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Introduction to EM theory 1

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Electromagnetic phenomena

The globe lights up due to the work done by electric current (moving charges).

Steady state current (simple DC circuit)

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Electromagnetic wave : signal propagation

The electrical signal propagate along the line trace at the speed of light.

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4Electromagnetic wave – Crosstalk

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Electromagnetic wave : radio communication

Moving charges on the antenna generate electromagnetic waves.

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Electromagnetic wave : automotive radar

Moving charges on the antenna generate electromagnetic waves.

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Electromagnetic wave : ground penetrating radar

The EM wave from the transmitter refracts into the ground and is reflected back by the underground facilities.

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Electromagnetic wave generation : antennas

Many kinds of antennas are built and utilized.

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• EM theory helps understand how electrical signals propagate along con-ductors as well as free space.

• Predicts voltages and currents using the concept of electric and magnetic field.

Importance of electromagnetic theory

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Basic laws – Maxwell equations

0

B

D

DJH

BE

t

t

1. Electromagnetic phenomena are explained by the four Maxwell equations.

2. Through the equations, electric field and magnetic field are coupled to each other.

3. Quantities on the right hand side are the source terms.

4. Quantities on the left side are the resulting phenomena.

5. The independent variables are current den-sity vector J and charge density .

Maxwell equations

'

'

')]ˆ(ˆ[4

1

'4

)]ˆ(ˆ[

V

V

jkR

dtR

dR

ej

JRRJ

JRRJE

Solution (free space)

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Electromagnetic theory

Electric field (E)

Magnetic field (H)

Electro-magnetic field (E,H )

Sources (q, J)

Material (ε, μ)

Mathematics

Coordinate systems

Vector calculus (diver-gence, curl, gradient)

EM-theory

Material

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1. Electric field

① Coulomb’s law

② Gauss’s law (divergence)

③ Electric potential (gradient)

④ Capacitance

⑤ Ohm’s law

2. Magnetic field

① Biot-Savart law

② Ampere’s law (curl)

③ Inductance

1. Sources

① Charge

② Current

2. Material

① Conductor (semi-conductor, lossy material)

② Dielectric (insulator)

③ Magnetic material

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3. Electro-magnetic field

① Faraday’s law

② Displacement current

③ Maxwell’s equations

④ Plane wave

⑤ Reflection/transmission

4. Transmission lines

① Impedance matching

② Smith chart

③ Waveguides

5. Radiation

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Electric field

A charged particle undergoes acceleration which is proportional to the electric field nearby.

EF q

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Coulomb’s law

1. The electric field is generated by the charge Q and spread into the space.

2. The speed of electric field transmission is the same as the speed of light.

rE ˆ4 2

0r

Q

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Electrons(-) are absorbed.(+) charges are generated

Electrons(-) are generated. (+) charges are absorbed.

Generation of charges : battery

e2ZnZn 2

234 HNH222NH e

Electrons are generated via electro-chemical reaction.

An amount of positive charges are generated such that the terminal voltages are sus-tained.

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B

A

dVr

rrE)(

Potential distribution near charged plates

VE

Charges emanate from a battery.

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18Induction charging

Droplets of an inkjet printer emission.

A conducting sphere can be charged by induction.

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19Micro-machine

MEMS devices can be con-trolled by electrostatic forces.

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Magnetic field

A charged particle in mo-tion generates magnetic field nearby.

In the same way, current s generate magnetic field nearby.

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Motion of a charge in a magnetic field

BvF q

Charged particles in motion are influenced by magnetic fields

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Biot-Savart law

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ˆ

R

Idd

Rs

H

'rrR 'r

r

sId

Direction of H-field

Current segment

The generated magnetic field can be predicted by Biot-Savart’s law

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loop closed

IdsH

Ampere’s law