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ENE 428 Microwave Engineering

ENE 428 Microwave Engineering. Lecture 1 Uniform plane waves. Syllabus. Asst. Prof. Dr. Rardchawadee Silapunt, rardchawadee.sil@kmutt.ac.th Lecture: 9:30pm-12:20pm Tuesday, CB41004 12:30pm-3:20pm Wednesday, CB41002 Office hours : By appointment

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ENE 428 Microwave Engineering

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  1. ENE 428Microwave Engineering Lecture 1 Uniform plane waves ENE428

  2. Syllabus • Asst. Prof. Dr. Rardchawadee Silapunt, rardchawadee.sil@kmutt.ac.th • Lecture: 9:30pm-12:20pm Tuesday, CB41004 12:30pm-3:20pm Wednesday, CB41002 • Office hours : By appointment • Textbook: Applied Electromagnetics by Stuart M. Wentworth (Wiley, 2007) ENE428

  3. Grading Homework 20% Midterm exam 40% Final exam 40% Vision Providing opportunities for intellectual growth in the context of an engineering discipline for the attainment of professional competence, and for the development of a sense of the social context of technology. ENE428

  4. Course overview • Maxwell’s equations and boundary conditions for electromagnetic fields • Uniform plane wave propagation • Waveguides • Antennas • Microwave communication systems ENE428

  5. Introduction • From Maxwell’s equations, if the electric field is changing with time, then the magnetic field varies spatially in a direction normal to its orientation direction • A uniform plane wave, both electric and magnetic fields lie in the transverse plane, the plane whose normal is the direction of propagation • Both fields are of constant magnitude in the transverse plane, such a wave is sometimes called a transverse electromagnetic (TEM) wave. http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=52 ENE428

  6. Maxwell’s equations (1) (2) (3) (4) ENE428

  7. Maxwell’s equations in free space •  = 0, r = 1, r = 1 Ampère’s law Faraday’s law ENE428

  8. General wave equations • Consider medium free of charge where • For linear, isotropic, homogeneous, and time-invariant medium, (1) (2) ENE428

  9. General wave equations Take curl of (2), we yield From then For charge free medium ENE428

  10. Helmholtz wave equation For electric field For magnetic field ENE428

  11. Time-harmonic wave equations • Transformation from time to frequency domain Therefore ENE428

  12. Time-harmonic wave equations or where This  term is called propagation constant or we can write  = +j where  = attenuation constant (Np/m)  = phase constant (rad/m) ENE428

  13. Solutions of Helmholtz equations • Assuming the electric field is in x-direction and the wave is propagating in z- direction • The instantaneous form of the solutions • Consider only the forward-propagating wave, we have • Use Maxwell’s equation, we get ENE428

  14. Solutions of Helmholtz equations in phasor form • Showing the forward-propagating fields without time-harmonic terms. • Conversion between instantaneous and phasor form Instantaneous field = Re(ejtphasor field) ENE428

  15. Intrinsic impedance • For any medium, • For free space ENE428

  16. Propagating fields relation where represents a direction of propagation ENE428

  17. Propagation in lossless-charge free media • Attenuation constant  = 0, conductivity  = 0 • Propagation constant • Propagation velocity • for free space up = 3108 m/s (speed of light) • for non-magnetic lossless dielectric (r = 1), ENE428

  18. Propagation in lossless-charge free media • intrinsic impedance • wavelength ENE428

  19. Ex1 A 9.375 GHz uniform plane wave is propagating in polyethelene (r = 2.26). If the amplitude of the electric field intensity is 500 V/m and the material is assumed to be lossless, find a) phase constant b) wavelength in the polyethelene ENE428

  20. c) propagation velocity d) Intrinsic impedance e) Amplitude of the magnetic field intensity ENE428

  21. Propagation in dielectrics • Cause • finite conductivity • polarization loss ( = ’-j” ) • Assume homogeneous and isotropic medium ENE428

  22. Propagation in dielectrics Define From and ENE428

  23. Propagation in dielectrics We can derive and ENE428

  24. Loss tangent • A standard measure of lossiness, used to classify a material as a good dielectric or a good conductor ENE428

  25. Low loss material or a good dielectric (tan « 1) • If or < 0.1 , consider the material ‘low loss’, then and ENE428

  26. Low loss material or a good dielectric (tan « 1) • propagation velocity • wavelength ENE428

  27. High loss material or a good conductor (tan » 1) • In this case or > 10, we can approximate therefore and ENE428

  28. High loss material or a good conductor (tan » 1) • depth of penetration or skin depth,  is a distance where the field decreases to e-1or 0.368 times of the initial field • propagation velocity • wavelength ENE428

  29. Ex2 Given a nonmagnetic material having r= 3.2 and  = 1.510-4 S/m, at f = 3 MHz, find a) loss tangent  b) attenuation constant  ENE428

  30. c) phase constant  d)intrinsic impedance ENE428

  31. Ex3 Calculate the followings for the wave with the frequency f = 60 Hz propagating in a copper with the conductivity,  = 5.8107 S/m: a) wavelength b) propagation velocity ENE428

  32. c) compare these answers with the same wave propagating in a free space ENE428

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