# [108] Custom Transformers – Leakage Inductance Considerations

*One equation governs the saturation of a transformer, but the leakage inductance provides strong direction to a design. *

Magnetics Design – Lessons Learned

After graduating from college, my first job was for a computer company outsideBoston. The project was to make a production power supply for computers using a full-bridge design at 850 W. These were the early days of FETs, so we were taking switching frequencies from the industry-standard 20 kHz or so to 100 kHz. The basic specifications were as follows:

Input voltage: 85 VAC to 265 VAC (300 V surge for 1 second)

Output Voltage: 5 V at 130 A (with margin to 5.25 V)

+ 12 V at 7 A

- 12V at 7 A

There was no PFC circuit in front of the full-bridge.Nobody had thought of that at the time, and there were certainly no control chips for PFC. This meant that the stresses on the full-bridge topology were quite high, with operation over an almost 3:1 range.

Very few FET full bridges had been built for production at the time, we were all just learning from experience. The design of the transformer was assigned to my mentor at the time, Dan Balulescu, since he was from the power utility industry and had some experience. (A warning for everyone – once you have experience in magnetics design through to production, you will always be the one that they call on!)

Dan spent many days in his office, buried deep in magnetics design notes, data sheets, and page after page of calculations. Finally, he emerged from the office, showed me the design, and it was sent off to be fabricated by the local magnetics manufacturer. The secondary of the transformer consisted of two turns of 20 mil foil, center-tapped with another two turns, so construction of this was not something we could do ourselves. We needed a professional company to handle the foil construction, the litz primary, and the full safety insulation for VDE approval.

Dan, of course, knew all about the one equation for design that we talked about in the last article of this series. He had the appropriate number of turns for the core selected. And, like many designers, he had a myriad of other equations to try to achieve an optimal design. It was a very painstaking process.

We were fully engaged in board layout, controller design, thermal design, packaging, and everything else that goes into a real-world power supply for several months. The first transformer showed up about a month after the initial design was started.It was my job to install the transformer on the board, and to begin the circuit board testing. When the switches were all turned off at any significant load, there was a strong ringing on the drain of the power FETs. At low line, there was so much energy in this ringing, the voltage rang up to the opposite rail, clamped through the diode of the opposite FET, then rang down again all the way to the bottom rail. This was a destructive situation. Force commutation of the antiparallel diode of the FET led to failures of the bridge.

There was a lot of pain in the lab. The IR rep was called in several times to bring more samples of the FETS (no Digikey existed!) Finally I told Dan – “The transformer has too much leakage – I cannot make it work in our circuit.”

He seemed somewhat unsurprised as though he had anticipated this might happen. This was my first big lesson in the real world – despite all the textbooks in the world, all the guidance, your power circuit is unique. You cannot fully anticipate every parasitic and every event that you are going to see. There will be design iteration, so expect this and be ready for it.

The next transformer cut the number of turns in half and increased the area of the core. This confused me – all that calculation, and after a test we are going to make such a drastic 2:1 change? But there was no choice – the only step down from two turns was one. All the optimization went out of the window. Trial and improvement are the name of the game. We will come back to this point later as it has a big impact on design direction.

Basic Power Transformer Construction

Figure 1 shows the basic construction of a transformer. For high-frequency, hard-switched converters, it is important to get good coupling of primary and secondary windings, so one winding is right on top of the other. (By contrast, a 60 Hz transformer on this shape of core commonly puts one winding on one side of the core, and one on the other. In this case, the high leakage created can actually be beneficial for protection of the system.)

Figure 1: High-Frequency Transformer Construction

The core shape shown here is a U-Core, but that is not important. We need to ensure that we have a closed magnetic circuit, and the actual shape and cross-sectional profile can vary widely. However, the concepts in this article remain the same. We are going to see that the leakage inductance that caused me so much pain in my first design is a function of the spacing between the primary and secondary windings. Small dimensions can make a big difference. Skill and repeatability are crucial in transformer manufacturing.

Power Transformer Equivalent Circuit

As we learned in the last article, it is not possible to make an ideal transformer. The most important extra element that forms the model of the transformer shown in Figure 2 is the magnetizing inductance, Lm, shown in blue. Preventing this inductance from carrying too much current and subsequently saturating the magnetic material led to the one design equation for a transformer. If the equation is satisfied, the transformer will not saturate.

However, while this one equation must ALWAYS be satisfied, an additional consideration on the leakage of the transformer will guide the choice of core and hence number of turns. The additional circuit element that must be added to the transformer model is leakage inductance, Ll,shown in red in Figure 2.

Figure 2: Transformer Equivalent Circuit with Leakage Inductance. We now have two inductors and an ideal transformer representing the real transformer.

The effect of the leakage inductance on the circuit operation is easy to see, and it can be severe. As you can see from Figure 3, the output diode on this particular secondary is supposed to see just 50 V. However, there is a spike of 175 V due to the leakage inductance ringing with the diode capacitance. Anyone who has built a transformer-isolated circuit is painfully aware of the magnitude of this effect.There is always a desire to lower the leakage in the transformer. Before we can do this, however, we need to know the quantities in the transformer that affect the leakage.

Figure 3: The Effect of Leakage Inductance on Circuit Waveforms with Hard-Switched Circuits

Calculating Leakage Inductance

Leakage energy is related to the fields that exist between the two windings of a transformer. No core material is involved, since the fields exist in the space. Hence the equation for leakage inductance is similar to the simple equation for an air-core solenoid, which is well known from basic physics.

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