# Transformer - Operation, Types, EMF Equation

Introduction

A transformer is a static electrical machine which transfers electrical energy from one circuit to another circuit without change in its frequency. Due to electromagnetic induction principle the transfer of energy takes place.

Transformer Construction

It consists of three essential parts , they are

1.Primary winding

2.Secondary winding

3.Laminated iron core

I/p - primary
O/p - secondary

Principle of operation

Transformer works on the principle of mutual induction. When an A.C supply is given to primary winding, an alternating flux is set up in the core. This flux cuts both primary and secondary windings. An e.m.f is induced in the primary winding according to self induction principle. According to faradays mutual induction principle, an e.m.f is induced in the secondary winding. if we connect a load to the secondary winding, current will follow through the load. In this way, electrical energy is transferred from the primary to secondary circuit.

Types of transformer

1.Step - down

If the number of turns in the secondary winding is less than that of the primary winding, the e.m.f induced in the secondary winding will be less than the e.m.f induced in the primary winding. This type of transformers is called step down transformers.

2.Step-up

If the number of turns in the secondary winding is more than that of the primary winding, the e.m.f induced in the secondary winding will be more than the e.m.f induced in the primary winding. This type of transformers is called step up transformers.

Ideal Transformer

An ideal transformer is static electric machine which transfers electrical energy from one circuit to another circuit without any losses. It consists two purely inductive coil of has loss-free core

Characteristics

1. no winding resistance therefore, there is no I2losses

2. no leakage flux

3. no core losses (or) iron losses in the core.

According to construction, transformer divided into two types

1. core type transformer
2. shell type transformer

CORE TYPE TRANSFORMER

In core type transformers the winding surround the core as shown in fig (a) & (b)

1    The core is made up of thin laminated silicon steel.

2    The laminated steel cores are insulated from each other by means of varnish.

3    The laminated core minimizes the eddy current loss.

4    The thickness of lamination varies from 0.35 mm to 0.55 mm

5    Since the core is made up of silicon steel, the hysteresis loss is reduced

6    The cross section of the core may be rectangular for small transformers

7    For large, the cross section of the core should be either square (or) stepped as shown in the fig.

8    The primary and secondary winding of core type transformer are wound helically.

9    Coil is insulated from one another using mica.

SHELL TYPE OF TRANSFORMER:

In shell type transformers the iron core surrounds the windings.

1. The core is made up of thin laminated silicon steel.

2. The laminated steel cores are insulated from each other by means of varnish.

3. The laminated core minimizes the eddy current loss.

4. The thickness of lamination varies from 0.35 mm to 0.

5. Since the core is made up of silicon steel, the hysteriesis loss is reduced

6. The cross section of the core may be rectangular for small transformers

7. For large, the cross section of the core should be either square (or) stepped as shown in the fig.

8. Coil is insulated from one another using mica.

EMF EQUATION OF A TRANSFORMER

Consider a transformer having

Let,

N1 =primary turns
N2 =secondary turns
Φ = maximum flux in the core
f=freq of the a.c voltage applied

Flux in the core will vary sinusoidal as shown in the waveform

The flux increases from zero value to max value ‘Φm’ is ¼ f second.
The change of flux is ¼ f second = (Φm-0) Weber’s.

Rate of change of flux is the second = Φm / (1/4f) = 4fΦm

Since the flux is varying sinusoidally, the r.m.s value of induced e.m.f is obtained by multiplying the average value with the form factor,

Form factor of sine wave = R.M.S value/average value = 1.11

R.m.s value of e.m.f induced is one turn = 4f Φm*1.11 = 4.44 f Φm

R.m.s value of e.m.f induced in primary winding E1 = 4.44 f Φm N1
R.m.s value of e.m.f induced in secondary winding E2 = 4.44 fΦm N2

In an ideal transformer, e.m.f induced in any winding is equal to the voltage across its terminals on no load.

Applied voltage, V1 = E1
Secondary terminal voltage, V2 E2

Voltage transformation ratio = E1 / E2 =  4.44 f Φm N1 / 4.44 f Φm N2 = N2 / N1 = K

If NN1, k > 1, then the transformer is called step up transformer

If N1 > N2, k < 1, then the transformer is called step down transformer

Current transformation ratio

In an ideal transformer,

Apparent input power = Apparent output power V1I1 = V2I2

I1 / I2 = V2 / V1 = W2 / W1 = K