# Calculating the Turns Ratio of a Transformer

## The turns ratio, or the turns-to-turns ratio, is the ratio of the number of turns in the primary to the number of turns in the secondary.

The turns ratio is expressed with two numbers, like 2:1 or 2 to 1. The first number represents the primary's relative number of turns, while the second number represents the secondary's relative number of turns. The turns ratio of a transformer is calculated by applying the following formula:

$$\frac{{{N}_{p}}}{{{N}_{s}}}$$

where

NP = number of turns in the primary winding

NS = number of turns in the secondary winding

Example: What is the turns ratio of a transformer with 500 turns in the primary winding and 1000 turns in the secondary winding?

$$\frac{{{N}_{p}}}{{{N}_{s}}}=\frac{500}{1000}=1:2$$

A step-up transformer is a transformer with the source connected to the winding with fewer turns and the load connected to the winding that has a larger number of turns. A step-down transformer is a transformer with the source connected to the winding with the most turns and the load connected to the winding with the fewest turns (see Figure 1).

*Figure 1. The turns ratio determines whether a transformer is a step-up or step-down transformer*

*Note*

*Most motor control circuits are powered from step-down transformers that reduce the voltage to the control circuit. A step-down transformer reduces the voltage to the control circuit to a level of 24 V or 12 V, as needed.*

For both step-up and step-down transformers, the power rating is always the same on the primary and secondary sides. The turns ratio can be used to calculate the secondary voltage and current as follows:

$$\frac{{{N}_{p}}}{{{N}_{s}}}=\frac{{{E}_{p}}}{{{E}_{s}}}=\frac{{{I}_{s}}}{{{I}_{p}}}$$

Where

NP = number of turns in primary

NS= number of turns in secondary

EP = voltage in primary (in V)

ES = voltage in secondary (in V)

IP = current in primary (in A)

IS = current in secondary (in A)

The turns ratio between the two coils determines if the device is a step-up or step-down transformer. For example, if the coil connected to the source has 500 turns and the coil connected to the load has 1000 turns, the device is a step-up transformer. The turns ratio is 1:2, and the flux from each turn in the primary cuts two turns in the secondary. If the source connected to the primary is 120 V, the secondary voltage is calculated as follows:

$$\frac{{{N}_{p}}}{{{N}_{s}}}=\frac{{{E}_{p}}}{{{E}_{s}}}\Rightarrow \frac{500}{1000}=\frac{120}{{{E}_{s}}}\Rightarrow 500\times {{E}_{s}}=120\times 1000\Rightarrow {{E}_{s}}=240V$$

If a 240 V source needs to be stepped down to 120 V, the coils could be reversed. The 240 V coils are the primary, and the 120 V coils are the secondary. However, the voltage rating of the coil must never be exceeded. A transformer with a 2:1 ratio with a 240 V primary and a 120 V secondary should not be connected to a 480 V line to build a 240 V secondary. The turns ratio is correct, but the inductance of the coils is too low to provide the required current limits in the coil due to the lower reactance.

## Volts per Turn

The turns ratio can be used to explain a related concept called volts per turn. Volts per turn (V/turn) is the voltage dropped across each turn of a coil or the voltage induced into each turn of the secondary coil. Each transformer has a design value for the volts per turn. For example, if a transformer primary has 120 turns with a source of 120 V, it has 1 V/turn. The secondary coil has the same volts per turn value. If the secondary coil has 24 turns, the voltage across the secondary is 24 V. Therefore, a transformer with a turns ratio of 120:24, volts per turn of 1, and a primary voltage of 120 V has a secondary voltage of 24 V

## Coil Taps

A coil tap on a transformer coil is an additional electrical connection that permits a variable number of coil turns to be part of the circuit (see Figure 2). Coil taps are sometimes necessary depending on the location of the service in reference to the substation that is providing power. At the end of the distribution line, a long distance from the source, the voltage will sometimes be below normal. In order to get the proper voltage to the equipment in the plant, taps on the transformer primary are offered. These taps allow the turns ratio of a transformer to be modified in the field to compensate for a low primary voltage.

*Figure 2. Coil taps are used to adjust the voltage output from a transformer.*

For example, if a primary coil is rated at 7200 VAC and has 1620 turns, what is the volts per turn value of the transformer? The transformer drops 7200 VAC across 1620 turns. The volts per turn is calculated as follows:

$${V}/{turn=\frac{E}{{{N}_{p}}}}\;$$

where

V / turn = volts per turn

E = voltage (in V)

turns = number of turns in primary

$${V}/{turn=\frac{E}{{{N}_{p}}}}\;=\frac{7200}{1620}=4.444$$

What is the volts per turn value of the transformer if the voltage is 5% low (6840 VAC)?

$${V}/{turn=\frac{E}{{{N}_{p}}}}\;=\frac{6840}{1620}=4.222$$

This shows that when the primary voltage is reduced by 5%, the secondary voltage is reduced by the same percent. By changing taps and removing some turns from the primary circuit, the volts per turn can be brought back up to a level that gives us the proper secondary voltage. The number of turns in the primary required to drop 4.444 V/turn at 6840 VAC is calculated as follows:

$${{N}_{p}}=\frac{E}{{V}/{turn}\;}$$

where

NP = number of turns in primary

E = voltage (in V)

V / turn = volts per turn

$${{N}_{p}}=\frac{6840}{4.444}=1539\text{ }turns$$

This type of transformer is normally furnished with coil taps at multiples of 2.5% above normal (AN) and 2.5% below normal (BN). For a primary with 1620 turns, 2.5% represents about 40 turns (1620 × 0.025 = 40.5). Moving the connection by two tap locations changes the number of turns in the primary coil by about 80 turns. The primary is changed from 1620 turns to 1540 turns. The turns ratio is changed so that the transformer can compensate for the low voltage and ensure that the secondary is at the rated voltage.

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