Magnetic Cores

SuperSpice implements a model proposed by John Chan et la. in IEEE Transactions On Computer-Aided Design, Vol. 10. No. 4, April 1991. This model defines the Hysteresis loop with three standard magnetic parameters:
Hc - Coercive force Amp-Turns/meter
Br - Remnant Flux Density - Tesla
Bs - Saturation Flux Density - Tesla (intersection on the B axis of the extended slope of the saturation region graph)

The basic formula is given by:

B+ = Bs .(H + Hc)/(abs(H + Hc) + Hc.(Bs/Br-1))

B- = Bs .(H - Hc)/(abs(H - Hc) + Hc.(Bs/Br-1))

Initial curve:

B = (B+ + B- )/2 + µoH

Up curve:

B = B+ + µoH

Down curve:

B = B- + µoH

With various translations, described in the above paper, to achieve continuity of the loops.

Model Format

The model is implemented in a paramatised .subckt, which can simply be copied to generate other models.

Each core material type will require the values of Hc, Bs and Br to be set. hct, bstc, brtc are their respective, optional, temperature co-efficients

.SUBCKT NonlinearHystereticInductor 1 2 params: n_turns=14 area=1 length=1 lg=0
A0 1 2 4 0 inductor_lcouple
A1 3 0 HystCore
cp 2 0 1p
Cconverge 3 0 2p
r1 4 3 {lg/12.56637061e-7/area + 1e-3}
.model inductor_lcouple lcouple num_turns = {n_turns}
.model HystCore core (mode=3 Hc=1 Br=250m Bs=300m hctc=0 bstc=0 brtc=0
+ area={area}
+ length={length}
+)
.ends

For a specific core, only the parameters on the first line of the model require to be modified. The parameters are self explanatory, lg being the air gap length, which is implemented by a series resistor between the basic core model and its L Couple device. To avoid a zero ohm resister a small value of 1e-3 has been included, which will have negligible effect for zero gaped cores. It can be removed by renumbering the A1 and A2 nodes so that they connect directly.

Cconverge is a convergence aid. Care must be taken so that its value do not significantly effect results. Setting mode=4 will eliminate hysteresis, but otherwise preserve the nonlinear behaviour. This usually results in faster simulation and much better convergence.

Cp is an optional parallel capacitance of the inductor, which can be removed if not required. Series resistance of the inductor can be included by inserting a resistor between the main input nodes.

AC Hysteresis

Hc is modified, as per the above paper, to reflect hysteresis varying with frequency:

Hc = Hc. (hcf1 + hcf2.Fhcf3)

hcf1, hcf2, hcf3 being the appropriate additional model parameters in the core model

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