Hello, Sotiris here! 👋

🚀 What’s the deal today? It’s about making things smaller whilst maintaining the same power rating. In other words the goal is power density. 🚀

Basics of power density:

👉   We usually measure the power density in W/inch² (watt per square inch) or in kW/dm³ (kilowatt per square decimetre). It’s a nice way to essentially compare volume VS power in a transformer or in a power converter in general. All you need to know is the volume of your object under question and its rated power. Dividing these values gets you the power density. Essentially, it’s a measure of how compact and dense a design is, that handles/converts power.

Frequency of operation place a big role as well. Think of a 50Hz iron transformer and its size to deliver 1kW of power. It weights more than 15kg and has a size of 5 Harry Potter books stacked on top of each other. Now compare this with the ferrite transformer sizes we examined in these newsletters (rated at 1kW/100kHz). For example, a PQ50/50 core has the volume of your fist and weighs less than a cup of coffee.

⭐️ The achievable power density limit increases as frequency increases.

Although power density doesn’t consider mass, extra weight is never good for a product. Keeping things light and small is key, when the logistics guy enters the chat 😎.  

💥   In his previous personal newsletter the CEO of Frenetic, Dr. Molina, shared his ideas about the state of the art power densities in magnetics. A 30-50 kW/dm³ power density level at 100kHz is considered a top design.

Let’s start with the power density-oriented design!

👉   Project file here!

Figure 1. Specs

Core stage:

I want to get the smallest core that can fit my windings. Easier said than done of course. I started thinking about the volume of the transformer, since we’re aiming for power density. It can be approximated by multiplying the length by the width by the height of the transformer. That approximation works well in many cases. Another indicator for quick comparisons is to check the core-set volume that is shown on our tool directly.

Looking at a PQ50/50, a PQ40/40 and a PQ35/35 core-set we get the following numbers:

Wanting to get a badge of honor 🎖️, I went for the PQ35/35 core that would get me the >30kW/dm³ density I could be proud of 🤗.

Then came the question of core material… 🤔. Since I aimed for power density, I know I run the risk of making a 🔥 design. I’m implying that reducing the volume of a transformer whilst having the same power losses will cause the hotspot temperature to increase. There are empirical lab created equations that predict temperature rise based on the core volume of the transformer alone like this one:

R_th = 53 * (V_core)^-0.54     (1)

Knowing the volume of a transformer we can find it’s thermal resistance (natural cooling) and multiplying it with the power losses the temperature rise is calculated.

ΔT = R_th P_{tot_loss}      (2)

So,

T_max = T_amb + ΔT      (3)

Where:

• R_th  is the thermal resistance in °C/W
• V_core  is the core volume in cm³
• ΔT  is the temperature rise of the transformer
• P_{tot_loss}  is the power loss of the transformer
• T_amb  is the ambient temperature
• T_max  is the hotspot temperature

🔑 My point for now is that there is a strong relationship between volume and temperature rise.

💡 Hey there is a starting point!

I went back to the PQ50/50 transformer I built a couple of weeks ago and checked the total transformer power losses I had in that design.

From the experiments I have the hotspot temperature of the sample which finally reached 69.6°C under 1kW load.

Based on (1), (2) I can calculate the power loss of the new PQ35/35 design that would equate the same hotspot temperature as the PQ50/50 sample already tested.

Without boring you with basic algebra ✍️ that number is 3.8W of total losses for the PQ35/35 design.

Returning to the core selection issue.

There is a new option on the Frenetic tool released that allows the user to limit his options of cores/wires to only part numbers that are available in our facilities for quick turnaround of samples. Check Figure 2 below.

Figure 2. Core selection

You can go back and forth between stock-only parts and all parts, by toggling the corresponding button marked above. I run the simulation for all 5 available materials, with the 3C97 giving the lowest core losses.

✅ Core material selected!

 Windings stage:

Figure 3. Primary winding

Figure 4. Secondary winding

In Figures 3-4 you can see the primary/secondary winding specs, as well as the total winding losses in the “General Results” box.

✅   I strived to get a manufacturable configuration with minimum windings power losses. After many iterations with different configurations and Litz wires, I achieved a total power loss of 4.1W 👍, which is close to the target 3.8W I set as a target before. I tried both PSP – PSPS (P: primary, S: secondary) winding configurations and I chose the PSP, since the other one wasn’t performing any better really (checking power losses as a metric) and it’s more complicated to manufacture.

✅   For the primary winding I got a current density of 6.5A/mm² which is not bad. For the secondary winding though despite my effort to go for a lower current density, I was pushed into designs that didn’t fit this bobbin… Maybe I missed something but I’m happy with the design as it is.

✅  Following the current density rule of thumb of 5A/mm² actually pushes the designer to use windings with lower DC resistance which in fact lowers the total copper losses. But there is a limit to this, as changing the windings may lower the DC resistance but the total losses may go up, because of increased skin/proximity losses. It’s a trial-and-error situation, but Frenetic online is allowing for iteration in a matter of minutes.

👉👉   If you are curious to know more about Frenetic Online, just click here to book a demo ! 👈👈

As always, if you have a question or an idea, let me know!

 👋  Until next week 👋 

Sotiris Zorbas, MSc 

Power Εlectronics Εngineer