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Transformer
Chapter-1
Impedance Transformation
For secondary circuit,
Z
L
E
=
I
Effective input impedance at primary terminals,
Using turns ratio,
Z
i
2
2
E N E N
= = ( ) = ( ) . Z
I
1 1 2 2 1 2
1 N2 I2
N2
An impedance of ZL when viewed ‘through’ a transformer of turns ratio (N1: N2) is seen as (N1:
N2) 2 ZL. A transformer thus acts as an impedance converter. The transformer can be
interposed in between a source and a load to ‘match’ the impedance for maximum power
transfer to take place.
Similarly, impedance Z1 in the primary circuit can be transferred (referred) to secondary side
as
⎡
⎢
⎣
2
N ⎤
2 Z
1 Z
1
N
⎥ =
1
⎦
'
L
Z
i
E
=
I
1
1
For an ideal transformer, it may be summarized:
(i) Voltage is transformed into direct turn ratio.
(ii) Current is transformed into inverse turn ratio.
(iii) Impedance is transformed into direct turn ratio squared.
(iv) Power remains same.
(v) Frequency remains same.
Practical Transformer
At no load
(a)
Effect of transformer core loss: The core loss consists of hysteresis loss and eddy
current loss and are always present in the ferromagnetic core of the transformer. Due to
Hysteresis, the exciting current I e leads the flux m by hysteretic angle α.
The exciting current consists of two components Iϕ and Ic. Iϕ is called reactive or
magnetizing component and it provides the required magnetic flux m . The second
component Ic is called core-loss component. Total core loss is given as Pc = V 1 ' Ic.
Pc
VI ′
1 c
= Pc or Ic
= Amp.
V ′
1
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