Magnetics is a terrible embarrassment to many engineers. I suspect they often end up pretending it doesn't really matter - 'magnetics-denial' - "Oh, I just toddle up to the bin and pick any inductor that works."
Considering that the entire movement in switching power conversion in the last decade to higher and higher frequencies is driven mainly by the burning desire to shrink magnetic components, there must be something wrong with this rather cool, laid-back attitude. It is of course my personal opinion that some engineers often make the problem sound even more complex, by spending all their remaining waking hours twiddling with the Nyquist criterion, double-edge modulation etc.
To put it in perspective, none of these issues have really ever been a show-stopper in any practical design scenario, nor have they allowed us to eventually reduce the size of the power supply. We note that size must ultimately dove-tail with reliability, because if we undersize the core for example, we will certainly cause core saturation and a fair amount of resulting silicon shrapnel in the lab! We saw that last month.
Above, I have extracted four key equations from my recent publication (see Editor's note). I hope to give you a simple insight into the art of reducing the core size. Here we are assuming that core and copper losses are not the limiting factor (as is usually the case with the modern geometries and materials), and that the inductor size is simply related to the energy storage requirement or ½*L*Ipeak2. In my book, I have introduced a useful variable called the 'z-factor,' defined in the same figure, since I found it helps simplify the equations considerably. (Also, see the magnetics on-line seminar at http://www.national.com/onlineseminar/.
Here is the logic: from the fourth equation, we see that to be able to keep the inductance fixed as z goes from 1 to 10 (air gap increased), we only need to increase the number of turns N by 100.5 = 3.2 times. Therefore, from the second equation we can see that if z went from 1 to 10, but the ampere-turns NI was increased only by a factor of 3.2 (so as to keep L fixed, as we usually want to do), then the operating B-field would be reduced to 1/3rd of its original value.
From the first equation, the energy stored in the core has remained unaltered in the process, though from the third equation we can see that its overload capability (i.e., measured up to a certain saturation flux density BSAT) has increased 10 times. So, any "headroom", as measured from the operating B-field value to the saturation level (BSAT), or from the operating energy storage level to the peak energy handling capability must have increased considerably, even though inductance has been kept a constant in this case.
All this could translate to a much higher field reliability where the converter will likely encounter severe abnormal or transient line/load conditions. However, if all the "bells and whistles" are present in the design of the control circuitry (e.g., feedforward, primary/secondary current limit, duty cycle clamp and the like), and they serve to protect the converter adequately against any such abnormal conditions, this gives us a great opportunity to select a smaller core for the same power level. In doing so we would be essentially returning to the point of optimum core size, which is defined as that where the peak operating flux density BPEAK is just under BSAT (with current limiting and/or duty cycle clamping present to ensure that BSAT is never exceeded, even for a cycle).
What do we learn here? That by increasing the gap of the core we can move to smaller core sizes. Yes, powdered iron cores for example have a distributed air gap, and come in various "effective permeabilities." So actually, lower permeability materials should in principle always lead to smaller core sizes, as they have a larger air gap in effect. All this is rather counter-intuitive I admit. The restricting factor is that to use very low permeability materials, we need more and more turns, and so we will either just run out of enough window space to accommodate these extra turns, or we will have our copper losses mount to the extent that the core size becomes a secondary issue.
Now returning to another issue, I promised to touch upon in last month's column. High voltage off-line integrated flyback switcher ICs are available from several vendors, but they are restricted because they usually come only in a family of fixed current limits. So if for example we have a 5A part, the next lower part being a 3A part, the 5A part is certainly optimum for peak currents slightly below 5A. But what if the peak current in our particular application is 4A? For lack of a suitably matching part, we would now be forced to use a 5A IC for a 4A application " but - we would still need to size the core for 5A! We may be able to reduce the copper diameter in going from a 5A application to a 4A application, but not the physical size of the inductor, as it must still continue to withstand 5A, which it would see under sudden step-load changes (or even under normal power-up or power-down).
So how do some such vendors manage to show a smaller magnetic component for the 4A application? By increasing the current ripple ratio 'r'! By the equations in the accompanying figure, it can also be shown that if L is allowed to decrease (fewer turns), the energy storage requirement decreases and so we can reduce the core size. Inductors operated with large current ripple ratios are therefore always smaller, though the problem is that they just transfer the burden to the input/output capacitors (more filtering required). But you may not notice that immediately.!
Write me at firstname.lastname@example.org. Please don't hesitate to ask for pdfs of my older articles, as some of you have already done. And also don't forget to also write Steve (at email@example.com).
Editor's Note: Sanjaya has a new book out, which the publisher, McGraw-Hill Professional is promoting as "The Bible" for power supply designers. Available through Amazon, the title is Switching Power Supply Design & Optimization