Fields and Waves I

1. Fields and Waves I Lecture 20 Introduction to Electromagnetic Waves K. A. Connor Electrical, Computer, and Systems Engineering Department Rensselaer Polytechnic Institute, Troy, NY Y. Maréchal Power Engineering Department Institut National Polytechnique de Grenoble, France

2. These Slides Were Prepared by Prof. Kenneth A. Connor Using Original Materials Written Mostly by the Following: • Kenneth A. Connor – ECSE Department, Rensselaer Polytechnic Institute, Troy, NY • J. Darryl Michael – GE Global Research Center, Niskayuna, NY • Thomas P. Crowley – National Institute of Standards and Technology, Boulder, CO • Sheppard J. Salon – ECSE Department, Rensselaer Polytechnic Institute, Troy, NY • Lale Ergene – ITU Informatics Institute, Istanbul, Turkey • Jeffrey Braunstein – Chung-Ang University, Seoul, Korea Materials from other sources are referenced where they are used. Those listed as Ulaby are figures from Ulaby’s textbook. Fields and Waves I

3. Linear property 2D wave http://people.rit.edu/andpph/exhibit-3.html Fields and Waves I

4. Overview • Time Harmonic Fields • Maxwell’s Equations in Phasor Form • Complex Permittivity • EM Wave Equation • Uniform Plane Waves • Traveling Waves • TEM Waves • Energy & Power Fields and Waves I

5. Full Maxwell’s Equations Added term in curl H equation for time varying electric field that gives a magnetic field. Fields and Waves I

6. Fully coupled fields Maxwell’s equations give a wave equation. Fields and Waves I

7. Time Harmonic Fields EM wave propagation involves electric and magnetic fields having 3 components, each dependent on all three coordinates, in addition to time. e.g. Electric field vector phasor instantaneous field Valid for the other fields and their sources Fields and Waves I

8. Phasor domain Time domain Maxwell’s Equations in Phasor Domain vector phasor + Try to symmetrize these 2 terms Fields and Waves I

9. Homogenous wave equations Complex Permittivity complex permittivity Homogenous wave equation (charge free) Combining and propagation constant Fields and Waves I

10. Plane Wave Propagation in Lossless Media There are three constitutive parameters of the medium: σ, ε, μ For lossless medium Wave number Homogenous wave equation for a lossless media Fields and Waves I

11. Some typical waves Ulaby Fields and Waves I

12. x z y Plane wave approximation At large distances from physical antennas and ground, the waves can be approximated as uniform plane waves Ulaby Uniform properties of the magnetic and electric field across x-y Fields and Waves I

13. Maxwell’s Equations in Phasor Domain In a Source Free Region: For Plane Waves (only z dependence, ) Note that there are now two independent field pairs Fields and Waves I

14. Traveling plane waves The Electric Field in phasor form (only x component) General solution of the differential equation 0 amplitudes (constant) For a traveling direction in the +z direction only Fields and Waves I

15. E and H field for a plane wave for a lossless medium E polarized in x traveling in +z direction Fields and Waves I

16. Transverse Electromagnetic Wave http://hibp.ecse.rpi.edu/~crowley/java/EMWave/emwave.html Spatial variation of and at t=0 Ulaby Fields and Waves I

17. Uniform Plane waves In general, a uniform plane wave traveling in the +z direction, may have x and y components The relationship between them Fields and Waves I

18. Example 1 – EM Waves The electric field of a plane wave is given by a. Write E in phasor form. b. Is E the solution of a wave equation like c. Find H using the phasor form of the  x E equation. Assume the E and H phasors are only a function of z. d. Evaluate the amplitude ratio, = |E| / |H in terms of material properties. e. If E was in the ay direction, what direction would H be in? f. How many independent parameters are there in the following set? Fields and Waves I

19. Example 1 – EM Waves Fields and Waves I

20. Example 1 – EM Waves Fields and Waves I

21. Transverse Electromagnetic Wave (TEM) • A plane wave has no electric or magnetic field components along the direction of propagation • Electric and magnetic fields that are perpendicular to each other and to the direction of propagation • They are uniform in planes perpendicular to the direction of propagation • At large distances from physical antennas and ground, the waves can be approximated as uniform plane waves Ulaby Fields and Waves I

22. Properties of a TEM • Defines the connection between electric and magnetic fields of an EM wave • Similar to the characteristic impedance (Z0) of a transmission line [Ω] Intrinsic impedance Phase velocity [m/s] Wavelength [m] If the medium is vacuum : up=3x108 [m/s], η0 =377 [Ω] Fields and Waves I

23. Typical values Typical values of f, b, l for X-rays, visible light, microwaves, and FM radio in free space http://www.esat.kuleuven.ac.be/sista/education/techecon/ Fields and Waves I

24. Fields and Waves I

25. Example 2 – EM Waves in Lossless Media • WRPI broadcasts at 91.5 MHz. The amplitude of E on campus is roughly 0.08 V/m. Assume a coordinate system in which the wave is polarized in the ay direction and propagating in the az direction. • Assume the phase is 0 at z = 0. • What are , and for this wave? • b. Write the electric and magnetic fields in phasor form. • c. Write the electric field in time domain form. Fields and Waves I

26. Example 2 – EM Waves in Losseless Media Fields and Waves I

27. Introduction to Electromagnetic Waves Power and Energy

28. Electromagnetic Power Density • Poynting Vector , is defined [W/unit area] is along the propagation direction of the wave Ulaby Total power [m/s] [W] [W] OR Average power density of the wave [W/m2] Fields and Waves I

29. Plane wave in a Lossless Medium [W/m2] Fields and Waves I

30. Example 3 – Energy & Power a. What is the average energy density of the electric and magnetic fields for the WRPI signal on campus? b. What is the time average Poynting vector of the wave, Sav? Divide its magnitude by the speed of light and compare with your answer from part a. c. The transmitter is about 10 km from campus. What transmitter power is required to radiate the same power density into a sphere of radius 10 km? Fields and Waves I

31. Example 3 – Energy & Power Fields and Waves I