1. Wave Incidence [Chapter 10 cont, Sadiku]
Dr. Cruz-Pol
Wave Incidence [Chapter 10 cont, Sadiku]
Dr. Sandra Cruz-Pol
Electrical and Computer Engineering Dept.
UPR-Mayagüez
Normal Incidence

2. Ex. Light traveling in air encounters the water; another medium.
Dr. Cruz-Pol
Ex. Light traveling in air encounters the water; another medium.
Normal Incidence

3. Dr. Cruz-Pol
Wave incidence
For many applications, [such as fiber optics, line power transmission], it’s necessary to know what happens to a wave when it meets a different medium.
How much is transmitted?
How much is reflected back?
Normal Incidence

4. We will look at… Normal incidence Wave arrives at 0o from normal
Dr. Cruz-Pol
We will look at…
Normal incidence
Wave arrives at 0o from normal
“Standing waves”
Oblique incidence
Wave arrives at another angle
Snell’s Law and Critical angle
Parallel or Perpendicular
Brewster angle
Normal Incidence

5. Reflection at Normal Incidence
Dr. Cruz-Pol
Reflection at Normal Incidence x Et Ht ak
Transmitted wave Ei Hi ak
Incident wave z Er Hr
Reflected wave
akr y
z=0
Medium 1
Medium 2
Normal Incidence

6. Now in terms of equations …
Dr. Cruz-Pol
Now in terms of equations …
Incident wave Ei Hi ak
Incident wave
Normal Incidence

7. Reflected wave It’s traveling along –z axis Er akr Hr Reflected wave
Dr. Cruz-Pol
Reflected wave Er Hr
Reflected wave
akr
It’s traveling along –z axis
Normal Incidence

8. Transmitted wave Et ak Ht Transmitted wave Dr. Cruz-Pol
Normal Incidence

9. The total fields At medium 1 and medium 2
Dr. Cruz-Pol
The total fields
At medium 1 and medium 2
Tangential components must be continuous at the interface
Normal Incidence

10. Define 1+ G= t Reflection coefficient, G Transmission coefficient, t
Dr. Cruz-Pol
Define
Reflection coefficient, G
Transmission coefficient, t
Note:
1+ G= t
Both are dimensionless and may be complex
0≤|G|≤1
Normal Incidence

11. PE 10.8 -3.33 ejb1z x V/m, 6.67 e-jb2z x V/m where b2 = 2b1 = 200 p/3
Dr. Cruz-Pol
PE 10.8
A 5GHz uniform plane wave Eis =10e-jbz ax in free space is incident normally on a large plane, lossless dielectric slab (z>0) having e = 4eo and m=mo.
Find:
the reflected wave Ers and
the transmitted wave Ets.
Answer:
-3.33 ejb1z x V/m,
6.67 e-jb2z x V/m
where b2 = 2b1 = 200 p/3
SEE
Normal Incidence

12. Case 1: Medium 1: perfect dielectric, s1=0
Dr. Cruz-Pol
Case 1:
Medium 1: perfect dielectric, s1=0
Medium 2: perfect conductor, s2=∞
Halla impedancias intrínseca.
Reflección,
Transmisión
y campos
Normal Incidence

13. The EM field forms a Standing Wave on medium 1
Dr. Cruz-Pol
The EM field forms a Standing Wave on medium 1
|E1|
2Eio z
Conducting material
Normal Incidence

14. Dr. Cruz-Pol
Standing Wave Applets
Normal Incidence

15. Case 2: Medium 1: perfect dielectric s1=0
Dr. Cruz-Pol
Case 2:
Medium 1: perfect dielectric s1=0
Medium 2: perfect dielectric s2=0
Normal Incidence

16. Standing waves due to reflection
Dr. Cruz-Pol
Standing waves due to reflection
|E1|
Lossless Medium 1
Eio (1+|G|) z
Lossless Medium 2
***At every half-wavelength, everything repeats! ***
Normal Incidence

17. Case 3: Medium 1 = perfect dielectric s1=0
Dr. Cruz-Pol
Case 3:
Medium 1 = perfect dielectric s1=0
Medium 2 = perfect dielectric s2=0
Normal Incidence

18. Standing waves due to reflection
Dr. Cruz-Pol
Standing waves due to reflection
|E1|
Lossless Medium 1
Eio (1+|G|)
Eio (1-|G|) z
Lossless Medium 2
At every half-wavelength, all em properties repeat
Normal Incidence

19. Dr. Cruz-Pol
Standing Wave Ratio, s
Measures the amount of reflections, the more reflections, the larger the standing wave that is formed.
The ratio of |E1|max to |E1|min or
Ideally
s=1 (0 dB)
No reflections
Normal Incidence

20. Dr. Cruz-Pol
PE 10.9
The plane wave E=50 sin (wt – 5x) ay V/m in a lossless medium (m=4mo, e=eo) encounters a lossy medium (m=mo, e=4eo, s=0.1 mhos/m) normal to the x-axis at x=0. Find G t s Er Et
←Answers:
= exp(j171o)
=0.23 exp(j33.56o)
=10.03
= sin (wt +5x + 171o) y
= 11.5 e -6.02x sin (wt x o) y V/m
Normal Incidence

21. Dr. Cruz-Pol
Ex. Antenna Radome
A 10GHz aircraft radar uses a narrow-beam scanning antenna mounted on a gimbal behind a dielectric radome.
Even though the radome shape is far from planar, it is approximately planar over the narrow extent of the radar beam.
If the radome material is a lossless dielectric with mr=1 and er=9, choose its thickness d such that the radome appears transparent to the radar beam.
Mechanical integrity requires d to be greater that 2.3 cm.
Antenna with radome
Antenna with no radome
Answer:
l/2=.5cm, d=2.5cm
Normal Incidence

22. Dr. Cruz-Pol
Power Flow in Medium 1
The net average power density flowing in medium 1 z Ei Hi ak
Incident wave Et Ht
Transmitted wave Er Hr
Reflected wave
akr y
z=0
Medium 1
Medium 2
Normal Incidence

23. Power Flow in Transmitted wave
Dr. Cruz-Pol
Power Flow in Transmitted wave
The net average power density flowing in medium 2 z Ei Hi ak
Incident wave Et Ht
Transmitted wave Er Hr
Reflected wave
akr y
z=0
Medium 1
Medium 2
Normal Incidence

24. Dr. Cruz-Pol
Power in Lossy Media
where
Normal Incidence

25. We will look at… Normal incidence Wave arrives at 90o from the surface
Dr. Cruz-Pol
We will look at…
Normal incidence
Wave arrives at 90o from the surface
Standing waves
Oblique incidence (lossless)
Wave arrives at an angle
Snell’s Law and Critical angle
Parallel or Perpendicular
Brewster angle
Normal Incidence