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Custom Inductor (B-H Curve)

This example shows a comparison in behavior of a linear and nonlinear inductor. Starting with fundamental parameter values, the parameters for linear and nonlinear representations are derived. These parameters are then used in a Simscape™ model and the simulation outputs compared.

Open Model

Specification of Parameters

Fundamental parameter values used as the basis for subsequent calculations:

  • Permeability of free space, $\mu_0, \rm{H/m}$

  • Relative permeability of core, $\mu_r$

  • Number of winding turns, $N_w$

  • Effective magnetic core length, $l_e, \rm{m}$

  • Effective magnetic core cross-sectional area, $A_e, \rm{m^2}$

  • Core saturation begins, $B_{sat_{begin}}, \rm{T}$

  • Core fully saturated, $B_{sat}, \rm{T}$

Calculate Magnetic Flux Density and Magnetic Field Strength Data


  • Magnetic flux density, $B, \rm{T}$

  • Magnetic field strength, $H, \rm{A/m}$

Linear representation:

  • $B = \mu_0 \mu_r H$

Nonlinear representation (including coefficient, a):

  • $B = B_{sat} \tanh(a.H)$

Display Magnetic Flux Density Versus Magnetic Field Strength

The linear and nonlinear representations can be overlaid.

Calculate Magnetic Flux and Current Data


  • Magnetic flux, $\phi, \rm{Wb}$

  • Current, $I, \rm{A}$

Linear representation:

  • $L = \mu_0 \mu_r A_e N_w^2/l_e$

  • $\phi = I L/N_w$

Nonlinear representation:

  • $I = H l_e/N_w$

  • $\phi = B A_e$

Display Magnetic Flux Versus Current

The linear and nonlinear representations can be overlaid.

Use Parameters in Simscape Model

The parameters calculated can now be used in a Simscape model. Once simulated, the model is set to create a Simscape logging variable, simlog_CustomInductorBHCurve.


The state variable for both representations is magnetic flux, $\phi$. Current, I, and magnetic flux, $\phi$, can be obtained from the Simscape logging variable, simlog_CustomInductorBHCurve, for each representation. Overlaying the simulation results from the representations permits direct comparison.

Results from Real-Time Simulation

This example has been tested on a Speedgoat Performance real-time target machine with an Intel® 3.5 GHz i7 multi-core CPU. This model can run in real time with a step size of 50 microseconds.