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Transformation Ratio and Turn Ratio of Single-Phase Transformer
What is Turn Ratio?
The turn ratio of a single phase transformer is defined as the ratio of number of turns in the primary winding to the number of turns in the secondary winding, i.e.
$$\mathrm{Turn\:Ratio=\frac{Number\:of\:Primary\:Turns(N_{1})}{Number\:of\:Secondary\:Turns(N_{2})}}$$
Since for a transformer, the voltage per turn being equal in both primary and secondary windings, therefore,
$$\mathrm{\frac{E_{1}}{N_{1}}=\frac{E_{2}}{N_{2}}}$$
$$\mathrm{\Rightarrow\frac{E_{1}}{E_{2}}=\frac{N_{1}}{N_{2}}=Turn\:Ratio}$$
Also, if the given transformer is an ideal one, then E1 = V1 and E2 = V2, thus,
$$\mathrm{Turn\:Ratio=\frac{N_{1}}{N_{2}}=\frac{E_{1}}{E_{2}}=\frac{V_{1}}{V_{2}}}$$
In case of ideal transformer, the input volt-ampere is equal to output volt-ampere, i.e.
$$\mathrm{V_{1}I_{1}=V_{2}I_{2}}$$
$$\mathrm{\Rightarrow\:\frac{V_{1}}{V_{2}}=\frac{I_{2}}{I_{1}}}$$
$$\mathrm{Turn\:Ratio=\frac{N_{1}}{N_{2}}=\frac{E_{1}}{E_{2}}=\frac{V_{1}}{V_{2}}=\frac{I_{2}}{I_{1}}}$$
What is Transformation Ratio?
The transformation ratio is defined as the ratio of output voltage to the input voltage of the transformer. It gives the information about the change in voltage level by the transformer.
$$\mathrm{Transformation\:Ratio(K)=\frac{Transformer\:Output\:Voltage(V_{2})}{Transformer\:Input\:Voltage(V_{1})}}$$
As we known for a transformer, the voltage per turn remains equal in both primary and secondary windings, hence,
$$\mathrm{\frac{V_{1}}{N_{1}}=\frac{V_{2}}{N_{2}}}$$
$$\mathrm{\Rightarrow\frac{V_{2}}{V_{1}}=\frac{N_{2}}{N_{1}}=K}$$
Also, for the ideal transformer, E1 = V1 and E2 = V2, thus,
$$\mathrm{K=\frac{V_{2}}{V_{1}}=\frac{N_{2}}{N_{1}}=\frac{E_{2}}{E_{1}}}$$
Also, for ideal transformer, the input volt-ampere is equal to output volt-ampere, i.e.
$$\mathrm{V_{1}I_{1}=V_{2}I_{2}}$$
$$\mathrm{\Rightarrow\:\frac{V_{2}}{V_{1}}=\frac{I_{1}}{I_{2}}}$$
Therefore,
$$\mathrm{Transformation\:Ratio, 𝐾=\frac{V_{2}}{V_{1}}=\frac{N_{2}}{N_{1}}=\frac{E_{2}}{E_{1}}=\frac{I_{1}}{I_{2}}\:\:\:\:...(2)}$$
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