POWER CIRCUIT & ELECTROMAGNETICS

EET 221

Transformer

A transformer is a device that changes ac electric energy at one voltage level to ac electric energy at another voltage level through the action of a magnetic field.

Introduction

The most important tasks performed by transformers are:

• changing voltage and current levels in electric power systems.• matching source and load impedances for maximum power transfer in

electronic and control circuitry.• electrical isolation (isolating one circuit from another or isolating dc

while maintaining ac continuity between two circuits).

Transformer consists of two or more coils of wire wrapped around a common ferromagnetic core. One of the transformer windings is connected to a source of ac electric power – is called primary winding and the second transformer winding supplies electric power to loads – is called secondary winding.

Type of transformer :

1. Power transformer

Power transformer is transformer which has power rating some VA to thousand VA

2. Instrument transformer

Instrument transformer is transformer which used as measurement, consist of current transformer and potential transformer.

Distribution

transformer

Current

transformer

The Iron-core Transformer

Iron-core Transformer The iron core will serve to increase the coefficient

of coupling between the coils by increasing the mutual flux m..

The magnetic flux lines will always take the path of least reluctance, which in this case is the iron core.

When the current Ip through the primary circuit of the ion-core transformer is a maximum, the flux m linking both coils is also a maximum.

The flux is directly proportional to the current through the winding.

The Iron-core Transformer

tIi pp sin2If;

then; tmm sin

By Faraday’s law;

tdt

dN

dt

dN

dt

dNe mp

mp

ppp

sin

Or; 90sincos tNtNe mpmpp

The Iron-core Transformer

The effective value of ep is;

mpmp

p fNN

E

44.42

Since the flux linking the secondary flux equals that of the primary;

msms

s fNN

E

44.42

The Iron-core Transformer

Dividing;s

p

s

p

N

N

E

E

ratiotion Transforma aN

N

s

p

For and ideal transformer; gp VE and Ls VE

Hence;

s

p

L

g

N

N

V

V

The Iron-core Transformer The ratio of the magnitudes of the induced

voltages is the same as the ratio of the corresponding turns:

The ratio Np/Ns , usually represented by the lowercase letter a, is referred to as the transformation ratio. If a < 1, the transformer is a step-up transformer. If a > 1, the transformer is a step-down transformer.

Example

(a) Find the maximum flux m.

(b) Find the secondary turns Ns.

sspp IEIE

)( rtransformeidealPP outin

Solution :

mpp fNE 44.4

p

pm fN

E

44.4

mWb 02.15506044.4

200

(a)

Solution :

s

p

s

p

N

N

E

E

turns600200

240050

(b)

p

sps E

ENN

Tutorial

a. What is the induced voltage ep in the primary if the primary flux changes at 300 mWb/s?

1. In Figure below :

b. What is the induced voltage ep in the primary if the primary current changes at a 5 A/s rate?

2. In Figure below

a. What is the transformation ratio for this transformer?

b. What is the voltage ES across the load?

c. What is the current IS through the load? d. If this transformer is an ideal device, how much power is transferred to the load?

3. A power transformer nameplate lists 2 kVA, 500/100 V, 60 Hz. If the applied primary voltageis 20 V, what is the maximum safe primary current?

4. A power transformer nameplate lists 2 kVA, 500/100 V, 60 Hz. If the 100 V number is the secondary voltage, find the current rating of the secondary.

5. An ideal transformer has 200 primary turns and 20 secondary turns. What is the secondary voltage if the primary voltage is 120 V?

6. If 0.3 A flows in the secondary and 30 A flow in the primary of a perfectly matched, ideal transformer, what is the primary to secondary turns ratio?

7. What is the volt-amp rating of this transformer if the transformer is operating at its rated capacity? (Look at figure in below)

8. In Figure below :

a. Find the magnitude of the induced voltage Es

b. Find the maximum flux

c. If the maximum flux passing through the core is 12.5 mW, find

the frequency of the input voltage.

m