1. Lesson 25: Magnetism and Transformers

2. Learning Objectives
Analyze the relationship between the transformation ratio, voltage ratio, current ratio, and impedance ratio.
Construct a circuit equivalent of a transformer and calculate primary and secondary voltage, current and polarity.
Explain the relationship between the power developed in the primary and secondary of a transformer.

3. Transmission of Power

4. Transformer Overview
A transformer is a magnetically coupled circuit whose operation is governed by Faraday’s Law.

5. Faraday’s Experiment #3: Mutually Induced Voltage
Voltage is induced across Coil 2 when i1 is changing.
When i1 reaches steady state, voltage across Coil 2 returns to zero.
NOTE: The coil to which the source is attached is the primary and the coil attached to the load is the secondary.

6. Transformer Overview
A time-varying current in the primary windings induces a magnetic flux (field) in the iron core.
The flux flows through the core and induces a current the secondary windings.
Thus power flows via the magnetic field without the windings being electrically connected.

7. Winding Direction
The polarity of ac voltages can be changed by changing the direction of the windings.
0º phase shift
180º phase shift

8. Iron-Core Transformers
Two basic types of iron-core transformers are the core type and the shell type.
In both, the core is constructed of laminated sheets of steel to reduce eddy current losses.
Core Type
Shell Type

9. Iron-Core Transformers
We will consider the ideal transformer which
Neglects coil resistance.
Neglects core losses.
Assumes all flux is confined to the core.
Assumes negligible current required to establish core flux.
Transformer operation is governed by Faraday’s Law.

10. Transformation Ratio
According to Faraday’s Law, voltage (e) is directly related to the number of turns (N) in the primary or secondary windings:
For each winding we can write:
Because the flux (m) is the same through both windings, we can write:

11. Transformation Ratio
“The ratio of the primary voltage to secondary voltage is equal to the ratio of primary turns to secondary turns.”
This ratio is called the transformation ratio (or turns ratio) and given by the symbol a.

12. Step-up and Step-down
Transformers are used to change or “transform” voltage.
Step-Up transformer:
The secondary voltage is higher than the primary voltage.
There are fewer primary windings than secondary windings (a < 1).
Step-Down transformer:
The secondary voltage is lower than the primary voltage.
There are more primary windings than secondary windings (a > 1).

13. Step-up and Step-down
Step-Up
Step-Down

14. Example Problem 1
Suppose the transformer depicted below has 4000 turns on its primary winding and 1000 turns on its secondary.
Determine it’s turns ratio (a). Is it step-up or step-down?
If the primary voltage epri = 480 sin t, what is it’s secondary voltage?
=> Step-Down since a > 4
Remember, this is a Step-Down for voltage, but a step-up for current.
=> esec = 120V sin (Ѡt)

15. Current Ratio and Power
Because we are considering an ideal transformer, power in equals power out (Pin = Pout).
If the voltage is stepped up, then the current is stepped down, and vice versa.

16. Impedance
The impedance of the primary of an ideal transformer is the transformation ratio (a) squared times the impedance of the load (secondary winding) and is derived as below:
NOTE: If the load is capacitive or inductive, the reflected impedance is also capacitive or inductive.

17. Example Problem 2
For the figure below Eg = 120 V 0º, the turns ratio is 6:1, and ZLD = j. The transformer is ideal. Find:
load voltage
load current
generator current
Active power to the load N
Note that Ohm’s law and regular power equations are used here.

18. The Dot Convention
The direction of the windings is not obvious looking at a transformer, therefore we use the dot convention.
Dotted terminals have the same polarity at all instants of time. Used for phase shifting (180).

19. Example Problem 3
For the figure below Ig = 25 30ºmA, the turns ratio is 4:1, and VLD = 600ºV. The transformer is ideal. Find:
Load current
Load impedance
Generator voltage
Real and Reactive load power a) b) c) d)

20. Example Problem 4
For the figure below i1 = 100 sin (ωt) mA and the transformer is ideal.
Determine the secondary currents i2 and i3.
Note the dot convention here, which switches the polarity 180⁰
Why -180⁰

21. Power Transformer Ratings
Just like ac motors and generators, power transformers are rated in terms of voltage and apparent power.
For example, a transformer is rated at 2400/120 volt, 48 kVA has:
On the primary winding, the current rating is ,000 VA / 2400 V = 20 A.
On the secondary winding, the current rating is ,000 VA / 120 V = 400 A.

22. Example Problem 5
A 7.2 kV, a=0.2 transformer has a secondary winding rated current of 3 A. What is its kVA rating?

23. Transmission of Power

24. Transformers
Mitsubishi 500 MVA Single-Phase Auto-Transformers

25. QUESTIONS?