Transformer Voltage Transformation Ratio

Transformer Voltage Transformation Ratio

How to define the voltage transformation ratio of a transformer?

The voltage transformation ratio of a transformer is nothing but the ratio of the transformer core turn number or induced voltage onto the cores.

In our previous article about Transformer E.M.F. Equation and Derivation, we have equated 2 equations for induced voltage of the transformer primary and secondary windings.

E₁ = 4.44fN₁Φ_m = 4.44fN₁B_mA

E₂ = 4.44fN₂Φ_m = 4.44fN₂B_mA

Definition of Transformer Voltage Ratio

The transformer voltage transformation ratio is defined as the ratio of the EMF in the secondary coil to that in the primary coil.

Symbolically transformer voltage transformation ratio defined by letter "K".

K = E₂/E₁ = (4.44fN₂Φ_m)/(4.44fN₁Φ_m )

Therefore,
K = E₂/E₁ = N_2/N_1....(equ-1)

Now,
V₁ = E₁ + voltage drop
E₂ = V₂ + voltage drop
Due to the resistance in the windings and some leakage flux, there is some loss in voltage. This is called Voltage Drop.

But, in the ideal case, the voltage drop can be neglected.
Hence,

V₁ = E₁
E₂ = V₂ 

Hence,
E₂/E₁ = V₂/V₁…..(equ-2)

Also, in a transformer, the power across the primary, as well as the secondary winding, is the same. 

Hence,
V₁ I₁= V₂ I₂

V₁/V₂ = I₂/I₁……..(equ-3)

Now, combining equation (1), (2) & (3), we get, transformer voltage transformation constant (K)

K = E₂/E₁ = N_2/N₁ = V₂/V₁ = I₂/I₁

Where,
1 represents the primary coil;
2 represents the secondary coil;
E is emf in the respective coil;
V is the voltage in the respective coil;
I is the current in the respective coil;
N is the number of turns of the respective coils;
Φ_m is the mutual flux in the core.

How do the transformer coil turn number and induced voltage determine whether the transformer is step-up or step-down?

The d    derivate equation of the voltage transformation of a transformer from the above is-  

E₂/E₁ = N_2/N₁ =K

This constant K is known as voltage transformation

ratio.

1. If N₂ > N₁ i.e. K > 1, then transformer is called step-up transformer;
2. If N₂ < N₁ i.e. K < 1, then the transformer is known as a step-down transformer.

Again, for an ideal transformer, input VA = output VA.

V₁ I₁= V₂I₂ or I_{2 /}I₁₌V_1/V₂

Hence, currents are in the inverse ratio of the (voltage) transformation ratio.

You may know the details about the electrical transformer from the following articles:

 

1. Working Principle of Transformer;
2. Transformer Construction;
3. Core-type Transformers;
4. Shell-type Transformers;
5. Elementary Theory of an Ideal Transformer;
6. E.M.F. Equation of Transformer;
7. Voltage Transformation Ratio;
8. Transformer with losses but no Magnetic Leakage;
9. Transformer on No-load;
10. Transformer on Load;
11. Transformer with Winding Resistance but no Magnetic Leakage;
12. Equivalent Resistance;
13. Magnetic Leakage;
14. Transformer with Resistance and Leakage Reactance;
15. Simplified Diagram;
16. Total Approximate Voltage Drop in Transformer;
17. Exact Voltage Drop;
18. Equivalent Circuit Transformer Tests;
19. Open-circuit or No-load Test;
20. Separation of Core Losses;
21. Short-Circuit or Impedance Test;
22. Why Transformer Rating in KVA?;
23. Regulation of a Transformer;
24. Percentage Resistance, Reactance, and Impedance;
25. Kapp Regulation Diagram;
26. Sumpner or Back-to-back-Test;
    
27. The efficiency of a Transformer;
28. Condition for Maximum Efficiency;
29. Variation of Efficiency with Power Factor;
30. All-day Efficiency;
31. Auto-transformer;
32. Conversion of 2-Winding Transformer into Auto-transformer;
33. Parallel Operation of Single-phase Transformers;
34. Questions and Answers on Transformers;
35. Three-phase Transformers;
36. Three-phase Transformer Connections;
37. Star/Star or Y/Y Connection;
38. Delta-Delta or ∆/∆ Connection;
39. Wye/Delta or Y/ Connection;
40. Delta/Wye or ∆/Y Connection;
41. Open-Delta or V-V Connection;
42. Power Supplied by V-V Bank;
43. Scott Connection or T-T Connection;
44. Three-phase to Two-Phase Conversion and vice-versa;
45. Parallel Operation of 3-phase Transformers;
46. Instrument Transformers;
47. Current Transformers;
48. Potential or Voltage Transformers.