Hello everyone, it’s Jonny here!

📝 There was an article back in 2018 following on from a wrap session at APEC that was debating which had made more of an impact on the power industry: was it Devices, or Magnetics? This strongly framed article was written by none other than Slobodan Cuk and he certainly didn’t mince his words (see reference in footer).

His opening quote read like this:

“This is like comparing Apples and Oranges! The only thing they have in common is that they are just components forced to operate at switching frequencies 100 times higher than needed!”

⚠️Now, in a world where we are all so intent on pushing up the frequency, this is quite a statement, and one that requires some thinking about. He issues it as a warning to all and clarifies that it was also one, he had given 30 years previous.

His main angle in this article is that, in fact, we would be better to spend our time on developing the right topologies and switching techniques to provide us with more power dense solutions, than looking for constant improvements to both devices and magnetics to allow for higher switching frequencies. At least, this is my interpretation.

📈 Still, a noble venture though, right? If it’s possible in both the devices and Magnetics, then why not? We can only improve their respective power densities by doing so.

He goes on to say things like:

“In fact, the buck Converter with its “simple” DC Inductor is the single reason for pushing to MHz switching frequencies to compensate for 100-fold reduction of inductance!”

💭 And:

“There is also huge collateral damage for isolated Converters! While that could indeed allow for smaller inductance, it also forces the Transformer in forward converter to also operate at the same 2MHz!”

“At least GaN proponents will be able to claim to use Transformers at 2MHz (with their 2MHz Inductors!) albeit without any size advantages compared to 100kHz optimized ferrite materials!”

☝️ There are so many things I want to decipher for you in this article, as there are so many important topics being addressed here. Whether or not I entirely agree right now is a different point, so I would rather let empirical data lead the way.

From my previous articles, you may have realized that I’m a little (a lot) obsessed with frequency. But I think I only scratched the surface, and I’m not happy about that, so I’ve set myself a mission. I won’t be able to squeeze all the information in only one release, so I’m calling this part I.

💡 Let’s start with the first point I want to tackle:

“In fact, the buck Converter with its “simple” DC Inductor is the single reason for pushing to MHz switching frequencies to compensate for 100-fold reduction of inductance!”

What does he mean by this?

Well, earlier in his article he expresses the importance of having an air gap that’s proportional to the DC load of the Buck Converter to prevent the Magnetic from saturating. He implies that even modest DC loads will render the material itself to a fraction of its original utility, with regards to its creation of inductance, that is. Then, he leads on to the comment I have highlighted above.

⚡I don’t agree with that statement, as in, I don’t think the reduction in inductance due to this necessary gapping is the reason we push up frequencies to MHz ranges. However, I do believe the convenience of increasing the frequency of these types of Converters is causing us one of the largest challenges in Magnetics today.

Let’s go to the technical, I will explain first why I disagree. When we increase the gap (and keep all else the same), you can see below that we reduce the inductance. This formula isn’t entirely accurate because I have discarded the reluctance of the material as negligible, and that’s not true, but it helps to show the point.

Where L is Inductance (H),

N is the number of turns

_μ0 is the permeability of free space (H/m) (material permeability insignificant as the gap dominates)

A_e is the core cross-section area (m²)

And l_g is the total length of the gap (m)

🤓 Another formula below tells us the same story:

Here we see that the flux density in each DC Inductor core is proportional to the value of its inductance, L (H) and the peak current it sees I_PK (A), whilst being inversely proportional to the number of turns it has, N and its core’s cross-sectional area A_e (m²).

📉 If we want to try and increase the power density of a converter, then we want to push more power through it:

• I_PK goes up.
• It follows that we don’t want to use a bigger core (because we’re trying to increase the power density) so let’s keep A_e the same.
• If we increase the number of turns the resistance will increase because we would be reducing the wire diameter to fit in the same window, so more copper losses, and greater temperature rise. No thanks, let’s keep N the same.
• Finally, if we want to keep B_MAX where it is to avoid saturation, we must reduce L.

So, we have two perspectives here that say we should be reducing L as we go up in power. But I still don’t see the motivation to push the frequency up because of this. I would love to hear to the contrary but it’s my understanding that an economic value of DC inductance, and we talk here about the economy of its size vs its efficiency, is found somewhere between:

👉 Not having an excessively large ripple current so that we have relatively insignificant core losses, and reasonably small output capacitors.

AND

👉 Not having an excessively small ripple current, so that the Inductor isn’t unnecessarily oversized and thus depreciating the power density we are striving to achieve.

In fact, much work has been done to prove this point exists at around +/- 20% ripple current. The image below shows an ideal point of operation for the inductor in a Buck when considering the energy of the inductor, the input/output RMS capacitances of the converter, and thus a nice balance between size and efficiency.

Figure 1 - Economic Ripple Ratio (Switching Power Supplies A-Z, Second Edition, Sanjaya Maniktala)  

The best value of ‘r’ lands on 0.4 (i.e. +/- 20%), where:

📊 So, I argue that as we go up in current, the inductance will be allowed to reduce to keep at this +/- 20% ripple magnitude without needing to increase the frequency.

Whereas I don’t agree with the statement Cuk made, and I’m not writing off the possibility that I’ve interpreted it wrongly, what I do believe is that the “simple DC Inductor” is absolutely a key reason we see it advantageous to push the operating frequency upwards for these converters. The main reason for this is because, with the DC Inductor, we are far less restricted by those fatal AC losses.

🔎 What I wanted to explore in more detail is how much we stand to gain both in terms of size and efficiency, and, if any, what the main limitations were.

Using Frenetic, I designed 30 individual DC Inductors, at varying DC loads, at varying frequencies and with both 10% and 20% ripple to make sure I covered a wide spectrum of possibilities.

🤯 Ranging between 20 kHz and 2 MHz, I found that, regardless of the ripple and load current, the outcome was similar in all cases, and clearly, I stood to make significant size reductions to the Magnetic. I chose to stop at 2 MHz, because this is the main frequency limit discussed in the Cuk article, and even with the use of Frenetic, designing 30 Magnetics in one evening is enough to make anyone mad.

Looking at the transition from 20 kHz to 2 MHz, we can reduce the size of the Magnetic 50 times! And even from relative positions which I have denoted on the graph, an inductor at 500 kHz is 0.28x the size of one at 100 kHz, and so on.

⚙️ As we increase the frequency, we can also reduce the inductance required by a proportional amount, which is a different mechanism to the one we discussed above for load. This allows us to both reduce the number of turns and the cross-sectional area of the core in whatever fashion we like, in order to achieve a similar level of peak flux density in the core. This is the main mechanism that allows us to significantly reduce the size.

You will also see from the graph that my gains are reducing as we go up in frequency. I would be skeptical of this as a reader, because I’m not working entirely in the world of ideal equations, I’m working with real and limited core options and the real world is messy. I don’t claim to have got it all down perfectly. But there will be a law of diminishing returns here which I think I mentioned briefly in my last article.

For copper losses we want to achieve the lowest DC resistance, this would be achieved with 1 single turn assuming we can’t do better. Eventually, because you are pushing the same current through the design, no matter what the frequency is, that single turn won’t be good enough and you won’t be able to reduce the winding area of the window any further.

🤔 Secondly, even with a low AC ripple component, to achieve 1 single turn on most occasions would probably require a hideously large gap, perhaps bigger than the core itself, and this leads to stray magnetic fields and inefficiencies which are hard to define (I won’t even enter the mechanical and manufacturing challenges of the design, in this article).

So, we will see that a sensible gap means more than one turn and thus we must find a balance here: this will be the main limitation to the size of your DC Inductor.

🚨 I also observed the losses for all these designs as I went up in frequency. You will see that it’s not as neat as before. I can attribute this mainly to the discrete core options I had available to play with. I genuinely wish I had the time to make my own custom core dimensions and make the perfect Inductor for each case, one day I think I would like to, but I also have a wife and child that I would like to spend time with. 😂

You can still see a significant reduction in losses as we go up in frequency, the losses at 2 MHz are a fifth of those at 20 kHz. We do see gains here more rapidly diminishing than before, and quite honestly, I don’t know how much I should accredit to the challenge of core size discreteness (probably quite a lot).

👌 But it makes sense, at least to me, that the losses which are linearly proportional to the resistance (the item changing as we reduce size) should change at a slower rate than the core area which is of course a value squared.

I think, all considered, the same limitations as I mentioned with the size will be those that inhibit us from further reducing losses past a certain frequency. You will notice that I haven’t mentioned core losses, and that’s because the economic ripple currents in these examples rendered the core losses virtually insignificant, meaning that it was almost entirely down to the DC losses in the conductor. This is one of the biggest reasons why we stand to gain so much by pushing up the frequency with “simple DC Inductors”.

So, albeit not directly, I do agree with Cuk on the sentiment of his DC Inductor statement. But this was the easy one…

😎 I’m looking forward to tackling his other comments in later newsletters. In the meantime, I would encourage you all to read the article if you haven’t, and thank you Cuk for writing it.

Reference

1. linkedin.com/pulse/devices-magnetics-slobodan-cuk/?published=t

Jonathan Church 

Director of Technical Marketing Strategy