Transformation ratio of transformer

Transformer Transforms energy from one circuit to another circuit without electrical coupling , in principle of electromagnetic induction. The energy needs to transformed and energy in form of transformation has to obey few relations with ratios of the transformer. These ratios are often called as transformation ratio of transformer. There are three types of ratios are involved in the transformer as listed below,

1. Voltage ratio
2. Current ratio
3. Turns ratio

An Elementary transformer connected with an alternating supply source and voltmeters V1 and V2 are connected across primary and secondary winding of the transformer, A load also has been connected across secondary winding of transformer. Ammeters A1, A2 are connected in series with both primary and secondary winding.

The voltage ratio of transformer defined as ratio of induced voltage between primary and secondary winding.

Let Emf induced in primary winding said as

E₁ = 4.44ΦmfN₁ volts   ——–(1)

And Emf induced in secondary winding

E₂ = 4.44ΦmfN₂ volts  ——–(2)

Where,

 E₁ –  Emf induced in primary winding

E₂ –  Emf induced in secondary winding

N₁ –  Number of turns in primary winding

N₂ – Numbers of turns in secondary winding

Then, taking ratio of equation (1) and (2)  and simplifying it, we get,

K shows transformation ratio constant

Under No load condition there is no flow of electric current (I₂) through secondary winding. So, there is no losses copper losses in secondary winding of transformer. So emf induced in secondary winding will be equal to terminal voltage available on terminal of secondary side.

E₂ = V₂  ——–(5)

Due to no load at secondary side , magnitude of primary current (I₁) also will be quite low to compensate fixed losses (core loss, iron loss) of transformer. So, it may also be considered as

E₁ = V₁ ——–(6)

Equation (6) and (7) can be re-written as

Substitute equation (3) , transformation ratio of no-load transformer in equation (7), we get

Equation (8) indicated voltage ratio of transformer under load condition proportional to voltage ratio under no load condition.

The turns ratio of the transformer defined as ratio of number of primary turns (N₁) and number of secondary turns (N₂) in the transformer

With Co-relation of  equation (8) and (9) clearly indicates that voltage ratio ultimately depends on turns ratio of transformer.  So, number of turns in primary and secondary winding decides magnitude of induced voltage in secondary winding to applied voltage / induced voltage in primary side.

We know that transformer transforms energy from one side to another side of electrical circuit without electrical coupling. As transformer is a static device there is no losses related to mechanical losses are produced like induction motors.

By negligible losses in transformer , let assume efficiency as 100% approximately.

I.e.,  

Input power given =  Power delivered to load

P_in = P_out

V₁I₁CosΦ₁ = V₂I₂CosΦ₂   ——–(10)

During energy transformation , power factor of input power supply (CosΦ₁) and power delivered to the load (CosΦ₂)well be remains same.

In Equation(10) I₁ and I₂ are primary and secondary current of transformer respectively.

By keep consideration of above terms equation (10) simplified as,

V₁I₁ = V₂I₂  ——–(11)

(or)

Substituting above current ratio equation (12) in voltage ratio equation (8), we get

The expression in equation (14) indicates current ratio  inversely proportional to voltage, turns ratio of transformer. Final Expression of Transformation ratio

Where K is known as transformation ratio constant. Depending upon value of K, a transformer classified as

1. Step-down transformer
2. Step-Up transformer
3. One-to-One Transformer.

Types of transformers depends upon transformation ratio constant

Particulars	Step-up transformer (K>1)	Step-down transformer (K<1)	One-To-One transformer (K=1)
Primary turns	Less	More	Equal to secondary turns
Secondary turns	More	Less	Equal to primary turns
Primary induced EMF	Less	More	Equal to secondary induced emf
Secondary induced EMF	More	Less	Equal to primary induced emf
Input voltage to primary	Less	More	Equal to secondary terminal voltage
Secondary terminal voltage	More	Less	Equal to primary input voltage
Primary input current	more	less	Equal to secondary current
Secondary current	less	more	Equal to primary current