Application Note

Using Coupled Inductors and Inductor Cores
Source: OrCAD Technical Support
Revised by: Brian Hirasuna, April 1999
Edited by: David Busdeicker, March 2000

This note gives information on coupling inductors and on modeling saturable cores to add hysteresis and saturation. The inductor coupling symbols may be used to couple up to six independent inductors (with or without Core models) on a schematic. The coupling symbols K_LINEAR and KBREAK are described, as well as Core models in the MAGNETIC library.



To Use the K_Linear symbol for an ideal transformer
  1. The K_LINEAR symbol in "analog.olb" is provided for specifying linear coupling, between inductors.
  2. Draw the schematic and assign the desired names (reference designators) to all of the symbols. (Reference designators are assigned automatically, but may be changed by double-clicking on them.)
  3. Place one coupling symbol, K_LINEAR, anywhere on the schematic, for each group of coupled inductors. These symbols have no pins; they are represented by the letter K enclosed in a box.
  4. Double-click on each coupling symbol (on the K-in-a-box, not the attributes) and enter the reference designators for the coupled inductors as the values for L i (i=1,2,...,6).
  5. Set the value of the COUPLING attribute to the value of the coupling factor, K.
To Use the Core symbols in "magnetic.olb"
  1. Draw the schematic and assign the desired names (reference designators) to all of the symbols. (Reference designators are assigned automatically, but may be changed by double-clicking on them.)
  2. Select the coupling symbol for the desired CORE model from "magnetic.olb", and place one coupling symbol, anywhere on the schematic, for each group of coupled inductors. These symbols have no pins; they are represented by the letter K enclosed in a box.
  3. Double-click on each coupling symbol (on the K-in-a-box, not the attributes) and enter the reference designators for the coupled inductors as the values for L i (i=1,2,...,6).
  4. Set the value of the COUPLING attribute to the value of the coupling factor, K.
To Use the Kbreak symbol with a custom Core model
A generic symbol, KBREAK, is provided in "breakout.olb" for specifying arbitrary nonlinear magnetic core models. KBREAK has a preassigned model attribute, but its corresponding model in "breakout.lib" has no parameters. CORE models can be created through use of the PSpice Model Editor.

Example extraction of B-H loop in the PSpice Model Editor
  1. In the Model Editor (formerly called Parts), choose File/New. Type in a new library name. Choose Model/New, then choose CORE, then enter the name. Click on Hysteresis Loop, go get the specification entry screen.
  2. First set the initial permeability (at the bottom of the specificatin screen) according to datasheet specifications.
  3. Pick 3-4 points along both limbs in the first quadrant of the B-H loop. Pick the first point on the y-axis intercept (for example, (0, 600) ). Pick another point at the x-axis intercept (for example, (0.04,0) ). Pick a fourth point where the limbs converge. Pick 2 additional points on either limb, for the same x-axis value (for example, (0.12, 2000) and (0.12, 1500) ).
  4. Input initial permeability - 10000 from datasheet for W material
  5. Enter H, B intercept points (0, 600) (0.04,0)
  6. Enter point where loop closes (0.4,3000)
  7. Plot/Display
  8. Plot/X-axis settings, set Data Range 0 to 0.45
  9. Extract/Parameters - rough fit of loop is achieved
  10. Enter points (0.12, 2000) (0.12,1500), one on each limb
  11. Extract for final fit
Because the extraction of the B-H loop is generally non-unique, the order of entering points and extracting is important. Please note also that many manufacturers show H in A/m. The Model Editor uses oersted. 100A/m is 1.25 oersted. For the CORE model, we do not recommend fixing (freezing) the Jiles-Atherton parameters MS, A, C, K. The parameters PATH and AREA are not extracted from the B-H loop, and must be entered by the user.

Completing the Model
After extracting the Jiles-Atherton parameters, in the Model Editor set the following parameters (in the spreadsheet) according to the datasheet specifications:

AREA=<cross section area in cm^2>
PATH=<magnetic path length in cm>

Using the model in Capture
The KBREAK symbol in the BREAKOUT library can be used with this new model.

To use KBREAK with your new CORE model:
  1. In Capture, place an instance of KBREAK from the BREAKOUT library.
  2. Double click the symbol to change the Implementation property to the new model name. This is the name given to the CORE model in the Model Editor.
    NOTE: If you are using using Schematics v8.0, use Edit Model-->Change Model Reference to change the model name.
  3. Check that the model library (created by the Model Editor) is configured in the Libraries tab in your Simulation Settings.
Additional Topics
DOT convention
The "dot" convention for the coupling is related to the direction in which the inductors are connected. The dot is always next to the first pin to be netlisted. When the inductor symbol, L, in the ANALOG library is placed without rotation, the "dotted" pin is the left one. Edit/Rotate (<Ctrl R>) rotates the inductor +90deg, which makes this pin the one at the bottom, etc.

Rules for symbol properties
Certain rules must be followed when setting the properties for coupling symbols and the inductors they affect.

Nonlinear CORE models may be applied to one or more inductors, so:
Linear coupling must be applied to two or more inductors (K_LINEAR only):
Fitting the Jiles-Atherton parameters without the Model Editor (PSpice Basics version only)

Characterizing core models may be done by trial and error using PSpice using a test circuit . This test circuit plots the B-H curve in Gauss vs. Oersted by running a transient analysis. Here are some guidelines for trial-and -error fitting of the B-H curve:

First, the anhysteric curve (K=0) is set-up. This curve is centered in the B-H loop, like a spine. Its slope at 0 is nearly the same as the slope of the curve whenever it crosses B=0 (X axis). So first set

MS = Bmax/0.01257, then tweak the parameter A until you get a curve you like. You can change the value of MS a little to get the saturation values right (MS affects B given infinite H).

Now make K non-zero to create hysteresis. K affects how "open" the B-H loop is. After getting the width corrct, you may want to nudge the anhysteric curve (above) to "tune" the Br (remnant flux) and Hc (coercive force) values.

Now, set C to obtain the initial permeability. In effect, C is the ratio of the susceptibilities of the inital and anhysteric curves. Since permeability is dB/dH, Probe will display this formula (probe calculates differences, not derivatives, so the curves will have a few kinis). It is useful to display this, superimposed on the B-H curve. The initial value of dB/dH is the initial permeability.


Fig 1. Test circuit to generate B-H curve

The transient analysis is run to 4 seconds (final time) and has a maximum time step of 0.01 seconds. The inductor (L1) has 20 turns around the K528T500_3C8 torroid core.


Fig 2. B-H curve: add Trace for B(K1); set X-axis variable to H(K1).

X-axis unit is Oersted; y-axis unit is Gauss.

Restrictions on coupling coefficients for systems of coupled inductors

When running a transient analysis, it is possible to have convergence difficulties with systems of coupled inductors. Systems of coupled inductors with physical solutions have the property that the coupling matrix (K matrix) be positive definite [1]. For three inductors this may be tested by the following inequality:

K 12 2 + K 13 2 + K 23 2 2*K 12 *K 13 *K 23 < 1

Where Kij is the coupling coefficient between the ith and jth inductor.

Example:

If K 12 =1, K 13 =0.9, and K 23 =0.95, then the LHS of the equation is 1.0025 (> 1.0000). This system of coupled inductors will not converge since it has no physical solution.

If K 12 =1, K 13 =0.9, and K 23 =0.9, the result is 1.0000, and the system will converge.

References
[1] Yilmaz, Tokad and Myril B. Reed, "Criteria and Tests for Realizability of the Inductance Matrix," Trans. AIEEE, Part I, Communications and Electronics, Vol. 78, Jan. 1960, p.924.