Transformer Winding

  

In the good old times it was a matter of fact that every electronic hobbyist or technician would wind himself any power transformers he needed, and rewind any that burned out. Unfortunately, nowadays transformer winding is fast becoming a lost art, and I have seen many people despair about where to find some very specific transformer, or pull their hair out about the cost of having one professionally wound to specifications.
Since I started in electronics, as a 12 year old boy, I have always wound my own transformers. I started using the basic, but useful instructions provided in The Radio Amateur's Handbook of the time, and later I came to better understand how transformers work, which enabled me to optimize a given transformer for the intended application.
Following a request by many readers of my web site, I've added this page, which is complementary to the previously published Transformers and coils. You should first read (and understand!) that page, before trying to design any transformer. Then come to this more practically-oriented page, to learn some tricks and hints about the design process, and about hands-on winding.
This page addresses mainly single-phase power transformers in the power range from about 1 watt to 10,000 watts, operating at line frequencies, but much of what's described here can be applied to a wide range of other transformers too.
Let's start with the materials. To make a typical transformer, you need the iron laminations for the core, enameled copper wire of several different diameters for the windings, a bobbin (or some material to make one), insulating material to apply between wire layers, between windings, around the whole winding assembly, and on exposed wires, and in most cases it's also a good idea to use an impregnation varnish.
The photo here shows several stacks of iron E-I laminations, two coils of wire (with cardboard protecting the wire from damage), one roll of thick, stiff Pressspan, another roll of NMN laminate (we will soon see what that is), two small bundles of spaghetti for wire protection, and a can of transformer varnish. Add to this some glue, cotton straps, ropes, adhesive tape, terminals, bolts, angle iron, and other small material, and that's it.
All these materials are sold by companies specializing in transformers and parts for transformers. Enameled wire is also sold by many other distributors, but is usually cheapest at the places that sell it together with the other materials. You will have to dig into the phone book or some other directory to find these companies, since they don't usually have a shiny nice store in the downtown shopping mall!

Transformer iron is an alloy of iron with silicon and some other minor components. It's characterized by a relatively high permeability, very high saturation flux density, relatively low hysteresis loss, and relatively high specific resistance. This latter factor, along with the practice of using the material in thin, insulated sheets, reduces the power losses produced by eddy currents.
The most common shape of these sheets is shown at right. It's the classic "economy E-I" shape. Why it's called E-I should be pretty obvious when looking at the photo! But the explanation for "economy" might be a bit more elusive: It's because at the exact proportions shown in the photo, the I's are nothing else than the cutouts to make the windows in the E's, when two E's are cut facing each other! This allows stamping E's and I's out of a large steel sheet, without any wasting of material, except for the little round bits cut out of the bolt holes. By the way, small laminations often don't have such bolt holes, and such cores are held together by clamps instead of bolts, or even welded.
The lamination in the photo is a large one, as the comparison with my hand shows. It's an E80 (the center leg is 80mm wide), typically used for transformers in the 3 to 10 kilowatt range!
In any E-I lamination you are likely to encounter, the center leg is twice as wide as each of the other parts. This is because the entire magnetic flux has to go through the center leg, but then splits up, with one half of the flux returning through each of the side legs. If you ever come across a lamination that has all three legs of the same width, then you are looking at a lamination intended for three phase transformers!
Such an economy E-I lamination like shown here has completely fixed proportions, beyond the rule above, that stem from the need to cut the I out of the winding window of two E's facing each other: If the center leg is 2 units wide, then the window is 1 x 3 units, the total E is 6 x 4 units, the I is 1 x 6 units, and so on.

Not all laminations follow the "economy" proportions, though. Here is an example of a lamination that comes in one piece, instead of being divided into an E and an I, and that has the windows proportionally much larger than the E-I lamination shown above. Such a lamination is a bit more expensive to make, because the steel cut from the windows is wasted, unless the manufacturer can find some other use for it. But being able to accomodate a much large winding assembly, it has some advantages in certain cases.
These "non-economy" laminations were quite usual in Europe, many years ago, but nowadays copper is so much more expensive than steel, that transformers are usually designed to use more steel and less copper. And for that goal, the economy lamination is very well suited. So you won't very often come across a lamination like this, unless you are restoring antique equipment.

The laminations should be thin, and reasonably well insulated from each other, to reduce eddy currents to an insignificant value. Typical thicknesses vary from 0.2 to 0.5mm, but higher frequency transformers (audio) use much thinner ones, while extremely large transformers might use slightly thicker ones.
The insulation is often applied at the factory that makes the big rolls of steel sheet, even before stamping the E's and I's. Different kinds of insulation are used: A thin oxide layer, a thin layer of enamel, or any of several chemical processes. Antique transformers sometimes even used very thin paper!
When I was young, patient and overly eager to do things right, I painted each and every E and I for my transformers, using diluted transformer varnish, to make a thin, nice layer. The photo shows the steel for a 200 watt transformer, drying. Later, getting old and lazy, I noticed that the layer of rust on old, recycled laminations is more than enough insulation, and that the very thin and imperfect insulation that comes on new laminations is enough too, even if it takes only a light scratch with the multimeter's test probe to puncture it and get through to the steel. We don't need perfect insulation between the sheets! We only need enough resistance to reduce eddy currents to a low level.
 Transformer steel is not all born alike. Manufacturers will provide data sheets about their products (often on their web sites), where you can see what they offer. There are usually many grades, with vastly different loss characteristics. At a given flux density and frequency, a good material might have ten times less loss than a cheap material! So it pays to look, investigate, and decide intelligently what to buy. Thinner sheets normally have lower loss, and the rest of the secret lies in the exact alloy. In any case, you need to know what material you have, to be able to make a meaningful transformer design!
Some transformer steel is grain-oriented. That means that when rolling the steel sheets, a process is used to align the crystalline grains in the direction of the rolling. This kind of material has particularly good behavior when the magnetic flux is aligned with the direction in which the sheet was rolled, but is worse than standard material in the perpendicular direction. Such grain-oriented material is ideal for toroidal cores, which are made by coiling up a long strip of steel, but is not a large improvement for E-I laminations, because in these a significant portion of the material has to work with the flux perpendicular to the rolling direction.

Enamelled copper wire comes in many different diameters, and with several different kinds of enamel. The diameters vary from less than that of a hair, to about that of a child's finger. Different standards exist for the wire diameter. A very common one is American Wire Gauge, shortened to AWG, which is used in much of the world. Britain has its own standard, and in many countries the wire is specified simply by its diameter in millimeters.
Thick wires usually are coated with a sort of enamel that is very tough, an excellent insulator, highly heat-resistant, highly resistant to solvents, and that clings to copper even better than dirt does to children! This enamel is usually yellowish clear, so that the wire coated in it looks mostly copper-colored, but many exceptions exist. To solder the ends of these wires, it's necessary to scrape off the enamel, using a sharp knife or similar tool. This procedure would be too difficult with a thin, fragile wire, so that these thin wires are instead covered with an enamel that has most of the same characteristics of the other one, except the heat resistance: It will melt and turn into solder flux at a temperature a common soldering iron easily achieves! This allows easily soldering these wires, without previously stripping them. But transformers using this latter kind of wire enamel cannot survive temperatures as high as those using only the former kind of wire enamel. The red wire on the right side in this photo has this kind of enamel. But be careful with colors! The clear wire on the extreme left side also has solderable enamel, while the dark violet one in the middle is of the non-melting variety!
The thickness of the enamel layer depends on the wire thickness, the manufacturer, and can sometimes be chosen: Some manufacturers will offer the wire with seeral different thicknesses of enamel. In any case, the diameter specified by a certain AWG number refers to the copper diameter, so that the complete wire, with enamel, will be slightly thicker than what the AWG standard tells!
Here is a wire table for AWG wire. It shows the AWG number, the diameter in millimeters excluding the enamel, the approximate typical total diameter including the enamel (but this varies somewhat), the cross sectional copper area in square millimeters, the area of the square of window space occupied by that wire in a transformer (including the enamel, of course), the current carrying capacity at a typical, average value of current density, the resistance in ohms per meter, and finally how many meters of that wire come in one kilogram, because enamelled wire is usually bought by weight, not length.
This table has wires from AWG #1 to #40, and for the thickest ones I didn't calculate all data. But you should be aware that there are wires exceeding this range! The thinnest I have ever used was #46. It breaks when you blow at it! The photo here shows a #39 wire lying on a #7 wire. The hairy thing below is my floor carpet. Note that even this #39 wire is not much thicker than the hairs of this carpet!
It's interesting to note that every three AWG numbers, the cross sectional area exactly doubles. Any deviation from this in my table is due to approximation errors.

Modern transformers of small to moderate size are usually wound on plastic bobbins. Here you can see simple ones. Some bobbins have pins or terminals molded into them, others have one or two divisions. Some don't have the slits for terminals, which the ones shown here do have.
Typically for a given size of E-I laminations, bobbins will be available in two or three sizes, accomodating different numbers of steel sheets. So you can vary the amount of steel in your transformer not only by choosing the lamination size, but also the height of the lamination stack!

Here is a little transformer using a divided (or split) bobbin. This is very practical, because it completely separates the primary from the secondary winding, making it much easier to achieve the degree of insulation required for safety. More about that later.

This article is about the electrical device. For the toy line franchise, see Transformers. For other uses, see Transformer (disambiguation).

Pole-mounted distribution transformer with center-tapped secondary winding. This type of transformer is commonly used in the United States to provide 120/240 volt "split-phase" power for residential and light commercial use. Note that the center "neutral" terminal is grounded to the transformer "tank", and a grounded conductor (right) is used for one leg of the primary feeder.

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors—the transformer's coils. A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core and thus a varying magnetic field through the secondary winding. This varying magnetic field induces a varying electromotive force (EMF), or "voltage", in the secondary winding. This effect is called mutual induction.
If a load is connected to the secondary, an electric current will flow in the secondary winding and electrical energy will be transferred from the primary circuit through the transformer to the load. In an ideal transformer, the induced voltage in the secondary winding (V_s) is in proportion to the primary voltage (V_p), and is given by the ratio of the number of turns in the secondary (N_s) to the number of turns in the primary (N_p) as follows:

By appropriate selection of the ratio of turns, a transformer thus allows an alternating current (AC) voltage to be "stepped up" by making N_s greater than N_p, or "stepped down" by making N_s less than N_p.
In the vast majority of transformers, the windings are coils wound around a ferromagnetic core, air-core transformers being a notable exception.
Transformers range in size from a thumbnail-sized coupling transformer hidden inside a stage microphone to huge units weighing hundreds of tons used to interconnect portions of power grids. All operate with the same basic principles, although the range of designs is wide. While new technologies have eliminated the need for transformers in some electronic circuits, transformers are still found in nearly all electronic devices designed for household ("mains") voltage. Transformers are essential for high-voltage electric power transmission, which makes long-distance transmission economically practical.

The transformer is based on two principles: first, that an electric current can produce a magnetic field (electromagnetism), and, second that a changing magnetic field within a coil of wire induces a voltage across the ends of the coil (electromagnetic induction). Changing the current in the primary coil changes the magnetic flux that is developed. The changing magnetic flux induces a voltage in the secondary coil.

An ideal transformer. The secondary current arises from the action of the secondary EMF on the (not shown) load impedance.

An ideal transformer is shown in the adjacent figure. Current passing through the primary coil creates a magnetic field. The primary and secondary coils are wrapped around a core of very high magnetic permeability, such as iron, so that most of the magnetic flux passes through both the primary and secondary coils. If a load is connected to the secondary winding, the load current and voltage will be in the directions indicated, given the primary current and voltage in the directions indicated (each will be alternating current in practice).

 Induction law

The voltage induced across the secondary coil may be calculated from Faraday's law of induction, which states that:

where V_s is the instantaneous voltage, N_s is the number of turns in the secondary coil and Φ is the magnetic flux through one turn of the coil. If the turns of the coil are oriented perpendicular to the magnetic field lines, the flux is the product of the magnetic flux density B and the area A through which it cuts. The area is constant, being equal to the cross-sectional area of the transformer core, whereas the magnetic field varies with time according to the excitation of the primary. Since the same magnetic flux passes through both the primary and secondary coils in an ideal transformer, the instantaneous voltage across the primary winding equals

Taking the ratio of the two equations for V_s and V_p gives the basic equation for stepping up or stepping down the voltage

N_p/N_s is known as the turns ratio, and is the primary functional characteristic of any transformer. In the case of step-up transformers, this may sometimes be stated as the reciprocal, N_s/N_p. Turns ratio is commonly expressed as an irreducible fraction or ratio: for example, a transformer with primary and secondary windings of, respectively, 100 and 150 turns is said to have a turns ratio of 2:3 rather than 0.667 or 100:150.

 Ideal power equation

The ideal transformer as a circuit element

If the secondary coil is attached to a load that allows current to flow, electrical power is transmitted from the primary circuit to the secondary circuit. Ideally, the transformer is perfectly efficient; all the incoming energy is transformed from the primary circuit to the magnetic field and into the secondary circuit. If this condition is met, the incoming electric power must equal the outgoing power:

giving the ideal transformer equation

Transformers normally have high efficiency, so this formula is a reasonable approximation.
If the voltage is increased, then the current is decreased by the same factor. The impedance in one circuit is transformed by the square of the turns ratio. For example, if an impedance Z_s is attached across the terminals of the secondary coil, it appears to the primary circuit to have an impedance of (N_p/N_s)²Z_s. This relationship is reciprocal, so that the impedance Z_p of the primary circuit appears to the secondary to be (N_s/N_p)²Z_p.

 Detailed operation

The simplified description above neglects several practical factors, in particular the primary current required to establish a magnetic field in the core, and the contribution to the field due to current in the secondary circuit.
Models of an ideal transformer typically assume a core of negligible reluctance with two windings of zero resistance. When a voltage is applied to the primary winding, a small current flows, driving flux around the magnetic circuit of the core. The current required to create the flux is termed the magnetizing current; since the ideal core has been assumed to have near-zero reluctance, the magnetizing current is negligible, although still required to create the magnetic field.
The changing magnetic field induces an electromotive force (EMF) across each winding. Since the ideal windings have no impedance, they have no associated voltage drop, and so the voltages V_P and V_S measured at the terminals of the transformer, are equal to the corresponding EMFs. The primary EMF, acting as it does in opposition to the primary voltage, is sometimes termed the "back EMF". This is due to Lenz's law which states that the induction of EMF would always be such that it will oppose development of any such change in magnetic field.

Practical considerations

[ Leakage flux

Leakage flux of a transformer

Main article: Leakage inductance

The ideal transformer model assumes that all flux generated by the primary winding links all the turns of every winding, including itself. In practice, some flux traverses paths that take it outside the windings. Such flux is termed leakage flux, and results in leakage inductance in series with the mutually coupled transformer windings. Leakage results in energy being alternately stored in and discharged from the magnetic fields with each cycle of the poer supply. It is not directly a power loss (see "Stray losses" below), but results in inferior voltage regulation, causing the secondary voltage to fail to be directly proportional to the primary, particularly under heavy load. Transformers are therefore normally designed to have very low leakage inductance. Nevertheless, it is impossible to eliminate all leakage flux because it plays an essential part in the operation of the transformer. The combined effect of the leakage flux and the electric field around the windings is what transfers energy from the primary to the secondary.
In some applications increased leakage is desired, and long magnetic paths, air gaps, or magnetic bypass shunts may be deliberately introduced to a transformer's design to limit the short-circuit current it will supply.Leaky transformers may be used to supply loads that exhibit negative resistance, such as electric arcs, mercury vapor lamps, and neon signs; or for safely handling loads that become periodically short-circuited such as electric arc welders.
Air gaps are also used to keep a transformer from saturating, especially audio-frequency transformers in circuits that have a direct current flowing through the windings
Leakage inductance is also helpful when transformers are operated in parallel. It can be shown that if the "per-unit" inductance of two transformers is the same (a typical value is 5%), they will automatically split power "correctly" (e.g. 500 kVA unit in parallel with 1,000 kVA unit, the larger one will carry twice the current)