Hello, Sotiris here! 👋

🚀 This week we will explore a common problem found in half/full bridge power topologies that employ a transformer: the issue of “flux walking” that causes saturation of the transformer core and results in the destruction of the power converter, eventually. Lately I’ve come across this issue again while designing a DAB charger, and I thought it would be an interesting topic to discuss for all the other designers out there.

🔎​ Some background story

Back in the old days, when the bipolar transistor was king and MOSFETs were a new and exotic component to use, engineers used to build their full/half bridge with bipolar transistors. Products were rolling out the factories and everything was normal.

However, after some months of a happy customer-manufacturer relationship, where for example the AC/DC converter was normally performing in the field, some units suddenly started failing. After the converter was brought back to the lab for service, the engineer realized that some transistors of the full bridge were shorted. They were replaced with new ones and the converter was tested to see if all subsystems were working as expected. As soon as it was repaired, the piece was shipped back. That same story was reported from several different products until the culprit was found!  

👩‍🏫 Transformer basics before we catch the culprit!

Let’s take Figure 1, a classic full bridge. QA-QD swings the primary voltage (V_pri) to V_in, whilst QC-QB swing V_pri to -V_in.

Figure 1. A full bridge configuration

Figure 2. Hysteresis loop – BH curves

According to Faraday’s law, we know that applying a voltage for a specific amount of time in an inductor/transformer causes the flux density B of the core to move positive or negative. For a full bridge application:

Where:

➡️​ N_pr is the primary turns number

➡️​ V_in is the DC voltage of the power rail

➡️​ t_on is the time that voltage is applied to the transformer

➡️​ B_pk is the flux density swing in T (Tesla)

➡️​ A_e is the core effective area in m²

Therefore, when QA-QD from Figure 1 are turned-on, equation (1) dictates that the flux density swings positive. In Figure 2, we can see that by applying a voltage to the transformer there is a certain positive magnetic field intensity, so flux density moves to +B (the core was in -B position - steady state conditions). When QC-QB are turned-on during the other half-period, the flux swing from +B to -B.

🧐 The culprit

You can see from (1) that for a certain Bpk (selected for a certain transformer) the only variable parameter is t_on, so if the time that QA-QD are ON and the time QC-QD are ON is the same, then the flux swings from +B to -B in every switching cycle, as described.

 ❓ But what about a slightly different t_on? That would make the flux swing to different point.

Imagine QA-QD conduct slightly more, then the flux density travels from -B to B1. Then QC-QB bring the flux density down to B2, but in the next cycle the flux starts increasing from B2. In a few hundred cycles the flux will walk up to Bsat were the transformer starts saturating. That will cause a steep drop in the magnetizing inductance, thus increasing the transformer current dramatically, finally shorting the bridge, as the switching components (mosfets usually) step outside their SOA (Safe Operating Area) 💥.

🤔 Why the converters failed after months in your story?

Nice question, if that was a question of yours as well. The parasitic element that saves the day is the series copper resistance of the transformer and that of the switching element (the mosfet’s Rds_on). In our scenario earlier, we assumed the QA-QD ON time is slightly more than QC-QB. That will set the flux walking in motion gradually increasing the flux in the core. But since QA-QD conduct for more time, current is larger in this transition (more magnetizing current), so the resistance in series introduces a voltage drop. That voltage drop is robed from the voltage applied to the transformer, and that causes the flux to swing to a lower value. This negative feedback mechanism ameliorates the flux imbalance issue. In mosfets, the Rds_on increases with higher junction temperature and, since we imagined QA-QD conducting for more time, they’d experience a higher current, thus conduction losses, thus a bigger temperature rise resulting in a higher Rds_on!

The better the design, equal QA-QD, and QC-QB transitions, the harder it is to see the phenomenon! Only during transient conditions, as seen easier, and even then, the parasitic resistance may save the day. But there is a failure possibility anyway because we don’t really know how far from saturation the core is under all possible conditions.  

🙌​ Fixing the problem

The horror show described above can be eliminated using the following:

✅ Solution 1

👉 DC blocking capacitor in series with the transformer

During flux walking a DC bias voltage appears in the primary winding. That DC bias cause a certain magnetic field intensity H, so from Figure 2, there is an increasing positive or negative offset of the flux density swing. In normal conditions there is no DC average voltage on the primary. If we insert a series capacitor, then the capacitor will absorb the charge and the primary winding DC bias voltage will be zero.

There are 2 side effects with the DC blocking capacitor solution:

☝️​ It robs some of the voltage applied to the primary winding as shown in Figure 3.

☝️​ It’s physically large, most of the times, since a non-polarized film-cap is usually appropriate

Figure 3. Transformer primary voltage using a DC blocking cap in a push-pull application

The DC voltage that the capacitor subtracts from the primary winding should be chosen at 10% maximum of the peak voltage.

From the basic capacitor equation, we get:

I_pk : is the peak primary current

✅ Solution 2

👉 Peak current mode control

The problem can be also solved by using current mode control. By its nature, this loop control method guarantees that the amplitude of the peak current during each pulse stays the same. Current imbalances are automatically corrected within 1 switching cycle by controlling the duty cycle. Equal currents in the positive/negative transformer transition means no flux walking. Therefore, there is no need for additional protection mechanisms.

😎​ Hope you like it, stay tuned!

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References:

Abraham l. Pressman, 1997, “Switching Power Supply Design”, 2nd edition, McGraw-Hill Professional

Sotiris Zorbas, MSc 

Power Εlectronics Εngineer