Lecture 7. Magnetic Circuits • Mon 9/23: Transformers

9/16/2019

Schedule • Mon 9/16: Magnetic circuits • Wed 9/18: Inductors ECE330: Power Circuits & Electromechanics • Fri 9/20: Review + Quiz 3 Lecture 7. Magnetic Circuits • Mon 9/23: Transformers

Prof. Richard Y. Zhang Univ. of Illinois at Urbana-Champaign [email protected]

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Today Role of Maxwell’s Equations and Fields

• Fields, potential, flow, and Ohm’s law • Analogs for magnetism • Magnetic circuits

“EM fields were invented to explain forces”

3 4 Source: MIT OpenCourseWare, 6.013 Electromagnetics and Applications Spring 2009 3 4

Coulomb’s law (scalar) Coulomb’s law (vector)

+q1 +q2 +q1 +q2

+q1 -q2 +q1 -q2

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Notion of an electric field Visualization of electric fields View E field like “wind”

Define E +q2 proportional

to F2 at different values of r -q2

7 8 http://www.as.wvu.edu/phys/rotter/phys201/6_Electricity/Electric_Forces_and_Fields.htm 7 8

Notion of a potential field E field as voltage gradient +1 [V] 0 [V] 1 [V/m] Electric field Voltage field (vector) (scalar) 0 1 [m] b c Recover “KVL” by integrating over closed-loop

a d

http://hyperphysics.phy-astr.gsu.edu/hbase/intare.html

Units of E field

Image: OpenStax College, Image: Metservice NZ, “How to 9 10 “Equipotential lines” read weather maps”. 9 10

Ohm’s law Summary V 0 E E E E E E Electric Sym Name Vector field E Electric field [V/m]

Potential VE Voltage [V] Flow J Current density density [A/m2] Flow I Current [A] Flow σ Conductivity [S/m] density per E electric field [V/m] field 2 J current density [A/m ] Potential R Resistance [S-1] σ conductivity [Ω-1/m] per flow

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Today Ampere’s law (scalar) Direction of current

• E field and Ohm’s law • H field and the Magnetic Ohm’s law • Faraday’s law +I1 +I2

Notation

Into Out of +I1 -I2 page page

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Notion of a magnetic field? Visualization of magnetic fields

+I2

-I2

Field points in an orthogonal direction to the force

15 Image: http://www.ukm.my/rahim/magnetic%20lecture.htm 16 15 16

Notion of a magnetic field Magnetic scalar potential and mmf Magn. pot. field Magnetic field (scalar) [A] (vector) [A/m]

b c current

Define H +I2

proportional mmf to F2 at different a d values of r -I2 mmf Model violation of KVL Units of H field mmf as discontinuity in potential field called magnetomotive force 17 18 17 18

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Magnetic Ohm’s law (Constituent law) Summary Electric Magnetic F 0 H H H H H H Sym Name Sym Name Vector field E Electric field [V/m] H Magnetic field [A/m]

Potential VE Voltage [V] VM Magn. Potential [A] Flow J Current density B Flux Density [Wb/m2] density [A/m2] Flow I Current [A] ϕ Flux Flow σ Conductivity [S/m] μ Permeability [H/m] density per field

H magnetic field [A/m] Potential R Resistance [S-1] R Reluctance [H-1] B flux density [Wb/m2] per flow μ permeability [H/m]

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Magnetic circuits Schedule • Mon 9/16: Magnetic circuits • Wed 9/18: Inductors • Fri 9/20: Review + Quiz 3 • Mon 9/23: Transformers

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