FINAL EXAM WILL BE

WEDNESDAY APRIL 29FROM 10:00AM – 12:00PM

IN THIS ROOM

DISREGARD THE SATURDAY DATE ON THE FINAL EXAM MATRIX

Ideal Transformers

nN

N

V

V

1

2

1

2

ˆ

ˆ

dt

dNv

dt

dNv

2211 and

2211 iviv nN

N

V

V

I

I

1

2

1

2

2

1

ˆ

ˆ

ˆ

ˆ

Ideal TransformersExample: Redraw the diagram below twice as a single electric circuit, the first time reflected to the high-voltage circuit, and the second time reflected to the low-voltage circuit.

Ideal Transformers

Reflected to the high-voltage circuit:

Ideal Transformers

Reflected to the low-voltage circuit:

Real TransformersMust account for:

• Resistance in the winding conductors• Power (I2R) losses

• Leakage reactance• Flux produced by one winding that does

not link the other

• Energy to magnetize core• Alignment of magnetic domains in core

steel

• Electrical losses in core• Hysteresis and eddy currents

Real Transformers

Polyphase Induction Motors

Polyphase Induction MotorsStator circuit produces a rotating magnetic field.

http://www.ece.umn.edu/users/riaz/animations/spacevectors.html

Polyphase Induction Motors

A voltage is induced across the rotor bars by transformer action (Faraday’s Law).

This is possible because the rotor turns slightly (3%-5%) slower than the rotating stator field.

The speed differential between the stator field and the rotor is the slip.

NO SLIP NO TRANSFORMER ACTION NO TORQUE

Polyphase Induction MotorsSpeed-Torque Curves

Polyphase Induction MotorsSpeed-Torque Curves

Polyphase Induction MotorsPower Flow / Losses