1. ELEC 401 MICROWAVE ELECTRONICS Lecture 5
Instructor: M. İrşadi Aksun
Acknowledgements:
Art work on most of the illustrations, and most examples have been taken from the following book:
Elecrtromagnetics, by Branislav M. Notaros
Pearson Int. Ed., 2010

2. Outline
Chapter 1: Motivation & Introduction
Chapter 2: Review of EM Wave Theory
Chapter 3: Plane Electromagnetic Waves
Chapter 4: Transmission Lines (TL)
Chapter 5: Microwave Network Characterization
Chapter 6: Smith Chart & Impedance Matching
Chapter 7: Passive Microwave Components

3. Plane Electromagnetic Waves Reflection and Transmission (Refraction)

4. Plane Electromagnetic Waves – Reflection & Transmission
Although we have plenty of experience on reflection and transmission of light, like reflections on mirrors, mirages and rainbow, we have very little information how these phenomena occur.

5. Plane Electromagnetic Waves – Reflection & Transmission
A Simple Case: Normal Incidence on a perfectly conducting plane
B.C:

6. Plane Electromagnetic Waves – Reflection & Transmission
Standing Wave: The resultant wave, which is a superposition of two opposite traveling waves, is defined as a standing wave.

7. Plane Electromagnetic Waves – Reflection & Transmission
Example: A right-handed circularly polarized uniform plane wave propagates in air and incident normally on a PEC plane. The associated time-harmonic electric field vector is given by
Find (a) the total electric and magnetic field vectors in air; (b) polarization state of the reflected wave; (c) complex surface current and charge density.
a) From B.C. on the tangential electric field at PEC interface (z=0),

8. Plane Electromagnetic Waves – Reflection & Transmission
Example (Cont.): b)
RHCP x
LHCP

9. Plane Electromagnetic Waves – Reflection & Transmission
Example (Cont.):
c) Knowing the total magnetic field intensity vector at the PEC surface, the surface current density can be calculated as
As expected, the current density is also Circularly Polarized.
Surface charge density can also be found from the following BC as

10. Plane Electromagnetic Waves – Reflection & Transmission
A Simple Case: Normal incidence on a penetrable planar interface
B.C:

11. Plane Electromagnetic Waves – Reflection & Transmission
Another Case: Oblique incidence on a dielectric interface
Snell’s law
n, the index of refraction, is mostly used in optics to characterize materials.

12. Plane Electromagnetic Waves – Reflection & Transmission
Oblique incidence – Perpendicular (normal) polarization

13. Plane Electromagnetic Waves – Reflection & Transmission
Oblique incidence – Parallel polarization

14. Plane Electromagnetic Waves – Reflection & Transmission
Example (from “Electromagnetics” by B. M. Notaros):
A light beam is incident obliquely on a glass slab surrounded by air. Prove that the emerging beam on the other side of the slab is always parallel to the incident beam.
Usıng Snell’s law of refraction
Incoming and outgoing beams are parallel to each other.

15. Plane Electromagnetic Waves – Reflection & Transmission
Example (from “Electromagnetics” by B. M. Notaros): A coin lies at the bottom of a water (n=1.33) fountain at a depth of d=50cm. What is the apparent depth of the coin below the water surface when viewed from above the water at an angle of 600 with respect to the normal on the surface.
The coin appears to the viewer higher than it is, because the brain perceives the information about the received light beam from the eyes without taking into account Snell’s law.

16. Plane Electromagnetic Waves – Reflection & Transmission
Total Internal Reflection (critical angle)
Snell’s law of refraction

17. Plane Electromagnetic Waves – Reflection & Transmission
Total Internal Reflection (critical angle)
Wave propagation inside the core of an optical fiber

18. Plane Electromagnetic Waves – Reflection & Transmission
Brewster Angle (Angle of no reflection)
For parallel polarization, Brewster angle

19. Plane Electromagnetic Waves – Reflection & Transmission
Example: Magnitude of reflection coefficients in total internal reflection.
Snell’s law of refraction ??

20. Plane Electromagnetic Waves – Reflection & Transmission
Example (from “Electromagnetics” by B. M. Notaros): A large leaf of approximately circular shape with a diameter of 50cm floats on the surface of the water (n=1.33) in a fountain. What is the maximum depth in the water directly under the center of the leaf for a small gold fish to be totally invisible from above the water?
Any location of the fish above the critical one makes the angle of incidence larger than the critical angle, and hence is also in the invisible zone.