1. Transformers

2. Primary and Secondary Windings
A two-winding transformer consists of two windings interlinked by a mutual magnetic field.
Primary winding – energized by connecting it to an input source
Secondary winding – winding to which an electrical load is connected and from which output energy is drawn.
Primary winding
Secondary winding

3. In instantaneous quantities
Ideal Transformers
An ideal transformer is a lossless device with an input winding and an output winding. fM
The relationships between the input voltage and the output voltage, and between the input current and the output current, are given by the following equations.
In instantaneous quantities

4. Ideal Transformers Np: Number of turns on the primary winding
In rms quantities
Np: Number of turns on the primary winding
Ns: Number of turns on the secondary winding
vp(t): voltage applied to the primary side
vs(t): voltage at the secondary side
a: turns ratio
ip(t): current flowing into the primary side
is(t): current flowing into the secondary side

5. Derivation of the Relationship
…………….. (1)
…………….. (2)
Dividing (1) by (2)
………………......……….. (3)
From Ampere’s law
…………………..……….. (4)
Equating (3) and (4)
………………….. (5)

6. Impedance Transformation through a TransformerZL Is Ip Vp Vs
Impedance of the load: ZL = Vs/Is The impedance of the primary circuit: Z’L = Vp/Ip = (aVs)/(Is /a) = a2 (Vs / Is ) = a2 ZL Ip Vp
Z’L Is Vs

7. Example 1
A 100-kVA, 2400/240-V, 60-Hz step-down transformer (ideal) is used between a transmission line and a distribution system.
Determine turns ratio.
What secondary load impedance will cause the transformer to be fully loaded, and what is the corresponding primary current?
Find the load impedance referred to the primary.

8. Solution to Example 1
Turns ratio, a = 2400 / 240 = 10
b) Is= 100,000/240 = A
Ip = Is /a = / 10 = A
Magnitude of the load impedance
= Vs/Is = 240/416.7 = ohm
Load impedance referred to the primary
= a2*0.576 = 57.6 ohm