ECE 231 -10

# ECE 231 -10 - ECE-231 Circuits and Systems I Spring 2011...

This preview shows pages 1–10. Sign up to view the full content.

ECE-231 Circuits and Systems I Spring 2011 Session 10 Professor Stewart Personick Office: ECEC Room 321 Stewart.Personick@NJIT.edu

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
AC Power: Transformers Residential Wiring: Grounding and Safety Generation and Distribution of Electric Power
Transformers Donut-shaped core made of a material with a high permeability : B = μ H (alloys of: iron, nickel, cobalt, …) N turns of wire wrapped around the core (2 turns shown)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Transformers Donut-shaped core made of a material with a high permeability : B = μ H (alloys of: iron, nickel, cobalt, …) Ampere’s law (roughly stated): The line integral around the dashed path of the H field is equal to the current in the wire x the number of turns that pass through the opening in the core. 2 π r x H(t) = N x i1(t) N turns of wire wrapped around the core (2 turns shown) i1(t)
Transformers Donut-shaped core made of a material with a high permeability : B = μ H (alloys of: iron, nickel, cobalt, …) N turns of wire wrapped around the core (2 turns shown) i1(t) 2 π r x H(t) = N x i1(t) - M x i2(t) But, in this transformer, with its high permeability core material, 2 π rH(t) is forced (by the physics) to be very small compared to either N x i1(t) or M x i2(t). Therefore: N x i1(t) M x i2(t) M turns of wire wrapped around the core (3 turns shown) R (Ohms) i2(t) M x i2(t) = N x i1(t) (approximately)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Transformers Donut-shaped core made of a material with a high permeability : B = μ H (alloys of: iron, nickel, cobalt, …) N turns of wire wrapped around the core (2 turns shown) i1(t) R (Ohms) i2(t) M x i2(t) = N x i1(t) v2(t) = M/N x v1(t) + v2 - + v1 - Faraday’s Law: v1 (t) = N d[ Φ 1(t)]/dt v2 (t) = M d[ Φ 2(t)]/dt But, in this transformer: Φ 1(t) = Φ 2(t) M turns of wire wrapped around the core (3 turns shown)
Transformers Donut-shaped core made of a material with a high permeability : B = μ H (alloys of: iron, nickel, cobalt, …) N turns of wire wrapped around the core (2 turns shown) i1(t) R (Ohms) i2(t) M x i2(t) = N x i1(t) v2(t) = M/N x v1(t) v1(t)/ i1(t)= [N/M]2 v2(t)/ i2(t) + v2 - + v1 - M turns of wire wrapped around the core (3 turns shown) v1(t) / i1(t) = [(N/M) v2(t)] / [(M/N) i2(t)] = [N/M]2 v2(t) / i2(t)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Transformers Example: Audio Amplifier (using vacuum tubes) vs(t ) 8 Ohm Load ~ + vs(t) = 250 sin (2000 π t) Volts Peak voltage = 250 Volts RMS voltage = 177 Volts Frequency = 1000 Hz Rs =5000 Ohms Matching a 5000 Ohm source to an 8 Ohm load ? How can we deliver the maximum amount of power from the source to the load? Thevenin equivalent circuit of the source With a direct connection, the peak power delivered to the load will be [250V /(5008 Ohms)]2 x 8 Ohms = 0.02 Watts
Transformers Example: Audio Amplifier (using vacuum tubes) N turns of wire wrapped around the core vs(t ) M= 10 turns of wire wrapped around the core 8 Ohm Load

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 03/26/2012 for the course ECE 231 taught by Professor Pietrucha during the Spring '08 term at NJIT.

### Page1 / 33

ECE 231 -10 - ECE-231 Circuits and Systems I Spring 2011...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online