The Spice file shown allows saturating inductors such as MPP or powdered iron cores to be modeled with relative ease. Such inductors are very common, but they feature a gradual saturation characteristic that’s difficult to model even using the “real” core materials provided with some Spice programs. The model gives accurate results from no load (no saturation) to full saturation, with proper behavior at the limits. It’s useful for modeling power-supply filters during large dynamic (inrush, step load) conditions.

At the heart of the model is a simple exponential equation implemented using pSPICE’s Analog Behavioral Modeling. Not empirically derived, it’s based on an equation that models the statistical distribution of the core’s magnetic particles. Integrating the base equation gives the percent saturation (integrating it once more would give the BH characteristics).

The equation is particularly useful because core groups with similar behavior may be modeled using one fixed equation. For example, the entire MPP core family may be modeled with typical accuracies of better than ±2% for up to 80% saturation. Cores of 550 m are the sole exception, since they used a flake rather than a powder material. A graph of the equation fitted to MPP cores is given (see the figure).

To use the equation for MPP cores, calculate the core constant:

0.4πU_{i}N/L_{m} (U_{i} × oersteds normalized to 1 A)

where N is the turns. The other parameters (magnetic path length and initial relative permeability) are provided in the manufacturer’s data (use a U_{i} of 1100 for a 550-µ core for better accuracy). When the constant is employed in the Spice formula via the passed parameter, the correct saturation characteristics are created.

Other distributed materials, such as powdered iron, may be modeled. Because different types use different mixes and materials, the group fit isn’t as good as in the MPP family. Use the table as a starting point, where the degree of the fit also is indicated by the Chi Square results.