# The Chan model

**The Chan model** is a hysteretic core model based on a model first proposed in by John Chan et al. in the *IEEE Transactions On Computer-Aided Design*, Vol. 10. No. 4, April 1991 but extended with the methods in United States Patent 7,502,723. Compared to older core models, the Chan model is particularly robust, computationally efficient and compact, requiring only three parameters to define most any commonly encountered magnetic hysteresis loop.

Once the core material's generic magnetic properties are set, establishing the circuit-level non-linear inductance requires specifying three more parameters to set the geometry of the specific core and one additional parameter to set the core winding turn-count. The Chan model as implemented in LTspice does not directly support Mutual Inductance, so unless only a single-winding inductor is being modeled, multiple windings must be added on via additional circuitry (see Transformers).

The Chan model as used by LTspice has a numerical problem for ratios of Br/Bs of over 2/3 or so, especially when asymmetrically driven very far into saturation. The curve segments for the "into" and "out of" saturation directions of the hysteresis loop do not line up exactly and the solver gets stuck because reducing the time step is not related to the basic problem and thus does nothing to help resolve it. This appears to be a shortcoming in the model as currently implemented. The "fix" is to either to avoid deep, unidirectional saturation (but then what's the point of the model?) or to avoid sharp ratios of Br to Bs.

This last strategy befits soft ferrites well enough, but offers an unsatisfactorily poor match to square-loop tape-wound cores. For this type of core a subcircuit-based Jiles-Atherton type approximation may be a better choice. These tend to be based on gyrator or flux space transforms of the magnetic circuit working via a non-linear equation based b-source driving capacitors that function as the magnetic "memory." Since these models don't just fit together nonlinear curve segments (but employ capacitors), they tend to get more linear at very small time steps and are not as likely to halt the simulation. But their complexity and b-sourced based non-linearity make them run much slower (>10x), especially if they are not optimized for LTspice.

This page is incomplete. Perhaps some discussion of how the model works and why and how it is more robust and computationally efficient than other core models. Equations supported with illustrative graphs would be helpful.

## example

Ferrite bead inductor using fair rite 73 material ref 2673000101

Instead of entering 1.5uH as inductor value, use Hc=19.1 Bs=.39 Br=.15 A=3.575u Lm=6.9m N=1 Lg=0

Parameters are derived from the fair-rite documentation page as follows:

- HC is the coercive force in A/M and should be the A/M equivalent of 0.24 Oersted (multiply by 1000 and divide by 4*PI)
- BS is the saturation in Tesla and should be the Tesla equivalent of the 3900 Gauss value (divide by 10000) giving .39T
- Br is the remanence (remnant) and should be the Tesla equivalent of the 1500 Gauss value
- A is the bead magnetic cross section in square meters, use dimensions C*(A-B)/2, area is in mm2 hence the u
- Lm is the length of the magnetic flux lines in meters, use PI*(A+B)/2
- N is the number of turns, use value between 1 and 0.5 in the case of a ferrite bead
- Lg=0 since we have no gaps