Copyright 20 13 Dorling Kindersley (India) Pvt. Ltd

n
2
+
–
+
–
nI
S
I
p
v
p
Z
L
j
L
1
ω

---

Ideal Transformer and Impedance Matching 
14.13
Therefore, we minimise the effect of that inductance by making L
1
(and consequently L
2 
and
M too) 
very large compared to the maximum value of Z
L
that we may use. This is done by using a large cross-
section iron core and a large number of turns in both windings keeping the turns ratio at the desired 
value. An ideal transformer is an idealised model for such a transformer.
An ideal transformer is a two-winding transformer with perfect coupling (
k
= 
1) and 
infinite self and mutual inductance values (
L
1 
→
∞
, 
L
2
→
∞
, 
M
→
∞
). Complex power is 
conserved in an ideal transformer.
Thus, the equations for an ideal transformer are:
V
V
n
I
I
n
V I
V I
Z
Z
n
s
p
s
p
p p
s s
in
=
=
∴
=
=
∗
∗
;
1
2
L
Complex power is conserved in an ideal transformer. That is, an ideal transformer absorbs zero 
active power, zero reactive power and zero complex power. Whatever active power and reactive power 
go into the primary winding go out of secondary winding into the load. An ideal transformer simply 
changes the voltage and current levels at which complex power transfer takes place. Moreover, an 
ideal transformer is an impedance transformer. It scales the secondary load impedance by a scaling 
factor of 
1
2
n
and presents it at the primary input. In fact, those two are the major applications of 
transformers – efficient voltage/current level translation in power engineering and impedance level 
translation (called impedance matching) in electronics engineering.