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Introduction to EM theory 2

Introduction to EM theory 2. Displacement current. With the help of displacement current, magnetic fields are also generated around the capacitor. Displacement current.

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Introduction to EM theory 2

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  1. Introduction to EM theory 2

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

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

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

  5. Induced magnetic field 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.

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

  7. Basic laws– Maxwell equations • Electromagnetic phenomena are explained by the four Maxwell equations. • Through the equations, electric field and magnetic field are coupled to each other. • Quantities on the right hand side are the source terms. • Quantities on the left side are the resulting phenomena. • The independent variables are current density vector J and charge density . Maxwell equations

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

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

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

  11. Magnetic field lines always form closed loops

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

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

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

  15. Radio communication

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

  17. Example – Signal propagation over a line trace H-field due to moving charges  E  H ZL     

  18. Example – PCB line trace

  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.

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

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

  22. Transmission line + + v (z, t) v (z, t) - - i (z, t) i (z+z, t) i (z, t) + L z v (z+ z,t) C z - z z

  23. Transmission line eq. solution

  24. V and I in a transmission line H • The ratio of E+/H+ propagating in the same direction is kept constant. • The ratio of V+/I+wave is also constant, which is called characteristic impedance (Z0) of the line. • If the ratio is broken at a certain point, reflections occur. propagation direction H E

  25. Line길이에 따른 반사파 영향 + V - + V - + V - + V - + V - Vin Vout R R MLIN R2 VtPulse R1 R=1k Ohm SRC1 R=20 Ohm t Impedance mismatched Z0= 50  Zs = 20  Z0= 50  ZL= 1k  0.5m

  26. Electromagnetic problem

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