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## August 13, 2001

### Measuring Leakage Inductance

**Question:** How do you measure leakage inductance?

**Original Question:** I'm facing severe problems relating to leakage inductance in a multiple output flyback converter. I have an LCR meter. Kindly tell me the practical way to measure leakage inductance in multiple output flyback transformers.

**Answer:** My algorithm for answering such question is to first answer off the top of my head, which may or may not be right, then use the search box on my website to see if I have discussed it, then to look it up in the primary reference I recommend, which is Erickson and Maksimovic, and then the introductory reference I recommend, which is (Basso) in my recommended personal power supply design library, and finally looking for any other information that is handy. First lets answer the measuring-leakage question.

My off-the-top-of-my-head answer is to short the secondaries, measure the primary reactance at the switching frequency, and calculate inductance from the reactance and frequency. As my following discussion shows, this is a major simplification.

Placing the phrase "leakage inductance" in the search box on my home page yielded a discussion on how do you design snubber circuits, a related topic, and a reference to Kiltie's book. Looking up the section in Kiltie's book found it to be a minor expansion of my top-of-the-head response. Searching just on leakage turned up a key paper, *Transformer Modeling and Design for Leakage Control*, in Volume I of a Middlebrook and Cuk book.

The Erickson and Maksimovic book gives a classical development for the two winding transformer (pp. 504,506). Since I know the authors are familiar with the magnetics work done at the California Institute of Technology, I was somewhat disappointed that they did not warn you that things get more complicated when windings are added, especially given their extensive coverage of proximity and other losses.

Basso's book (pp. 46-48, pp. 231-234) where he discusses modeling of two and three winding transformers and how to make the measurements did better. For more details he refers to a paper he wrote, *Living With Leakage Elements in Flyback Converters*, in PCIM, April 1999. The hard copy of the article says that it is available on the PCIM on-line magazine. However a search there indicated the archives only go back to Jan 2001. But all is not lost. The paper is available as *On Semiconductor* application note AN1679/D, *How to deal with Leakage in Flyback Converters*, and is downloadable from the On Semiconductor website as a pdf document. He also references the *Transformer Modeling and Design for Leakage Control* paper above, whose abstract follows.

Shi-Ping Hsu, R. D. Middlebrook, and Slobodan Cuk, *Transformer Modeling and Design for Leakage Control* in Middlebrook, R. D., and Slobodan Cuk, Advances in Switched-Mode Power Conversion, Volumes I and II, 2nd Edition, TESLAco, 1983. 533 p. Available from TESLAco, #10 Mauchly, Irvine, CA 92718, Phone (714) 727-1960. (First edition c 1982.).

The pi-model of a transformer, convenient because of its close connection with the physical structure, is expressed in terms of the permeances associated with magnetic paths. The pi-model is under-determined for a two-winding transformer, and uniquely determined for a three-winding transformer. However, although the pi-model is over-determined for transformers of four or more windings, it can still be usefully employed if the windings satisfy certain constraints, some examples of which are given for a four-winding transformer. Several predictions of the model important for practical designs are experimentally confirmed: the leakage inductance of one winding of a three-winding transformer is increased by closer coupling between the other two windings; the leakage inductances are essentially independent of air gap, although the coupling coefficient decreases with increasing air gap length. (AUTHOR ABSTRACT)

The bottom line is that the relationships are too complex to explain in a short email and you need to look at some of the references above.

Posted by Jerrold Foutz at August 13, 2001 11:25 AM