How to calculate the transformer turns ratio

Transformer is a very important electrical equipment in power system, which is mainly used to change the AC voltage to meet the power demand of different occasions. The "turns ratio" of transformer is one of the key parameters to determine its voltage conversion ability. This paper will introduce the concept, calculation method and significance in practical application of transformer turns ratio in detail.

1. What is the turn ratio of transformer?

A transformer consists of two or more windings, which are called primary winding (primary side) and secondary winding (secondary side) respectively. Turns Ratio refers to the ratio of coil turns of primary winding to secondary winding, which is usually represented by the symbol "n".

The basic formula of the turns ratio is:

$$
n = frac{N_1}{N_2}
$$

Among them:
-$ N_1 $: the number of turns of the primary winding;
-$ N_2 $: the number of turns of the secondary winding.

In addition, the turns ratio can also be indirectly expressed by the voltage ratio, that is:

$$
n = frac{U_1}{U_2}
$$

Among them:
-$ U_1 $: the voltage of the primary winding;
-$ U_2 $: the voltage of the secondary winding.

The premise of this relationship is to ignore the loss and flux leakage inside the transformer.

Second, the calculation method of turns ratio

1. Find the turns ratio of the known voltage.
In practical application, the turns ratio is often calculated by measuring the primary and secondary voltages. For example, if the primary voltage is 220V and the secondary output voltage is 110V, then:

$$
n = frac{U_1}{U_2} = frac{220}{110} = 2
$$

It means that this is a step-down transformer with a turn ratio of 2:1.

2. Find the ratio of turns with known turns.
If it is known that the primary winding has 1000 turns and the secondary winding has 500 turns, then:

$$
n = frac{N_1}{N_2} = frac{1000}{500} = 2
$$

It also shows that this is a transformer with a turn ratio of 2:1.

3. Calculation of turns ratio of multi-winding transformer
For a transformer with multiple secondary windings, each secondary winding can separately calculate the turns ratio with the primary winding, which corresponds to different voltage outputs.

4. Consider the current relationship of variable ratio.
The turns ratio is also inversely proportional to the current, that is:

$$
frac{I_1}{I_2} = frac{N_2}{N_1} = frac{1}{n}
$$

This shows that if the number of turns is large, the secondary current will be larger than the primary current, and vice versa.

Third, the practical application of turns ratio

1. Voltage conversion
The turns ratio determines whether the transformer will step up or step down. When $ n > 1 $,it is a step-down transformer; When $ n < 1 $,it is a step-up transformer.

2. Impedance matching
Transformer can be used to realize impedance matching between different circuits, thus improving energy transmission efficiency. The impedance transformation is proportional to the square of the turns ratio:

$$
Z_2 = left(frac{N_2}{N_1}
ight)^2 Z_1 = left(frac{1}{n}
ight)^2 Z_1
$$

3. Isolation and security
By using different turns ratio, the transformer can be electrically isolated from the secondary system, which plays a protective role in industrial and household electricity consumption.

Fourth, summary

The turns ratio of transformer is one of its basic parameters, which determines the transformation relationship between voltage and current, and also affects impedance matching and energy transmission efficiency. Mastering the calculation method of turns ratio is of great significance to the design and selection of transformers and the operation and maintenance of power systems. By actually measuring the voltage or the number of turns of the winding, the turn ratio can be accurately calculated, which provides theoretical support and technical guarantee for power engineering practice.