Transformers and coils

Transformers and coils

There are many electronicians, both hobby and professional, who are at war with electromagnetism. Whenever they need to design a coil or a transformer, an abyss of desperation opens in front of these poor people. The worst thing is that usually these poor victims are not really at fault, since the authors of electronic textbooks seem to have struck a plot to explainthese things in such a messy way that nobody can really understand them! Or maybe these authors themselves didn't have a clue about the matter?
Well, internet to the rescue! I will explain the basics, in simple, understandable terms. Here you will find most information required to design electromagnetic parts for electronic use.
 

The units

There is one request I have: When you enter thispage, you have to leave out all obsolete, absurd units of which most textbooks and catalogs are full: Most notably, inches, Gauss and Oersted. Delete these three words from your vocabulary! They have no place here. They are the principal culprits in confusing people attempting magnetic design to the point of driving them crazy. Now, that we have gotten rid of them, we can start.
The first unit wewill use is the Weber, written as Wb. This is the official unit for magnetic flux. If you take a loop of wire, and apply 1V to this wire during 1s, then the magnetic flux inside this loop will have changed by 1Wb. Note that this is true regardless of size or shape of the loop, and regardless of the matter that's inside the loop! Officially this definition of the Weber is written as:
Wb = V * s
butI prefer a modification of this equation that is more practical, taking into account the number of turns of a multiturn coil. So, this is one of our basic truths:
(1)    Wb = V * s / t
meaning that the change of magnetic flux (Weber) is the tension (Volt) multiplied by time (second) divided by the amount of turns. This is one of the most powerful and useful formulas we have.
If we squeeze acertain amount of magnetic flux through a certain area, then we can speak of magnetic flux density. The unit for this is the Tesla, written as T. Its definition is simple and obvious:
(2)    T = Wb / m2
Note that talking about square meters in electronics may look a little removed from practice, as we use parts that have cross-sections more in the square centimeter range. But please, believe methat accepting such "impractical" things is very much more practical than using dozens of different conversion constants! Using the basic units has the large advantage that absolutely no conversion constant are needed.
 
The basic characteristic of any coil is inductance. It is measured in Henry, written as H, and its definition is:
(3)    H = V * s / A
or, in words, one Henry is the amount ofinductance that will allow the current to rise by one Ampere when applying one Volt during one second. This equation is also very useful for our purposes. And now we can start to play! We can join equations 1 and 3 to make the following:
H = Wb / A / t
Such algebraic conversions are always true too, and can give us the means to calculate some value we did not know how to determine!
But now let'sgo to practical things.
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Designing power line transformers

While almost any electronician knows that the voltage ratio of a transformer depends on the turns ratio, the question that arises for most novices is: "How many turns-per-Volt must I use???"
It's very simple. You have an iron core, and you want to wind it. First, measure the section of iron through which the magnetic flux willflow. Say, the central leg of the transformer core measures 2cm wide, and the entire stack of laminations, well compressed, measures 3 cm. This gives you 6cm2, or 0.0006m2 of cross-sectional area.
Now you need to decide how much flux density you will put through your iron. At low frequencies, like those of power line applications, the limiting factor is saturation of the core. The most humble...