# Calculation of the windings of the transformer and its core

The transformer, the history of which has been around for almost a century and a half, has been faithfully serving humanity all this time. Its purpose is AC voltage conversion. This is one of the few devices, the efficiency of which can reach almost 100%.

Winding scheme of the welding transformer.

How to calculate and wind the transformer windings, what its core can be, what are the design features of transformers for various purposes, how they work - questions that may be of interest to many. Below are the answers to most of these questions.

## What is a transformer?

### A bit of history

In the 1870s, the Russian scientist P.N. Yablochkov invented the electric arc light source - “Yablochkov candle”. Initially, the power sources of the arc were powerful galvanic batteries, but in this case the anodes burned faster. Then the scientist decided to use the alternator as the current source for his invention.

In this case, another difficulty arose: after one electric candle was lit, due to a decrease in the voltage at the terminals of the generator, the ignition of other lamps was difficult. The problem was solved when a transformer was used to supply each light source. These first transformers had open cores of steel wire bundles and, as a result, had low efficiency. Transformers with closed cores, similar to the modern, appeared only after 9 years.

### How does the transformer work and how does it work?

Figure 1. Diagram of the simplest transformer.

The simplest transformer is a core of a substance with high magnetic permeability and two windings wound around it (Fig. 1a). When passing through the primary winding of alternating current by force Ione in the core there is a varying magnetic flux F, which is threaded by both the primary and secondary windings.

In each of the turns of these windings is the same for the numerical value of the induced emf. Thus, the relationship of the EMF in the windings and turns in them are the same. At idle (I2 = 0) the voltages on the windings are almost equal to the induced emf in them, therefore, the following relation is also valid for voltages:

Uone / U2 ≈ None / N2, Where

None and N2 - the number of turns in the windings.

Ratio uone / U2 also called the transformation coefficient (k). If uone > U2, the transformer is called step-up (Fig. 1b), with Uone < U2 - lowering (Figure 1B). The first transformer has a higher transformation ratio, and the second has less than one.

One and the same transformer, depending on which winding is applied to, and with which the voltage is removed, can be either increasing or decreasing. The secondary winding is not necessarily one - there may be several. From the equality of power in the windings, it follows that the currents in them are inversely proportional to the number of turns:

Ione / I2 ≈ N2 / None.

If the secondary winding is an integral part of the primary (or primary - secondary), the transformer becomes an autotransformer. In fig. 1d and 1d are shown diagrams of, respectively, step-down and step-up autotransformers.

The design of transformers for spot welding of copper.

An alternating magnetic field causes the formation of eddy currents in the core, which heat it, on which part of the energy is wasted. To reduce these losses, cores are recruited from separate, isolated from each other, special transformer steel sheets with low reversal energy.

Most often in modern transformers magnetic cores of three types are used:

1. Rod (U-shaped), consisting of two rods with windings and a yoke connecting them. This is how the cores of high-power transformers are usually arranged.
2. Armor (W-shaped). The magnetic circuit is a yoke, inside of which is a rod with a winding. The yoke protects each winding of the transformer from external influences - hence the name. Most often used in low-power transformers for electronic circuits.
3. Toroidal - the torus-shaped magnetic core consists of a transformer tape wound with a dense roll. Advantages - relatively low weight, high efficiency, minimum interference. The disadvantage is the complexity of the winding.

## How to calculate the transformer?

Welding transformer for arc welding.

The most important parameters of a transformer are the nominal values ​​of currents and voltages and power for which it is designed. Absolute accuracy in calculating the characteristics of the transformer for these parameters does not matter much, so you can limit yourself to approximate values.

The sequence of calculations is as follows:

1. Calculation of current through the secondary winding, taking into account losses: I2 = 1.5 * I2n, where i2n - rated current in it.
2. Calculation of power removed from the secondary winding: P2 = U2 * I2, where u2 - tension on it. If such a winding is not one, then the result is the sum of their powers.
3. Determination of the resulting power: PT = 1.25 * P2 with an efficiency of about 80%.
4. Calculation of the current through the primary winding of the transformer: Ione = PT / Uone, where uone - tension on it.
5. The area of ​​the required section of the magnetic circuit: S = 1.3 * √PT, where s is measured in cm2.
6. The number of turns for the primary winding of the transformer: None = 50 * Uone / S, where S is measured in cm2.
7. The number of turns for its secondary winding: N2 = 55 * U2 / S, where S is measured in cm2.
8. The diameter of the conductors of any of the transformer windings: d = 0.632 * √I, where I is the current strength in it. The formula is correct for copper wire.

For example, the secondary winding of a transformer included in a 220-volt network should produce a current of 6.7 A at a voltage of 36 V. Calculate the parameters of the transformer.

The main parts of the design of the transformer.

1. I2 = 1.5 * 6.7 A = 10 A.
2. P2 = 36 V * 10 A = 360 watts.
3. PT = 1.25 * 360 watts = 450 watts.
4. Ione = 450 W / 220 V ≈ 2 A.
5. S = 1.3 * √450 (cm2) ≈ 25 cm2
6. None = 50 * 220/25 = 440 turns.
7. N2 = 55 * 36/25 = 79 turns.
8. done = 0.632 * √2 (mm) = 0.9 mm, done = 0.632 * √10 (mm) = 2 mm.

If there are no wires of the required diameter, then one thick wire can be replaced with several thinner ones connected in parallel. The cross-sectional area of ​​the conductor with a diameter d can be calculated by the formula: s = 0.8 * d2.

For example, you need a wire with a diameter of 2 mm, and there is only a conductor with a diameter of 1.2 mm. The cross-sectional area of ​​the desired wire s = 0.8 * 4 (mm2) = 3.2 mm2, the area available, calculated by the same formula, is 1.1 mm2. It is easy to understand that one conductor with a diameter of 2 mm can be replaced by three with a diameter of 1.2 mm.

## Transformer manufacturing

The process of manufacturing a power transformer consists of a series of sequential operations.

### Assembly of coil frames for core or armor core

Figure 2. Scheme of assembly of the frame for the transformer.

A fairly convenient material for assembling these frameworks is cardboard or press board. An even stronger frame can be made of plastic. The frame assembly is shown in Fig. 2a It is assembled from parts shown in Figures 2b-2g. Must be made of two copies of each part. Holes in the cheeks (g) are intended for conclusions.

The frame assembly procedure:

• two cheeks overlap each other;
• parts (b) are embedded in their windows and are diluted, one up, the second down;
• parts (c) are installed so that their projections coincide with the notches of parts (b).

The resulting frame is strong enough and no longer crumbles. Before winding the coils, gaskets are prepared in advance (Fig. 2e) made of strips of cable paper. The strips are carefully cut along the edges to a depth of several mm. These cuts, adjoining the brushes, will protect the turns of the next layer from falling into the previous one.

### Winding coils

Figure 3. Diagram of the loop for the coil.

Before winding, it is necessary to prepare sections of flexible stranded wire in heat-resistant insulation for leads and sections of heat-resistant cambric. Winding is performed so that the wire fits the turn to the turn with some tension. Subsequent coils should press the previous ones. In order to prevent the coils from falling down near the cheek, it is advisable that the next row should not be drawn a few mm before it, filling in the free areas with string or threads.

After the winding of each row is completed, the tension of the wire must be maintained so that when laying a cable paper strip, the coiled portion does not open. Such gaskets should be laid after each layer.

If the coiled wire is thin, then to the beginning and end of the winding, as well as to the bends from it, the prepared pieces of flexible stranded wire are carefully soldered. The place of the spike is isolated. If the magnet wire is thick enough, the leads and outlets (in the form of loops) are made from the same wire. Both the conclusions and the bends should be worn with cambric segments.

The loop (Fig. 3a) is passed through the hole of the folded strip of thick paper or cotton tape, which is tightened after it is pressed by the next turns (Fig. 2b). An example of a branch from a thin winding wire is shown in fig. 2c.

Approximately the same way, the ends of the winding are made of thick wire, but only a cotton band is used. The scheme of fixing the beginning of the winding is shown in Fig. 2g, of its end - in fig. 2d

And a few words about how to wind the winding of a toroidal transformer. Usually, for their winding, homemade shuttles are used, on the surface of which a sufficient supply of wire is wound. The shuttle with the wire must pass into the hole of the toroidal magnetic circuit.

Figure 4. Bicycle wheel rim design.

It is much easier to wind up using the device, which is based on the rim of the bicycle wheel (Fig. 4). The rim is sawn in one place, threaded into the hole of the magnetic circuit, after which the cut parts are carefully connected. Then a winding wire of the required length is wound on its outer surface with a small margin. For convenience, the rim can be hung with its upper part on a hammered nail, pin or some other suitable suspension. It is convenient to fix the coiled wire with a suitable rubber ring.

The winding is wound due to the rotation of the rim. After completing each turn, move the rubber ring to the appropriate distance. The coils should be laid carefully, with tension. Conclusions and taps can be formed in the same way as in the above-mentioned coils. Each layer and winding must be separated by a layer of insulation. On top of the last layer, the transformer is wrapped with keeper tape and soaked with varnish.

### Transformer Assembly End

Diagram of a single-phase transformer.

When the coils are ready, the core or armor core is assembled. It should try to make as narrow as possible magnetic gaps, for which the assembly should be made in the lid. It continues until the entire window is filled. The final plates often have to be hammered using a wooden hammer or a wooden lining.

At the end of the assembly, the core is sealed, crimping the yoke or tightening, if the plates have corresponding holes, with pins, which are insulated from the core with cardboard tubes or several layers of paper. At the ends of the studs, electrical insulating and conventional washers are put on and nuts are screwed on, with which the core is tightened. A badly compressed core will buzz heavily and vibrate.

### Check transformer manufactured

Scheme of the machine for winding transformers.

First of all, using a megohm meter, measure the resistance between the individual windings, as well as between the core and the windings. It should not be less than 0.5 Mom. If there is no megohm meter, you can evaluate these resistances with an ordinary gauge. It should show infinity.

After checking the insulation, the primary winding of the transformer is supplied with a voltage equal to half the nominal. You can use, for example, Latte. If the product does not smoke, does not buzz, does not heat up much, a nominal voltage is applied to the primary winding.

Without load, the current in the primary winding of the transformer should not be more than 5-10% of its nominal value. The transformer itself should not be very hot and buzz loudly. If the buzz is strong, you should either pull it even harder, or drive wooden or plastic plates into the gap between the plates.

For the final test, the rated load is connected to the transformer, the voltages on all windings are checked. If everything is normal, the transformer is kept under load for 3-4 hours. If there is no buzz, there is no burning smell, and the transformer does not heat up more than 70°C, the test can be considered successfully completed.

Not always on sale you can find a transformer with the necessary parameters.

But it is safe to say that the required device is not overly complex, and it can be calculated and manufactured independently.