This article covers various transformation ratios of a transformer such as voltage (turns) ratio, current ratio, and impedance ratio (matching) in detail along with solved examples.

**Voltage (Turns) Ratio**

The **mutual flux** is common to each winding. Therefore, it must induce the same voltage per turn in each winding. If *V*_{1}^{′} is the total induced voltage in the primary winding having *N*_{1} turns, then the induced voltage per turn is *V*_{1}^{′}/*N*_{1}. Similarly, the induced voltage per turn in the secondary winding is *V*_{2}^{′}/*N*_{2}.

On no load, the applied voltage *V*_{1} and the self-induced voltage *V*_{1}^{′} are almost equal and *V*_{2} = *V*_{2}^{′}, so the above ratios are transposed and usually expressed as:

\[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{{{N}_{1}}}{{{N}_{2}}}\]

That is, on no load, the ratio of the voltages is equal to the ratio of the turns.

**Turns Ratio Example**

A transformer has 1000 turns on the primary winding and 200 on the secondary. If the applied voltage is 250 V, calculate the output voltage of the transformer.

**Current Ratio**

When the transformer is connected to a load, the secondary current *I*_{2 }produces a demagnetizing flux proportional to the secondary ampere-turns *I*_{2}*N*_{2}. The primary current increases, providing an increase in the primary ampere-turns *I*_{1}*N*_{1} to balance the effect of the secondary ampere-turns. Because the excitation current *I*_{0} is so small compared with the total primary current on full load, it is usually neglected when comparing the current ratio of a transformer. Therefore the primary ampere-turns equal the secondary ampere-turns:

\[{{I}_{1}}{{N}_{1}}={{I}_{2}}{{N}_{2}}\]

By comparing the current and voltage ratios, it can be seen that the current **transformation ratio** is the inverse of the voltage transformation ratio:

\[\frac{{{I}_{1}}}{{{I}_{2}}}=\frac{{{N}_{2}}}{{{N}_{1}}}\]

**Impedance Ratio**

Although a main concern of audio and radio technicians, impedance ratio is important to understand for electrical workers. The reason is that when the voltage goes down as a result of the turns ratio, the current will go up for the very same reason. The impedance, or resistance if it makes it easier to understand, is a result of both changes, therefore **the impedance ratio is the square of the turns ratio**.

\[\frac{{{Z}_{2}}}{{{Z}_{1}}}={{\left( \frac{{{N}_{2}}}{{{N}_{1}}} \right)}^{2}}\]

**Impedance Ratio Example**

A typical situation is when a TV antenna has been designed with an impedance of 300 Ω but needs to be connected to the coaxial cable that has an impedance of 75 Ω.

A transformer is used with a turns ratio of 2:1, therefore the voltage ratio will also be 2:1 so the output voltage will be a half of the input voltage. Meanwhile the output current will be twice the input current. Therefore the output impedance *Z*_{2} = *V*_{2}/*I*_{2} = 0.5 *V*_{1}/2*I*_{1} = 0.25*Z*_{1} or a quarter the input impedance. That is, the ratio of *Z*_{2}/*Z*_{1} is found from (*N*_{2}/*N*_{1})^{2}.

- You May Also Read: Three Phase Transformer Connections