Concept about the transformation ratio


What is the transformation ratio

In the electrician and the radio technician often there is the need to transform the alternating voltage of one size to the alternating voltage of other veyolichina. In these cases use the device, koyotory is called the transformer.

Обмотка трансформатора

Transformer winding.

The transformer represents system from two or more windings placed on one obyoshchy iron rod (core). One of these windings is connected to the external source pereyomenny э. of page is also called primary obmotyoky. All other windings carry the name of vtoyorichny
windings, and sootyovetstvuyushchy energy consumers (fig. 1) are connected to them.

The principle of operation of the transformer is based on the interinduction yavleyoniya.

Схема трансформатора

Fig. 1 Scheme of the transformer.

At inclusion of the source peyoremenny э. of page in primary winding proceeds alternating current, and in the transformer core the variable magnetic flux sozyodatsya. This flow proyonizyvat rounds of primary and secondary windings and on each separate round, according to the law of elektroyomagnitny induction, directs induced э. of page. As rounds of each winding are reeled up in one party, э. of page, acting on the ends of this obyomotka, it will be equal to the sum э. of page of its separate rounds.

If the number of rounds of secondary winding of W2 are less than number of rounds of the primary winding W1, then and tension on the ends of secondary winding of U2 will be less napryayozheniye, acting on the ends of primary winding, i.e. U1. In this case the transformer lowers tension of the external source therefore it nazyyovatsya by lowering. If the number of rounds of the vtorichyony winding of W2 are more than number of rounds of the primary winding W1, then tension of U2 will be more napryayozheniye of U1. In that case the transformer povyyoshat tension created by the external source and is called raising.

Having separated stress amplitude on the secondary obyomotka of U2 on stress amplitude operating on the primary winding U1 we will receive the size which hayorakterizut extent of transformation of size of the napryayozheniye and is called transyoformation coefficient:

n = U2: U1

As the magnetic flux is the general for both windings, tension relation on the vtorichyony winding to tension on primary winding can be replaced with the relation of numbers of rounds of these the obyomotok:

n = U2: U1 = W2: W1

If n> 1, the transformer raising, if n <1 — lowering.

From this expression it is possible to determine the sizes U2 and W2

U2 = U1n,  W2 = W1n

Схема измерения коэффициента трансформации силовых трансформаторов

Scheme of measurement of the transformation ratio of power transformers.

During the operation of the transformer tension of U2 acts on the ends of nagruzochyony resistance of Rn and in secondary winding I2 current proceeds. Therefore, in secondary winding some moshchyonost of P2 develops. This power in secondary winding sushcheyostvut because electrical energy, poyotreblyaemy primary winding from the power line, is transmitted to secondary winding. If to consider ко­эффициент useful effect of the transformer blizyoky to unit (— 100%), then the power consumed by primary winding from the power line has to be equal to the power created in secondary winding:

P1 = P2

Capacities in both windings can be expressed through tension and current of this winding:

P1 = U1I1,  P2 = U2I2

Having substituted expressions for capacities in the formula, we will receive:

U1I1 = U2I2

Let's separate both parts of the received equality into the same size I1U2:

U1I1: I1U2 = U2I2: I1U2,

Having made reduction, we will finally receive:

U1U2 = I2I1

From the formula it is visible that tension on windings is inversely proportional to the currents proceeding in these windings. The more tension on the winding, the less there has to be current in this winding and the less section of the wire of the winding. Therefore secondary winding in the reducing transformer is reeled up, as a rule, by the wire with big section, i.e. provoyody which section is much more section of the proyovod of primary winding.

From the formula we will define I2

I2 = I1 (U1: U2),

But expression (U1: U2) represents size, the return to the transformation ratio, i.e.

U1: U2 = 1: n, then I2 = I1: n,

These formulas are fair for the case when the transformer has only two windings — primary and secondary. In more general case the transformer can have the bigger quantity of secondary winding, and then ratios between currents and tension in separate windings will look differently. However and in these cases there is spravedliyovy the equality of capacities primary and all vtorichyony windings.

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