Download transformation ratio.

POWER CIRCUIT &
ELECTROMAGNETICS
EET 221
Transformer
Introduction
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.
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
Distribution
transformer
2. Instrument transformer
Instrument transformer is transformer which used as measurement,
consist of current transformer and potential 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 ioncore 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
If;
i p  2 I p sin t
then;
m   m sin t
By Faraday’s law;
ep  N p
Or;
d p
dm
d
 Np
 N p  m sin t 
dt
dt
dt

e p  N p m cos t  N p m sin t  90

The Iron-core Transformer
The effective value of ep is;
Ep 
N p  m
2
 4.44 fN p  m
Since the flux linking the secondary flux equals that of the
primary;
Es 
N s  m
2
 4.44 fN s  m
The Iron-core Transformer
Ep
Dividing;
Es
Np
Ns

Np
Ns
 a  Transforma tion ratio
For and ideal transformer;
Hence;
Vg
VL

Np
Ns
E p  Vg
and
Es  VL
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.
E p I p  Es I s
Pin  Pout
(ideal transformer )
Example
(a) Find the maximum flux m.
(b) Find the secondary turns Ns.
Solution :
(a)
E p  4.44 fN p  m
m 
Ep
4.44 fN p
200

 15.02 mWb
4.44  60  50
Solution :
(b)
Ep
Es

Ns 
Np
Ns
N p Es
Ep
50  2400

 600 turns
200
Tutorial
1. In Figure below :
a. What is the induced voltage ep in the primary if the primary flux
changes at 300 mWb/s?
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  m
c. If the maximum flux passing through the core is 12.5 mW, find
the frequency of the input voltage.