Not all engineers are aware that there are two types of inductors, AC Inductors and DC (actually, DC+AC) Inductors. Typically, an AC inductor cannot take much DC current before saturating and effectively turning into a piece of wire with near zero inductance. This can happen with just a few milliamps of DC current or even less. A DC Inductor, on the other hand, can handle significant amounts of DC current, but will have a limit on DC current at which point it will saturate. To be clear, when a magnetic core, whether for a transformer or inductor saturates, the inductance due to the magnetic core goes away, leaving an air core. A magnetic core will typically have an inductance compared to an air core, of from a few thousand for Ferrite to as much as 60,000 or more for the best core available. This blog will discuss the basics of AC Inductor design.

As an aside, there's another factor that can cause a transformer or inductor to lose it's magnetic core's properties and thus, become little more than a piece of wire in an air core and that is high temperature. Each type of core material has it's own temperature for when this happens and it's called the Curie Temperature. For magnetic-grade Silicon Steel, the Curie temperature is about 730° C and for Ferrite, it can be as low as 200° C. And these are rather high temperatures; however, Ferrites can have significant degradation of magnetic properties at as low as 100° C with a major increase in core losses.

Back to AC Inductor design. In order to make an AC Inductor, an inductor that's not designed to carry an significant DC current, the core material used is often the same as that used for a transformer. AC inductors can be designed to have a magnetic core with or without an air gap. But usually, at least some air gap is used to adjust the inductance value. Of course, the number of turns also affects the inductance. An AC inductor, as it is with a transformer, has to support the peak magnetic flux without saturation and this is determined by the applied voltage and number of turns for a given core size and core material. The following equation is used to determine the minimum number of turns:

N = Vin*10^8/'(Kf*F*Ac*B), where: Vin is the maximum applied RMS voltage in volts, Kf is a constant depending on the waveform type and is equal to 4.0 for a square wave and 4.44 for a sine wave, F is the applied frequency in Hz, Ac is the effective core area in cm^2, and B is the maximum flux density in the core. Note that the maximum flux density is usually chosen as some percentage of the core's rated maximum flux density, 0.95 as an example, so that the core will never actually be in saturation.

Regarding the Effective Core Area, Ac, this is always less than the core area computed by the core's center leg. And there are a few reasons for this. If the core is made up of steel laminations, there's something called Stacking Factor, and this is a constant less than one (<1) that gets multiplied by the computed core area and is based largely on the thickness of the laminations and whether they're stacked (interleaved) one-by-one or three-by-three, up to no interleaving at all, called butt-joint. The stacking factor is typically 0.95 for 29 gauge, M6 grade Silicon Steel with a one-by-one interleave and goes down from there. Similarly, for a Ferrite core, the effective core area is usually given by the manufacturer in the core's data sheet. It's less than the actual computed core area since the manufactured cores often have some of the core's center leg removed, as with the center mounting hole in a pot core. That mounting hole reduces the core area and must be taken into consideration as it is significant.

Before the number of turns can be computed, the specific core size and core material must be chosen. If the inductor is for a power line frequency (50/60 or 400 Hz), then a Silicon Steel or a tape-wound core can be used. For 400 Hz up to about 1KHz, a 1 mil thick tape is advised to keep the core loss down to a reasonable level. I'll avoid any more on that topic for now. The core size must also be determined. In many cases, a standard transformer lamination can be used in a butt-stack configuration so that a gap can be inserted between the lamination's Es and Is. A typical gap material is FR4, G10, or other glass-epoxy board material. For very small gaps, Nomex 410 is a good choice as it comes in many standard thicknesses (1mil thru 30 mil). Sometimes, to get the precise gap thickness, some combination of glass-Epoxy board and Nomex 410 is necessary. Whatever gap material is chosen should be mechanically stable with heat and pressure so that the gap remains relatively constant.

I don't want to get too deep into core choice, except to refer those readers interested in it to a book by Col. William T. McLyman of JPL. He created a system of choosing core size based on relating the maximum power in VA to the core's Area Product including a special core constant based on core geometry with the idea being that any core with an Area Product greater than or equal to the specified Inductor (or transformer) VA rating would fit the amount of magnet wire needed for the inductor or transformer. The book's title is: TRANSFORMER AND INDUCTOR DESIGN HANDBOOK and is published by Marcel Decker. The Colonel also wrote a companion book titled: DESIGNING MAGNETIC COMPONENTS FOR HIGH FREQUENCY DC-DC CONVERTERS, published by KG Magnetics, Inc. I highly recommend both books as Col McLyman was the authority on the subject. The area product is: Aw* Ac*kg, where: Aw is the Window Area or available winding area, Ac is the core cross-sectional area, and Kg is a constant based on core geometry. Please refer to the books by Col. McLyman for more details on Area Product calculations and use in determining minimum core size.

Back to AC inductor design and core size choice. For those not inclined to use the area product method, it's certainly viable to use the trial and error method. The only thing that matters much is choosing a core size that will fit the wire needed for the design. So, an initial core size choice can be made, and the turns and wire size computed, then using the insulated magnet wire's area times the number of turns, the total required winding area can be determined, called Window Area, and this is a parameter of the core size chosen and can be looked up in a data book. But keep in mind that if a bobbin is to be used, it takes away part of the usable window area for the core used. Also, when making this calculation, it's best to use a magnet wire chart with Insulated OD of the magnet wire. I recommend the chart from Superior Essex that can be found here: https://essexfurukawa.com/wp-content/uploads/2019/09/Essex-Wire-Engineering-Data-Handbook-EN.pdf . This chart typically has three sets of columns for each wire type, minimum, nominal, and maximum. I recommend you use the worst-case column when determining if the needed wire will fit, and that would be the maximum diameter column.

For determining the wire size for the AC inductor, if the specification calls for a current rating, then the wire chart can be used directly by choosing an appropriate current density. A good rule of thumb choice for an inductor would be either 500 C.M./A (circular mils per Amp) or 600 C.M./A. The higher value can be used if better load regulation is needed, with the drawback being that it will need more magnet wire in the winding window (more Aw).

The approximate air gap (filled with a stable filler material and not actually filled with air) can be calculated as follows for an AC Inductor: L= 0.4*Pi*N^2*Ac*10^8/(lg + [MPL/u]), where: L= Inductance, PI = 3.14159265, N=number of turns calculated previously, Ac= effective core area, lg=length of the gap, MPL= Magnetic Path Length (property of the core, get it from the datasheet), and u= magnetic permeability of the core material. We can rearrange this formula to solve for the gap needed for a particular inductance as follows: lg = (0.4*PI*N^2*Ac*10^8/L ) - MPL/u. In most cases, u is so large that the term MPL/u becomes so small that it can be left out of the equation for lg and in that case, i he equation simplifies to: lg=0.4*PI*N^2*Ac*10^8/L. The final inductance can be fined tuned by adding or subtracting various thicknesses of Nomex 410, Aramid paper.

I'll discuss the wire we use on inductors and transformers and it's called magnet wire. It's called this since we use it in electromagnetic components, like transformers and inductors and not because it has any magnetic properties as it does not. The wire is just solid copper wire with a film coating that can be single or heavy, with the diameter increasing for the heavy coated wires. The type of plastic film used in these coatings can vary, but they're largely based on the film's properties of temperature rating and abrasion resistance. Some of the names are: Formvar (105° C), Soderon (155° C and is solderable), and GP/MR-200 (220° C). The available shapes of magnet wire are: round, square, and rectangular. Some are made for extreme abrasion and temperature resistance and take a high-temp magnet wire and wrap it in a very tough type of paper called Nomex 410. It really is not like paper as it cannot be torn by hand and it can take a flame without igniting. For most inductors and transformers, the round variety is used with one the coatings mentioned (and there are more available film coating types).

I'll write a companion blog for DC inductors soon.