho_{20}=1/58$ Ω·mm²/m and $\alpha_R=0.00393$ K⁻¹. Resistance is evaluated at the input winding temperature. Triangular ripple has $I_{AC,rms}=\Delta I/\sqrt{12}$; total RMS current is the root-sum-square of mean and ripple.

The foil model uses Hurley, Gath and Breslin (2000), Eq. (1), attached source s4 p.2: the Dowell factor with $x=t/\delta$, $m=N$ layers and $\delta=\sqrt{\rho/(\pi f\mu_0)}$. Its normalized harmonic mean-square weights are $w_n=6\sin^2(\pi nD)/[\pi^4n^4D^2(1-D)^2]$. Sum $w_nF(x\sqrt n,m)$ through harmonic 80, assigning the remaining current variance to DC resistance. This omits the excess tail loss. Small- and large-argument evaluations use stable series/asymptotes. The alternative measured ratio applies to the winding body for the specified ripple; leads are modeled at DC resistance.

The displayed AC ripple loss includes its baseline I²R component. Total copper loss is $I_{DC}^2R_{DC}+I_{AC,rms}^2R_{AC}$. It does not add total RMS copper loss again.

iGSE core loss

Venkatachalam et al. (2002), DOI 10.1109/CIPE.2002.1196712, give $P_v=k_if^\alpha(\Delta B)^\beta[D^{1-\alpha}+(1-D)^{1-\alpha}]$ for two monotonic ramps. This is equivalent to their cycle integral. Princeton's MagNet handbook, attached s3 p.5, also gives this method and its limitations.

Attached s5 records the MagNet coefficient snapshot at commit bf6d361. To avoid ambiguous coefficient units, the material table normalizes its SI $k_i$ to sinusoidal loss density at $f_0=100$ kHz and $B_0=100$ mT peak: $P_0=k_if_0^\alpha B_0^\beta(2\pi)^{\alpha-1}2^{\beta-\alpha}C_\alpha$, with $C_\alpha=\int_0^{2\pi}|\cos\theta|^\alpha d\theta$. These are derived reference densities, not extra measurements.

The calculator evaluates $P_v=P_0(f/f_0)^\alpha(\Delta B/(2B_0))^\beta Q(D)$, where $Q=2^\alpha[D^{1-\alpha}+(1-D)^{1-\alpha}]/[(2\pi)^{\alpha-1}C_\alpha]$. Multiply by ferrite volume and the user correction factor. The gamma-function expression evaluates the normalization integral exactly.

• One winding, one linear magnetic circuit, uniform effective section, constant relative permeability, negligible leakage and fringing.
• Nonnegative mean current plus periodic triangular ripple. A negative trough is permitted for bidirectional ripple; there are no flat intervals or nested minor loops.
• The default 100 mm² area, 80 mm path and 8 cm³ volume are an illustrative generic core, not a manufacturer's part. Initial permeability and loss coefficients are separate approximations to real biased operation.
• Foil has one turn per radial layer, equal mean turn length, full winding width and a one-dimensional field. Mean length is entered for the complete winding. Insulation and terminations add unmodeled resistance and occupy window space.
• Copper temperature is prescribed; ferrite coefficients are not temperature-corrected automatically. A measured correction is only as transferable as its operating conditions.
• The table's raw k_i values use MagNet's Hz, tesla and W/m³ convention. Their physical units depend on the exponents; the normalized reference density is used in the actual unit-checked calculation.

Use this as a first design pass for gapped ferrite power inductors below the selected hot flux limit. A flux-limit failure suppresses results because the linear model cannot establish operation beyond the knee. Neither the peak-current result nor a passing check certifies a production saturation rating.

Core-loss uncertainty is material and operating-point dependent. At the source-based N87 measurement (99.9 kHz, 97.1 mT peak AC, zero DC bias, 25 °C), this global fit predicts about 158.5 kW/m³ against 125.9 kW/m³ measured: 25.95% high. The 30% reference-check band is an approximate-model acceptance band, not numerical precision or a universal accuracy claim. It is not a held-out fit test. MagNet presets do not predict temperature or DC-bias dependence. Use characterization near the actual operating point, especially with a large mean flux.

The broad MagNet data range cited in How MagNet is roughly 50–500 kHz and 10–300 mT peak AC flux; this is not a guarantee for every point, material, temperature or bias. Custom exponents must satisfy 1 < alpha < beta and stay within the input bounds. Ramp fraction is limited to 0.05–0.95. Harmonic truncation and gap fringing make the foil model unsuitable for precise hot-spot prediction; concentrated gap fields can cause substantial additional copper loss.

Gap sweeps show the uncorrected linear model. The duty sweep holds frequency, flux excursion and the correction factor fixed. There is no nonlinear B–H, i²GSE relaxation, automatic DC-bias correction, thermal solution, self-resonance, tolerance stack or insulation design. Measure inductance under bias and verify loss and hot-spot temperature on the final prototype.