Inductance

MKF calculates inductance using magnetic circuit analysis with reluctance-based methods. The fundamental relationship is:

\[L = \frac{N^2}{\mathcal{R}_{total}}\]

Where \(N\) is the number of turns and \(\mathcal{R}_{total}\) is the total magnetic circuit reluctance (sum of core and gap reluctances).

For coupled inductors and transformers, MKF uses matrix theory to compute the full inductance matrix including self and mutual inductances.

Available Models

Reluctance-based

Primary inductance calculation from magnetic circuit analysis:

\[L = \frac{N^2}{\mathcal{R}_{core} + \mathcal{R}_{gap}}\]

Core reluctance: \(\mathcal{R}_{core} = \frac{l_e}{\mu_0 \mu_r A_e}\)

Gap reluctance: Uses selected reluctance model (Zhang, Mühlethaler, etc.)

For multi-winding components, the inductance matrix is:

\[[L] = [N]^T [\mathcal{P}] [N]\]

Where \([\mathcal{P}]\) is the permeance matrix and \([N]\) is the turns matrix.

Leakage Inductance

Leakage inductance represents flux that doesn't link all windings. It's critical for: - Transformer voltage regulation - Resonant converter design (LLC, phase-shifted full-bridge) - EMI and voltage spikes

MKF calculates leakage inductance using energy-based methods:

\[L_{leak} = \frac{2 W_{leak}}{I^2} = \frac{1}{I^2} \int_{volume} \frac{B^2}{\mu_0} dV\]

The magnetic field distribution is computed using the selected magnetic field model (Binns-Lawrenson, Dowell, etc.), then integrated over the winding window volume.

Reference: Spreen, J.H. "Electrical Terminal Representation of Conductor Loss in Transformers." IEEE Trans. Power Electronics, 1990. IEEE

Model Comparison

Model	Error	Reference

Inductance Calculation Settings

Key settings affecting inductance calculations:

Setting	Effect
reluctance_model	Determines gap fringing accuracy
magnetic_field_strength_model	Affects leakage calculation
magnetic_field_include_fringing	Include gap fringing in field calc
leakage_inductance_grid_auto_scaling	Auto-adjust grid density

For resonant converters: Accurate leakage inductance is critical. Use Mühlethaler reluctance model and Binns-Lawrenson field model with fine grid resolution.