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EMLAB 1 Introduction to electromagnetics

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EMLAB 2 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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EMLAB 3 Radiation by oscillating charges

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EMLAB 4 Oscillator circuit Output voltage Oscillating voltage source forces electrons to be accelerated, which generates electromagnetic wave Generation of electromagnetic wave

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EMLAB 5 Electromagnetic wave : radio communication Moving charges on the antenna generate electromagnetic waves.

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EMLAB 6 Electromagnetic wave : automotive radar Moving charges on the antenna generate electromagnetic waves.

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EMLAB 7 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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EMLAB 8 Electromagnetic wave generation : antennas Many kinds of antennas are built and utilized.

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EMLAB 9 Electromagnetic wave : signal propagation The electrical signal propagate along the line trace at the speed of light.

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EMLAB 10 EM theory helps understand how electrical signals propagate along conductors 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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EMLAB 11 Electromagnetic theory Electric field (E) Magnetic field (H) Electro-magnetic field (E,H ) Sources (q, J) Material (ε, μ) Mathematics Coordinate systems Vector calculus (divergence, curl, gradient) EM-theory Material

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EMLAB 12 Contents 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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EMLAB 13 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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EMLAB 14 Mathematics -Glossary Scalar : a quantity defined by one number (eg. Temperature, mass, density, voltage,... ) Vector : a quantity defined by a set of numbers. It can be represented by a magnitude and a direction. (velocity, acceleration, …) Field : a scalar or vector as a function of a position in the space. (scalar field, vector field, …) Scalar field Vector field

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EMLAB 15 Example of a vector field +q Magnitudes and directions of vectors change with positions. Electric field generated by a charge (+q 1 ) The electric field is a field quantity because its magnitude and direction changes with positions.

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EMLAB 16 +q Usefulness of the field concept -q +q-q This equation states only the forces between the two charges +q and –q. It does not state about the interactions that occur between them. It is misleading that this equation may imply that the interaction occurs instantaneously. The electric field due to +q spread into the space. Then (–q) feels the attractive force by way of the electric field.

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EMLAB 17 Analogy to the mechanical law Newton’s law of gravity : Point-to-point reaction (action at a distance)

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EMLAB 18 Gravitational field Earth Moon Gravitational field mediates interactions between the earth and the moon.

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EMLAB 19 This law is discovered by Coulomb experimentally. In the free space, the force between two point charges is proportional to the charges of them, and is inversely proportional to the square of the distance between those charges. +q 1 +q 2 O If q 1, q 2 have the same polarity, the force is repulsive. Coulomb’s law only states that the force between two charge is related to the distance between them and their charges. It does not tells us how the interaction occurs. Coulomb’s law ε 0 : permittivity of vacuum.

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EMLAB 20

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EMLAB 21 Definition of electric field +q 1 +q 2 Electric field is measured by the force divided by charge quantity with the amount infinitesimally small. This limit process is necessary for not disturbing the original electric field by q 1.

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EMLAB 22 Simple circuit example Electrical signal transmission means the propagation of the electromagnetic field, not the movement of charges.

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EMLAB 23 Generation of charges : friction charging

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EMLAB 24 Electrons “lost” Electrons “gained” Contact Separation Friction charging

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EMLAB 25 Induction charging Metallic sphere

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EMLAB 26 Electrons(-) are absorbed. (+) charges are generated Electrons(-) are generated. (+) charges are absorbed. Generation of charges : battery Electrons are generated via electro-chemical reaction. An amount of positive charges are generated such that the terminal voltages are sustained.

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EMLAB 27 Charge transport example : battery with open wire Positive charges are plenty. Charges in a wire are moved by diffusion and electromagnetic laws. Charge movement by diffusion Negative charges are plenty. Diffusion

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EMLAB 28 Repelling force by Coulomb’s law Contention between diffusion and Coulomb’s law Positive charges are accumulated. The accumulated charges repel charge movement by diffusion Attracting force by Coulomb’s law Movement by diffusion Repelling force by Coulomb’s law Net charge flow becomes zero only when the voltage difference between the wires is equal to the voltage between the battery terminals. The accumulated charges repel charge movement by diffusion

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EMLAB 29 Electric field distribution near charged plates If a charge is brought between the plates, it will be accelerated along the direction of electric field.

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EMLAB 30 Magnetic field A charged particle in motion generates magnetic field nearby. In the same way, currents generate magnetic field nearby.

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EMLAB 31 Motion of a charge in a magnetic field Charged particles in motion are influenced by magnetic fields

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EMLAB 32 Biot-Savart law Direction of H-field Current segment The generated magnetic field can be predicted by Biot-Savart’s law

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EMLAB 33 Electromagnetic law – Maxwell equations 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. J 5.The independent variables are current density vector J and charge density . Maxwell equations E: electric field D: electric displacement flux density H: magnetic field B: magnetic flux density

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EMLAB 34 Ampere’s law Current or increase of electric field strength E, J H

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EMLAB 35 E H Increase of magnetic field Faraday’s law

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EMLAB 36 Faraday’s law The time-varying magnetic field generates electric field nearby.

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EMLAB 37 Gauss’ law +Q -Q E E Electric field lines emanate from positive charges and sink into negative charges.

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EMLAB 38 Magnetic field lines always form closed loops

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EMLAB 39 Example – Hertzian dipole antenna Heinrich Hertz ( ) spheres for storing electric charges arc monitoring

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EMLAB 40 Schematic diagram of Hertz experiment Transformer for high voltage generation

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EMLAB 41 Electric field : red Magnetic field : blue Propagation of electromagnetic wave

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EMLAB 42 Radio communication

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EMLAB 43 V Reception of EM wave current Transmitting antenna Receiving antenna The charges on the receiving antenna move toward the antenna terminal, which causes voltage drop across them.

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EMLAB 44 E ZLZL H-field due to moving charges Example – Signal propagation over a line trace H

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