Transformer Ratio and Its Equivalent Circuit

1. Transformer Ratio &
Equivalent Circuit of
Transformer
P. MARIA SHEEBA
AP/ECE, MZCET

2. Summary
 In last class, we have discussed about
the ideal transformer and its
properties.
 We also derived the emf equation of a
transformer.
 In today’s class, we will discuss about
the transformer ratio and also the
equivalent ciruit of a transformer.

3. Ratio of transformer
 1.Voltage ratio.
 2.Current Ratio.
 3.Volt Amp Ratio.
Voltage ratio
MZCET/ECE/III Sem/EE6352- Unit 2 3
2.3

4. Transformation Ratio=K
MZCET/ECE/III Sem/EE6352- Unit 2 4
2.3

5.  Current ratio:
Volt Amp Ratio:
MZCET/ECE/III Sem/EE6352- Unit 2 5
2.3

6. The maximum flux density in the core of 240/2400
V, 50 Hz, Single phase transformer is 1 Wb/m2.
If the e.m.f. per turn is 8 V, Determine:
1. Primary and secondary turns.
2. Area of the core.
Solution:
MZCET/ECE/III Sem/EE6352- Unit 2 6
Example 12.3

7. MZCET/ECE/III Sem/EE6352- Unit 2 7
2.3

8. MZCET/ECE/III Sem/EE6352- Unit 2 8
2.3

9. Phasor diagram: Transformer on
No-load
MZCET/ECE/III Sem/EE6352- Unit 2 9
2.4

10. Fig shows the Phasor diagram of a
transformer
on load by assuming
1.No voltage drop in the winding
2.Equal no. of primary and secondary turns
2.4
MZCET/ECE/III Sem/EE6352- Unit 2 10

11. Transformer on load
MZCET/ECE/III Sem/EE6352- Unit 2 11
Fig. a: Ideal transformer
on load Fig. b: Main flux and leakage
flux in a transformer
2.5

12. Phasor diagram of transformer with UPF
load
MZCET/ECE/III Sem/EE6352- Unit 2 12
2.5

13. Phasor diagram of transformer with lagging p.f
load
MZCET/ECE/III Sem/EE6352- Unit 2 13
2.5

14. Phasor diagram of transformer with leading p.f
load
MZCET/ECE/III Sem/EE6352- Unit 2 14
2.5

15. Equivalent circuit of a
transformer
MZCET/ECE/III Sem/EE6352- Unit 2 15
𝐼 𝑚 = 𝐼0 𝑆𝑖𝑛∅0
𝐼𝑐 = 𝐼0 𝐶𝑜𝑠∅0
𝑅0 = 𝑉1
𝐼𝑐
𝑉0 = 𝑉1
𝐼 𝑚
2.6

16. Referred to primary and secondary
sides respectively
MZCET/ECE/III Sem/EE6352- Unit 2 16
2.5

17. Contd.,
 circuit parameters shouldn’t be
changed while transferring the
parameters from one side to another
side.
 It can be proved that a resistance of
R2 in sec. is equivalent to R2/k2 will be
denoted as R2
MZCET/ECE/III Sem/EE6352- Unit 2 17
2.6

18. Contd.,
 Equivalent sec. resistance w.r.t primary- which
would have caused the same loss as R2 in
secondary,
MZCET/ECE/III Sem/EE6352- Unit 2 18
2
2
2
'
2
2
1 RIRI 
2
2
1
2'
2R R
I
I







2
2
k
R

2.6

19. Transferring secondary parameters to
primary side
MZCET/ECE/III Sem/EE6352- Unit 2 19
2.6

20. Contd.,
MZCET/ECE/III Sem/EE6352- Unit 2 20
2.6

21. Contd.,
MZCET/ECE/III Sem/EE6352- Unit 2 21
2.6

22. Equivalent circuit referred to secondary
side
 Transferring primary side parameters to
secondary side
MZCET/ECE/III Sem/EE6352- Unit 2 22
2.6

23. Contd.,
 Similarly exciting circuit parameters
are also transferred to secondary as
Ro’ and Xo’
MZCET/ECE/III Sem/EE6352- Unit 2 23
2.6

24. Contd.,
MZCET/ECE/III Sem/EE6352- Unit 2 24
2.6

25. equivalent circuit w.r.t primary
MZCET/ECE/III Sem/EE6352- Unit 2 25
2.6

26. MZCET/ECE/III Sem/EE6352- Unit 2 26
2.6

27. Approximate equivalent circuit
 Since the noload current is 1% of the full load
current, the nolad circuit can be neglected
MZCET/ECE/III Sem/EE6352- Unit 2 27
2.6

28. A 6600/400 V single phase transformer has
primary resistance of 2.5 ohms and secondary
resistance of 0.01 ohms. Calculate the total equivalent
resistance with respect to primary and secondary.
Solution :
The given values are
MZCET/ECE/III Sem/EE6352- Unit 2 28
Example 22.6

29. MZCET/ECE/III Sem/EE6352- Unit 2 29
2.6

30. MZCET/ECE/III Sem/EE6352- Unit 2 30
2.6

31. MZCET/ECE/III Sem/EE6352- Unit 2 31
2.6