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EMLAB 1 Introduction to EM theory 2

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EMLAB 2 Displacement current With the help of displacement current, magnetic fields are also generated around the capacitor.

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EMLAB 3 Displacement current The time-varying displacement vector and charged particles in motion form current flow. Despite their origin, magnetic fields are generated.

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EMLAB 4 Faraday’s law The time-varying magnetic field generates electric field nearby.

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EMLAB 5 The induced electric field forces current to flow along the loop. The induction current generates a magnetic field that decreases the external magnetic flux change. Induced magnetic field

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EMLAB 6Transformer The current flowing through the primary circuit generates magnetic flux, which influences the secondary circuit. Due to the magnetic flux, a repulsive voltage is induced on the secondary circuit.

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EMLAB 7 Basic laws – 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

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EMLAB 8 Ampere’s law Current or increase of electric field strength E, J H

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EMLAB 9 E H Increase of magnetic field Faraday’s law

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EMLAB 10 Gauss’ law +Q -Q E E Electric field lines emanate from positive charges and sink into negative charges.

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EMLAB 11 Magnetic field lines always form closed loops

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EMLAB 12 Example – Hertzian dipole antenna Heinrich Hertz (1857-1894) spheres for storing electric charges arc monitoring

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EMLAB 13 Schematic diagram of Hertz experiment Transformer for high voltage generation

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EMLAB 14 Electric field : red Magnetic field : blue Propagation of electromagnetic wave

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EMLAB 15 Radio communication

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EMLAB 16 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 17 E ZLZL H-field due to moving charges Example – Signal propagation over a line trace H

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EMLAB 18 Example – PCB line trace

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EMLAB 19 EM field of a simple circuit In circuit theory, capacitances and inductances of wires are ignored The inductor L models the effect of magnetic field. The capacitor C models that of electric field.

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EMLAB 20 Increasing current Increase of current A line inductance blocks the variation of current in that it generates opposing voltage across its terminals. Line inductance

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EMLAB 21 The voltage difference between wires are always accompanied by a capacitor.Capacitance direction of current

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EMLAB 22 i (z, t) v (z, t) + - zz L z C z i (z+ z, t) v (z+ z,t) + - i (z, t) zz v (z, t) + - Transmission line

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EMLAB 23 Transmission line eq. solution

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EMLAB 24 V and I in a transmission line H E propagation direction H 1.The ratio of E + /H + propagating in the same direction is kept constant. 2.The ratio of V + /I + wave is also constant, which is called characteristic impedance (Z 0 ) of the line. 3.If the ratio is broken at a certain point, reflections occur.

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EMLAB +V-+V- +V-+V- +V-+V- +V-+V- +V-+V- Z s = 20 Z 0 = 50 Z L = 1k 0.5m Line 길이에 따른 반사파 영향 Impedance mismatched VinVout R R2 R=1k Ohm MLIN R R1 R=20 Ohm VtPulse SRC1 t Z 0 = 50

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EMLAB 26 Electromagnetic problem

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Lecture 5: Time-varying EM Fields

Lecture 5: Time-varying EM Fields

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