# Modeling Magnetics in SIMPLIS -- Part II Transformers

### Date

Previously Held on Jan 19th, 2017

This Webinar presents the SIMPLIS best practices approach to modeling energy-storage transformers for power electronic applications. We first illustrate the SIMPLIS T-Equivalent circuit transformer model, which is good for the large majority of switching power supply applications, such as predicting device stresses and output voltage cross regulation. We also address an approach for modeling more complex magnetic structures based on a reluctance model.

The webinar recording can be viewed at this link: Modeling Magnetics in SIMPLIS -- Part II Transformers (54:09)

## Abstract

1. Brief review on how to characterize single-winding magnetic devices
2. T-Equivalent transformer model
• Good for most applications
• SIMPLIS best-practices model
• Measuring leakage flux effects
• Open and Short Circuit measurements
• Modeling leakage flux effects
• Applications
• Predicting voltage stresses
• Predicting cross regulation
3. Modeling more complex magnetic structures
• Electrical equivalent circuit of a reluctance model
• Relates physical structure of magnetic device to transformer model
4. A Brief word on modeling losses

## Reference Materials

Schematics and presentation slides for the webinar can be downloaded here: jan_2017_SIMPLIS_Transformer_Modeling.zip.

Q1: What did you mean by transformer impedance?

A1: For a flyback dc-to-dc converter where current flows only in the primary winding during the ON-time of the switch and only flows in the secondary windings during the OFF-time of the switch, the shape of the secondary current waveforms depends on the relative impedances of the secondary windings as well as the average currents being delivered to each output winding.  The relative winding resistance and relative leakage inductance of each secondary winding have quite similar effects on the current waveforms.  By contrast, in the ideal case where each secondary winding has zero resistance and zero leakage inductance, both currents will be triangular with a constant negative slope and go to zero at exactly the same time.

One helpful image is the following.  During the ON-time of the switch, energy is being stored in the flyback transformer.  When the switch turns off, that energy now will be delivered to the outputs through the secondary windings.  If one secondary winding is perfectly coupled to the primary and the other secondary winding has significant leakage inductance, then at the instant that the switch turns off, more energy will be delivered to the output with zero leakage inductance.  It will take time for the current in the other secondary winding to build up to a value that is commensurate with the load on its output.  Just in a two output case, the shape of the two secondary windings can vary quite dramatically depending on their relative coupling to the primary.

Here are two references that go into this in way more detail than you probably want to know:

"Cross Regulation in An Energy-Storage DC-to-DC Converter with Two Regulated Outputs", T. G. Wilson, Jr., Bell Telephone Laboratories, IEEE Power Electronics Specialists Conference Record 1977, pp. 190-199.

"Cross Regulation in a Two-Output DC-DC Converter with Application to Testing of Energy-Storage Transformers", T. G. Wilson, Jr., Bell Telephone Laboratories, IEEE Power Electronics Specialists Conference Record 1978, pp. 124-134.

Q2: Aren't different times to zero for the sec currents dues to different load currents rather than due to leakage inductance?

A2: No. See A1.

Q3: How is the secondary leakage inductance determined in multiple secondary transformers.

A3: As we discussed in the Webinar, we are always going to be one measurement short of being able to uniquely measure each leakage inductance on a multi-winding transformer.  So, that means that engineering judgment is needed.  When you want to get a good measurement of the relative leakage inductance between two secondary windings, then you might consider in addition to shorting one secondary winding and measuring the inductance looking into the other secondary winding, make a  measurement looking into each secondary winding with both the other secondary and the primary winding shorted.  Depending on the turns ratios, shorting the primary may help to get a closer measurement of each secondary leakage inductance.  In the end, though, you will need to use your engineering judgment, often based on the physical arrangement of the windings, as to how to proportion the measurement of leakage you can make, which always is a sum of at least two leakage inductances appropriately reflected to the measured winding.

Q4: Do you plan on modeling proximity losses?

A4: Yes, we do plan to do this at some point in the future.  But that involves describing the physical arrangement of the windings relative to the core and each other.