Four-Parameter Curve Fitting

The three-parameter curve fitting technique fits the demagnetization curve well. For the nonlinear permanent-magnetic material, the real operating point lies often not on the demagnetization curve, but on the recoil line. The relative recoil magnetic permeability calculated with the three-parameter curve fitting technique will cause deviation, therefore RMxprt employs a more accurate fitting technique: four-parameter curve fitting technique, as introduced below.

Given the four characteristic parameters Br, Hc, (BH)max and mr, the principles of the four-parameter curve fitting algorithm are summarized as follows:

  1. Draw a line through the point (0, Br) with the slope equal to -mrmo as shown in the figure. The segment of this line in the second quadrant is termed the ideal recoil line.
  2. Find the virtual magnetic flux density Br0.
  3. With Br0, Hc, and (BH)max, draw the demagnetization curve with the three-parameter curve fitting technique. The curve should touch the ideal recoil line at the tangent point (Ht, Bt).
  4. Any magnetic flux density B in the interval 0 ≤ B ≤ Br corresponds to the magnetic field intensity H:

The virtual magnetic flux density Br0 is found by iteration:

  1. Start from the initial guess for the lower and the upper bounds for the virtual magnetic flux density Br0:

  2. Let

  3. With Br0, Hc, and (BH)max, draw the demagnetization curve with the three-parameter curve fitting technique.

  4. The curve should touch a line parallel to the ideal recoil line at the tangent point (Ht, Bt).

    5. and

For any magnetic flux density B in the interval 0 ≤ B ≤ Br, the corresponding magnetic field intensity H will be calculated by:

  1. Calculate the value of Hr corresponding to Br using:

  2. If Hr > 0, the assumed virtual Br0 is too small, the lower bound of the interval needs to be increased, so let B0 = Br0. If, however, Hr < 0, the assumed Br0 is too big, the upper bound of the interval needs to be decreased, so let B1 = Br0.
  3. Repeat steps (2) through (7) until Hr converges to 0 within satisfactory precision.