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# Nonlinear Inductor

Model inductor with nonideal core

Passive Devices

## Description

The Nonlinear Inductor block represents an inductor with a nonideal core. A core may be nonideal due to its magnetic properties and dimensions. The block provides the following parameterization options:

### Single Inductance (Linear)

The relationships between voltage, current and flux are defined by the following equations:

$i={i}_{L}+v{G}_{p}$

$v={N}_{w}\frac{d\Phi }{dt}$

$\Phi =\frac{L}{{N}_{w}}{i}_{L}$

where:

• v is the terminal voltage.

• i is the terminal current.

• iL is the current through inductor.

• Gp is the parasitic parallel conductance.

• Nw is the number of winding turns.

• Φ is the magnetic flux.

• L is the unsaturated inductance.

### Single Saturation Point

The relationships between voltage, current and flux are defined by the following equations:

$i={i}_{L}+v{G}_{p}$

$v={N}_{w}\frac{d\Phi }{dt}$

where:

• v is the terminal voltage.

• i is the terminal current.

• iL is the current through inductor.

• Gp is the parasitic parallel conductance.

• Nw is the number of winding turns.

• Φ is the magnetic flux.

• Φoffset is the magnetic flux saturation offset.

• L is the unsaturated inductance.

• Lsat is the saturated inductance.

### Magnetic Flux Versus Current Characteristic

The relationships between voltage, current and flux are defined by the following equations:

$i={i}_{L}+v{G}_{p}$

$v={N}_{w}\frac{d\Phi }{dt}$

$\Phi =f\left({i}_{L}\right)$

where:

• v is the terminal voltage.

• i is the terminal current.

• iL is the current through inductor.

• Gp is the parasitic parallel conductance.

• Nw is the number of winding turns.

• Φ is the magnetic flux.

Magnetic flux is determined by one-dimensional table lookup, based on the vector of current values and the vector of corresponding magnetic flux values that you provide. You can construct these vectors using either negative and positive data, or positive data only. If using positive data only, the vector must start at 0, and the negative data will be automatically calculated by rotation about (0,0).

### Magnetic Flux Density Versus Magnetic Field Strength Characteristic

The relationships between voltage, current and flux are defined by the following equations:

$i={i}_{L}+v{G}_{p}$

$v={N}_{w}\frac{d\Phi }{dt}$

$\Phi =B\cdot {A}_{e}$

$B=f\left(H\right)$

$H=\frac{{N}_{w}}{{l}_{e}}{i}_{L}$

where:

• v is the terminal voltage.

• i is the terminal current.

• iL is the current through inductor.

• Gp is the parasitic parallel conductance.

• Nw is the number of winding turns.

• Φ is the magnetic flux.

• H is the magnetic field strength.

• B is the magnetic flux density.

• le is the effective core length.

• Ae is the effective core cross-sectional area.

Magnetic flux density is determined by one-dimensional table lookup, based on the vector of magnetic field strength values and the vector of corresponding magnetic flux density values that you provide. You can construct these vectors using either negative and positive data, or positive data only. If using positive data only, the vector must start at 0, and the negative data will be automatically calculated by rotation about (0,0).

## Dialog Box and Parameters

### Main Tab

Parameterized by

Select one of the following methods for block parameterization:

• Single inductance (linear) — Provide the values for number of turns, unsaturated inductance, and parasitic parallel conductance.

• Single saturation point — Provide the values for number of turns, unsaturated and saturated inductances, saturation magnetic flux, and parasitic parallel conductance. This is the default option.

• Magnetic flux versus current characteristic — In addition to the number of turns and the parasitic parallel conductance value, provide the current vector and the magnetic flux vector, to populate the magnetic flux versus current lookup table.

• Magnetic flux density versus magnetic field strength characteristic — In addition to the number of turns and the parasitic parallel conductance value, provide the values for effective core length and cross-sectional area, as well as the magnetic field strength vector and the magnetic flux density vector, to populate the magnetic flux density versus magnetic field strength lookup table.

Number of turns

The total number of turns of wire wound around the inductor core. The default value is 10.

Unsaturated inductance

The value of inductance used when the inductor is operating in its linear region. This parameter is only visible when you select Single inductance (linear) or Single saturation point for the Parameterized by parameter. The default value is 2e-4 H.

Saturated inductance

The value of inductance used when the inductor is operating beyond its saturation point. This parameter is only visible when you select Single saturation point for the Parameterized by parameter. The default value is 1e-4 H.

Saturation magnetic flux

The value of magnetic flux at which the inductor saturates. This parameter is only visible when you select Single saturation point for the Parameterized by parameter. The default value is 1.3e-5 Wb.

Current, i

The current data used to populate the magnetic flux versus current lookup table. This parameter is only visible when you select Magnetic flux versus current characteristic for the Parameterized by parameter. The default value is [ 0 0.64 1.28 1.92 2.56 3.20 ] A.

Magnetic flux vector, phi

The magnetic flux data used to populate the magnetic flux versus current lookup table. This parameter is only visible when you select Magnetic flux versus current characteristic for the Parameterized by parameter. The default value is [0 1.29 2.00 2.27 2.36 2.39 ].*1e-5 Wb.

Magnetic field strength vector, H

The magnetic field strength data used to populate the magnetic flux density versus magnetic field strength lookup table. This parameter is only visible when you select Magnetic flux density versus magnetic field strength characteristic for the Parameterized by parameter. The default value is [ 0 200 400 600 800 1000 ] A/m.

Magnetic flux density vector, B

The magnetic flux density data used to populate the magnetic flux density versus magnetic field strength lookup table. This parameter is only visible when you select Magnetic flux density versus magnetic field strength characteristic for the Parameterized by parameter. The default value is [ 0 0.81 1.25 1.42 1.48 1.49 ] T.

Effective length

The effective core length, that is, the average distance of the magnetic path. This parameter is only visible when you select Magnetic flux density versus magnetic field strength characteristic for the Parameterized by parameter. The default value is 0.032 m.

Effective cross-sectional area

The effective core cross-sectional area, that is, the average area of the magnetic path. This parameter is only visible when you select Magnetic flux density versus magnetic field strength characteristic for the Parameterized by parameter. The default value is 1.6e-5 m^2.

Parasitic parallel conductance

Use this parameter to represent small parasitic effects. A small parallel conductance may be required for the simulation of some circuit topologies. The default value is 1e-9 1/Ω.

Interpolation option

The lookup table interpolation option. This parameter is only visible when you select Magnetic flux versus current characteristic or Magnetic flux density versus magnetic field strength characteristic for the Parameterized by parameter. Select one of the following interpolation methods:

• Linear — Uses a linear interpolation function.

• Cubic — Uses the Piecewise Cubic Hermite Interpolation Polinomial (PCHIP).

For more information on interpolation algorithms, see the PS Lookup Table (1D) block reference page.

### Initial Conditions Tab

Specify initial state by

Select the appropriate initial state specification option:

• Current — Specify the initial state of the inductor by the initial current through the inductor (iL). This is the default option.

• Magnetic flux — Specify the initial state of the inductor by the magnetic flux.

Initial current

The initial current value used to calculate the value of magnetic flux at time zero. This is the current passing through the inductor. Component current consists of current passing through the inductor and current passing through the parasitic parallel conductance. This parameter is only visible when you select Current for the Specify initial state by parameter. The default value is 0 A.

Initial magnetic flux

The value of magnetic flux at time zero. This parameter is only visible when you select Magnetic flux for the Specify initial state by parameter. The default is 0 Wb.

## Examples

For comparison of nonlinear inductor behavior with different parameterization options, see the Nonlinear Inductor Characteristics example.

## Ports

The block has the following ports:

+

Positive electrical port

-

Negative electrical port