This article based on Frenetic newsletter written by Jonathan Church, Frenetic product director, is exploring selection of core and transformer optimal operation conditions for phase-shifted full bridge converter.

**Phase-Shifted Full-Bridge** (PSFB) configuration is a popular converter topology for its wide power handling range, isolation, control simplicity and its ability to take advantage of Zero Voltage Switching (ZVS).

To that end you’ll find it in many modern applications.

See Figure 1. for typical PSFB circuit topology.

In this case study lets consider arbitrary and simple specification shown in Table 1, the less detail the better at this point.

**Optimal Frequency for Power Converters**

Finding the right balance between size and efficiency to achieve the greatest power density may be challenging. Selection of optimum operating frequencies may be a key design element here, but it requires a well-rounded understanding of your system.

Increasing the operating frequency will reduce converter size, but eventually the gains will be eroded by the need for additional heatsinking or other forms of more advanced and costly cooling. Alas, another plate to spin. Let’s take a holistic look at the effect that the changing of frequency has on our power system components below.

Intuitively, your switching losses and gate-drive losses are going to proportionally increase. Many great innovations are reducing the gradient to which these losses increase but despite this and despite any type of soft-switching resonant converter you may be using, this is still going to happen so keep an eye on them.

The reactive components in the system will reduce in size as you increase the frequency, notably your input and output filtering. This is a quick win for your power density providing you have well in hand (sorry Luke) the knowledge required to design an effective filter, plus you understand the control and stability aspects of your design.

Now let’s talk about the “bottleneck”, or perhaps a better term I think would be the “pacemaker”. When we increase the operating frequency from the magnetics’ perspective it isn’t as straight forward. If we increase the frequency we want a Return On Investment (ROI), we want to see a reduction in core size ideally. This can be achieved, and you may or may not be able to maintain your core losses I would hate to say… Bear in mind however, the same losses in a smaller object will result in a greater temperature rise and that must be managed somehow.

In addition, as we increase the frequency and cash in by reducing our core size, our winding window gets smaller, the current density increases and so will the effect of AC losses in our wires. Needless to say, magnetics are the most complex part of a power converter design, especially as we push the boundaries.

It’s clear however, that one of the main challenges facing power engineers in design is the non-linearity of the magnetics relationship with frequency. This complexity warrants a section of its own, so today lets only talk about the Transformer.

**Transformer Operating Frequency Optimization**

You may have read in one place or another that in order to design a Transformer for efficiency, you need to find a balance between the core and winding losses. To prove this point, I’m going to run a thought exercise. However, it requires me to assert a simplification and you should bear in mind that this only works because it’s a PSFB topology.

*If the magnetizing inductance is sufficiently large enough, the operation of the converter will be consistent over a range of frequencies, thus allowing me to observe the optimal frequency of a fixed transformer design.*

I started my design on Frenetic, deliberately choosing to start big and simple with an E71/33/32, un-gapped 3C95 core as shown in Figure 3. Using the simulator, I was able to calculate the distribution of core and copper losses between 20 kHz and 150 kHz – see Figure 4.

As the frequency increases, we can see that the core losses decrease. This is because, whilst all other parameters stay the same (or Ceteris Paribus for those who still use Latin), the increase in frequency reduces the volts-seconds imposed across the transformer primary which reduces the flux density.

Following that, when calculating the core losses, **over this frequency range (and with this material) **the Steinmetz coefficient for flux density has a more dominant effect on the overall equation than the coefficient for frequency. So as the frequency increase adds to the core losses, the drop in flux density has the larger net effect and therefore the core loss tends to reduce. If I was to go beyond 150 kHz and upwards, we would see the gap between the coefficients close, and the dominance of the flux density reduce. I think this is a topic for another day… Oh my.

Regarding the copper losses, the best outcome is that these losses are only caused by the DC resistance of the wires and the RMS currents through them (I_{rms}^{2}Rdc). As you increase the frequency however, this reality slowly fades away along with all your hopes and dreams.

So, you have on one side the core losses decreasing with frequency and on the other side the copper losses increasing. It becomes quite clear then why the intersection of these two loss mechanisms provides you with the most efficient magnetic design. For us, our magnetic here is the most efficient at around 50 kHz.

Is this the best design I could have achieved having started knowing I would use 50 kHz? I suspect I could have done a little better. But let’s continue this journey together and see where it takes us.

**What happens if we change the core?**

I conducted a similar analysis for two other cores E65/32/27 and E55/28/25, see the data below in Figure 5. and 6.. Before reading further though, what conclusions can you draw?

From my initial case, I have gone through three consecutive E cores reducing in size each time. I kept the number of turns the same following my rule: *that I don’t particularly care about the magnetizing inductance providing it is sufficiently large*. However, to make it work I have reduced the number of strands in the Litz wire to ensure there is always a comparable fit.

The first thing I notice is that the loss intersection point moves to a higher frequency as I reduce the size of the core. Why is that? Look a little deeper, you might notice that the core losses are getting **higher** as we reduce the size of the core and the copper losses are getting **lower**, so that explains why the intersection point is moving forwards.

Regarding the core losses, the only thing that I’ve changed is the effective area A_{e} of the core. Reducing this will increase my flux density at any given frequency. As we’ve discovered, the flux density is currently dominant for us in the core loss calculation and therefore we would expect to see an increase, this all makes sense.

Regarding the copper losses, when I reduce the size of the core, I’m also reducing the size of the window and increasing the current density. Why aren’t the copper losses increasing?

Well, I’m also reducing the amount of wire used to rap around the smaller core and therefore the DC resistance. This also has the net effect of reducing the aggressiveness of the AC resistance as we go up in frequency and overall, it softens the copper loss gradient we observe in the graphs.

I’ve managed to find an optimal operating point for a fixed transformer design using Frenetic, by simply moving the frequency around until the core and copper losses arrive at a balance. Playing with different cores whilst keeping some other parameters fixed, we saw that the optimal frequency point moved around, only on the horizontal axis though…

I wonder then what levers (if any) I can pull to make significant changes in the vertical axis? In the next part to this series, I’m going to look at how the rest of the converter is affected by frequency changes. Can I justify an optimal transformer design for a specific frequency, or are there bigger things at play?

Meanwhile, I encourage you to use Frenetic, not just as a design tool but as a learning platform and a place to be curious. Look for novel and interesting ways to optimize your designs whilst becoming a better engineer in the process.