Design & Theory

Informational Articles on the Science Behind Electromagnetics

coil round

Technical Articles: Design and Theory

General Linear Systems is proud to present a new technical information portion of our website. The purpose of this technical page is not so much for business promotion, but for the education of the community at large, to serve as a roadmap to needed technical information, and to provide related articles to the magnetics industry.

We welcome input and additions to this page from those of you with the skills and technical information who would like to contribute. Each subject will be marked with the appropriate icon. After clicking on the icon, please scroll down to read the article.

Thank you.

W.G. Hartney President
Note: A (CT) is short for a current transformer.


Theory of Magnetic Cores and Magnetism Tutorial

If the bible were rewritten, the book of Genesis should start with: "In the beginning, He created the electron. " Let’s call it here the e-!

The e- is the most important thing in all of electrical engineering, despite the fact that nobody knows what it really is. According to physicists, it can be a particle as well as a wave. Strange? How can anything be a particle and a wave at the same time? Wrong! Not at the same time! If you show it being a particle, it forgets to be a wave. If you show the wave character, it does not show itself as a particle!

[read more] Einstein considers these things higher-dimensional (length, width, height, time, and what else?) If you project such a thing into our 3 or 4-dimensional world, it will have multiple 3D or 4D projections, which do not necessarily make sense to our thinking.

In an atom, the e- is said to orbit around the nucleus (seemingly as a particle), but it is the wave function that tells the probability where it is at a certain moment. Only the probability, because Heisenberg says that location and speed can only be determined together with a certain minimum error,

In other words: If you know where it is, you cannot tell where it’s going, and if you know its speed, you cannot tell where it is.

e- has an electric charge, so it can be accelerated by a voltage (not only in a wire but also in a vacuum (see CRT). It also has something physicists stupidly call "spin," which has nothing to do with it spinning around its axis. (What axis?) That spin comes only in 2 kinds, up and down. (referred to what?) and has something to do with magnetism, for which there is only a sketchy description as a condition of space that makes a compass needle move.

Also, you cannot distinguish one e- from another, they are all the same and you cannot label one e- such that it stands out from the others. No way!

If an e- moves, its charge moves, and if a charge moves, that is called a current. No sense asking why the charge moves, it doesn’t matter! It takes 1.6E16 e- (yes, that’s 16 zeroes after the one) every second to move past a certain point to make 1 ampere! That’s a bunch!

If that amp flows for one second into a 1 farad capacitor (a big one!), it raises the voltage on the capacitor by one volt. An amp flowing a sec long is called a coulomb [Cb]. (That’s a charge). And 1Cb into 1F makes 1V. (1Cb into 1µF would make 1MV, keep fingers off!

If a current flows, all the tiny magnets of the e-‘s line up to add together to a much bigger magnetic field which does not move, but stands still as long as the current keeps flowing unchanged. If the current flows in a wire, that field wraps itself around the wire and gets weaker, the farther away from the wire you go to measure it.

And if you flow the current through a turn of wire and stick a magnetic material into the center, this core will concentrate the fields along its length which is perpendicular to the plane of the turn. (Magnetic field is always and 90º to the direction of the current).

Unfortunately, the core does not catch all of the field, some squeezes through between the turn and the core, and that part is called leakage flux. (There is no such thing as an insulator for magnetism).

You run that wire around twice, you have 2 turns. But, since you cannot label individual e-‘s, you cannot label individual currents, so the field sees 2 currents of the same strength and gets twice as strong, even if the 2 currents come from different sources! So, the important quantity is not amps or turns, it is ampere-turns (AT) and the field sums up all the contributing AT’s.

And the core concentrates this field and kind of multiplies it by the permeability [µ] of the core material and the result is the active field in the device. This goes on until the AT’s are so high that the material reaches saturation and says “Yechch, I can no more!” Then the leakage increases because the excess field now bypasses the core and any further increase of AT’s is useless for most practical purposes.

The magnetization in the core is the gausses [G], and it gets higher as the AT’s increase and lower as the cross-section of the core increases and as the magnetic pathlength of the core increases. So another important parameter for the gausses is the AT’s per square inch of core! But the length of the magnetic path in the core comes into play too. So first, you have amperes per meter which, times a weird factor, become oersteds (Oe). And the oersteds multiplied by the effective permeability of the core become the Gausses.

Naturally in their infinite wisdom, the standards people could not leave well enough, so they screwed up systems and we have webers and teslas and other new (old) names around, but just let’s be happy with Oe and G. (The old mho is now a siemens but who uses that?)

The magnetic material is characterized by the magnetization curve, where the x-axis is calibrated in Oe and the y-axis in G. So if you have a completely demagnetized material, this curve starts at the origin (0/0), rises linearly, and then bends over and reaches a saturation value. This is the virgin curve. [Never thought there would be electrical or magnetic virgins.]

Now when you reduce the Oe to 0, the curve will not retrace but will cross the y axes at a point above 0, so with 0 Oe there will still be some G left and that is the remanence. The core stays slightly magnetic! If you do that with cobalt steel or with alnico or other selected materials, a lot of G’s will be left at the 0 Oe point and you have now a permanent magnet!

By the way, the tangent of the angle at which the virgin leaves the origin (if you plot it as a straight line) (G/Oe) is the initial permeability µsub0 and that’s what the manufacturer advertises since is higher than the µ anywhere else. (Despite the fact that, in actual use, it does not mean a thing.)

Now, if you start applying negative Oe’s (by reversing the current) the G’s will go down from the remanence point and will reach 0. The Oe needed to do that is called the coercive force. Go farther with your negative Oe’s and you will now trace a G/Oe curve in the third quadrant into saturation and back to a negative remanence value.

Now your Oe’s must go positive again and you trace a G/Oe curve in the first quadrant and so on and so on. At any point of these curves, the steepness (which is the angle of the tangent to the curve at this point [dG/dOe] is the effective permeability at that point. But you will never get back to the virgin!

But when you go into saturation, the curve has bent to almost parallel to the Oe axis so the G’s don’t increase much when the Oe’s increase so the perm tends to go to 0. (Really to 1, because that’s the perm of empty space. So, effectively, the core has disappeared, or you are now left with an air core which has a perm of very close to 1.) But efficient cores have perms in the 1000’s or 10’000’s, so the saturation point perm of 1 is so negligible, you may as well call it 0 and state that at saturation the perm disappears!

Hans R. Meyer P.E.

basic inductor

Basic Inductor Theory

An inductor is an energy storage device. It can be as simple as a single loop of wire or consist of many turns of wire wound around a special core. Energy is stored in the form of a magnetic field in or around the inductor. Whenever current flows through a wire, it creates a magnetic field around the wire. By placing multiple turns of wire around a loop, we concentrate the magnetic field into a smaller space where it can be more useful.

When you apply a voltage across an inductor, a current starts to flow. It does not instantly rise to some level, but rather increases gradually over time. The relationship of voltage to current vs. time gives rise to a property called inductance. The higher the inductance, the longer it takes for a given voltage to produce a given current.

[read more] Whenever there is a moving or changing magnetic field in the presence of an inductor, that change attempts to generate a current in the inductor. An externally applied current produces an increasing magnetic field, which in turn produces a current opposing that applied externally, hence the inability to create an instantaneous current change in an inductor. This property makes inductors useful as filters in power supplies.

Many types of cores are commonly used in inductors. The simplest core is basically nothing or air. Any core consisting of non-magnetic material behaves essentially the same as air. Most commonly used inductors, however, use some type of magnetic material in the core. This tends to concentrate the inductor’s magnetic field inside the core and increases the effective inductance.

While a magnetic core can provide greater inductance in a given volume, there are also drawbacks. A magnetic core can contain only a limited magnetic field. As you increase the current in a magnetic core inductor, the magnetic field increases. At some point, further increasing the current no longer produces an increase in the magnetic field. At this point, the core is said to be saturated, a condition that generally is undesirable.

The relationship between the inductance with a given core and the number of turns on it is called its AL value. The unit of inductance is the henry. The formula for inductance is L = n2(squared) x AL where L is the inductance in henries and n is the number of turns.

Most commercially available cores have published AL values. Inductor cores with higher AL values tend to saturate more readily than cores with lower AL values.

Written by Les Beckwith