ENE 428 Microwave Engineering

1. ENE 428Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions RS

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: Microwave Engineering by David M. Pozar (3rd edition Wiley, 2005) • Recommended additional textbook: Applied Electromagnetics by Stuart M.Wentworth (2nd edition Wiley, 2007) RS

3. Grading Homework 10% Quiz 10% 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. RS

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

5. Introduction http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=52 • Microwave frequency range (300 MHz – 300 GHz) • Microwave components are distributed components. • Lumped circuit elements approximations are invalid. • Maxwell’s equations are used to explain circuit behaviors( and) RS

6. Introduction (2) • 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 • Knowledge of fields in media and boundary conditions allows useful applications of material properties to microwave components • A uniform plane wave, both electric and magnetic fields lie in the transverse plane, the plane whose normal is the direction of propagation RS

7. Maxwell’s equations (1) (2) (3) (4) RS

8. Maxwell’s equations in free space •  = 0, r = 1, r = 1 0= 4x10-7 Henrys/m 0= 8.854x10-12 farad/m Ampère’s law Faraday’s law RS

9. Integral forms of Maxwell’s equations RS

10. Fields are assumed to be sinusoidal or harmonic, and time dependence with steady-state conditions • Time dependence form: • Phasor form: RS

11. Maxwell’s equations in phasor form (1) (2) (3) (4) RS

12. Fields in dielectric media (1) • An applied electric field causes the polarization of the atoms or molecules of the material to create electric dipole moments that complements the total displacement flux, where is the electric polarization. • In the linear medium, it can be shown that • Then we can write RS

13. Fields in dielectric media (2) • may be complex then  can be complex and can be expressed as • Imaginary part is counted for loss in the medium due to damping of the vibrating dipole moments. • The loss of dielectric material may be considered as an equivalent conductor loss if the material has a conductivity  . Loss tangent is defined as RS

14. Anisotropic dielectrics • The most general linear relation of anisotropic dielectrics can be expressed in the form of a tensor which can be written in matrix form as RS

15. Analogous situations for magnetic media (1) • An applied magnetic field causes the magnetic polarization of by aligned magnetic dipole moments • where is the electric polarization. • In the linear medium, it can be shown that • Then we can write RS

16. Analogous situations for magnetic media (2) • may be complex then  can be complex and can be expressed as • Imaginary part is counted for loss in the medium due to damping of the vibrating dipole moments. RS

17. Anisotropic magnetic material • The most general linear relation of anisotropic material can be expressed in the form of a tensor which can be written in matrix form as RS

18. Dn2 Et2 Bn2 Ht2 Et1 Ht1 Dn1 Bn1 Boundary conditions between two media RS

19. Fields at a dielectric interface • Boundary conditions at an interface between two lossless dielectric materials with no charge or current densities can be shown as RS

20. Fields at the interface with a perfect conductor • Boundary conditions at the interface between a dielectric with the perfect conductor can be shown as RS

21. General plane wave equations (1) • Consider medium free of charge • For linear, isotropic, homogeneous, and time-invariant medium, assuming no free magnetic current, (1) (2) RS

22. General plane wave equations (2) Take curl of (2), we yield From then For charge free medium RS

23. Helmholtz wave equation For electric field For magnetic field RS

24. Time-harmonic wave equations • Transformation from time to frequency domain Therefore RS

25. 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) RS

26. 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 RS

27. 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) RS

28. Intrinsic impedance • For any medium, • For free space RS

29. Propagating fields relation where represents a direction of propagation RS