Chapter 3 Wave Reflection and Transmission

LINES, FIELDS AND WAVES
Chapter 3
Wave Reflection and Transmission
Huynh Phu Minh Cuong

hpmcuong@hcmut.edu.vn
Department of Telecommunications
Faculty of Electrical and Electronics Engineering
1
Ho Chi Minh city University of Technology
11/24/2017 1
Chapter 3 Wave Reflection and Transmission
Chapter Contents
EM Waves at Boundaries
3-1 Wave Reflection and Transmission at Normal Incidence
3-2 Snell’s Laws
3-3 Fiber Optics
3-4 Wave Reflection and Transmission at Oblique Incidence
3-5 Waveguides
Summary
Problems
11/24/2017 2
Signal path between a shipboard transmitter (Tx) and a submarine receiver (Rx).
11/24/2017 3
Revision of Maxwell’s Equations
11/24/2017 4
11/24/2017 5
11/24/2017 6
11/24/2017 7
Unbounded EM Waves
11/24/2017 8
Discontinuity between two different transmission lines is analogous

to that between two dissimilar media.
11/24/2017 9
3-1.1 Boundary between Lossless Media
11/24/2017 10
At the boundary (z = 0), the tangential components of the electric and magnetic fields
are continuous. Hence,
The quantities  and  are called the

reflection and transmission coefficients.
11/24/2017 11
11/24/2017 12
3-1.2 Transmission-Line Analogue
Transmission line theory can be used to solve plane-wave propagation problems.

11/24/2017 13
3-1.3 Power Flow in Lossless Media
 The net average power density flowing
in medium 1 is:
The average power density of the

transmitted wave in medium 2 is:
11/24/2017 14
3-1.4 Boundary between Lossy Media
 In a medium with constitutive parameters (,μ, σ), the propagation constant γ = α+jβ
and the intrinsic impedance ηc are both complex.
Because ηc1 and ηc2 are, in general, complex,

and  may be complex as well.
11/24/2017 15
11/24/2017 16
11/24/2017 17
3-2 Snell’s Laws
 In the preceding sections we examined reflection and transmission of plane waves that are
normally incident upon a planar interface between two different media.
 We now consider the oblique-incidence case depicted in Fig. 8-9, and for simplicity we assume
all media to be lossless.
 The angles of incidence, reflection,
and transmission (or refraction),
defined with respect to the normal to
the boundary (the z axis), are θi, θr,
and θt, respectively.
 These three angles are interrelated
by Snell’s laws:
11/24/2017 18
3-2 Snell’s Laws
 The index of refraction of a medium, n, is defined as the ratio of the phase velocity in free
space (i.e., the speed of light c) to the phase velocity in the medium. Thus,
 For nonmagnetic materials, μr1 = μr2 = 1, in which case:
11/24/2017 19
3-2 Snell’s Laws
 Snell’s laws state that θr = θi and sin θt =

(n1/n2) sinθI.
 Refraction is
(a) inward if n1 < n2 and
(b) outward if n1 > n2; and
(c) the refraction angle is 90◦ if n1 > n2 and θi
is equal to or greater than the critical angle
θc = sin-1(n2/n1).
 If θi exceeds θc, the incident wave is

totally reflected.
11/24/2017 20
3-3 Fiber Optics
11/24/2017 21
 A wave of arbitrary polarization may be described as the superposition of two orthogonally

polarized waves, one with its electric field parallel to the plane of incidence (parallel
polarization) and the other with its electric field perpendicular to the plane of incidence
(perpendicular polarization).
 The plane of incidence is defined as the plane containing the normal to the boundary and the
direction of propagation of the incident wave.
11/24/2017 22
3-4.1 Perpendicular Polarization
Given:
Find:
11/24/2017 23
11/24/2017 24
given
find
find
11/24/2017 25
 Applying the boundary condition for E and H:
11/24/2017 26
 Those equations should satisfy for all possible values of x (i.e., all along the
boundary), it follows that the arguments of all three exponentials must be
equal. That is,:
11/24/2017 27
 These two equations can be solved simultaneously to yield the following
expressions for the reflection and transmission coefficients in the perpendicular
polarization case:
 These two coefficients, which formally are known as the Fresnel reflection and
transmission coefficients for perpendicular polarization, are related by
11/24/2017 28
See text book for solution . . .

11/24/2017 29
3-4.2 Parallel Polarization
11/24/2017 30
3-4.2 Parallel Polarization
11/24/2017 31
3-4.3 Brewster Angle
 The Brewster angle θB is defined as the incidence angle θi at which the Fresnel
reflection coefficient  = 0.
 Perpendicular polarization
Because the denominator of above Eq. goes to zero when μ1 = μ2, θB⊥ does not exist for
nonmagnetic materials.
 Parallel polarization
11/24/2017 32
Summary
11/24/2017 33
Quiz –Dec 01, 2016
11/24/2017 34

Chapter 3 Wave Reflection and Transmission

Uploaded by

Copyright:

Available Formats

Chapter 3 Wave Reflection and Transmission

Uploaded by

Document Information

Original Description:

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Chapter 3 Wave Reflection and Transmission

Uploaded by

Copyright:

Available Formats

LINES, FIELDS AND WAVES

Huynh Phu Minh Cuong

Discontinuity between two different transmission lines is analogous

The quantities  and  are called the

Transmission line theory can be used to solve plane-wave propagation problems.

The average power density of the

Because ηc1 and ηc2 are, in general, complex,

 For nonmagnetic materials, μr1 = μr2 = 1, in which case:

 Snell’s laws state that θr = θi and sin θt =

 If θi exceeds θc, the incident wave is

 A wave of arbitrary polarization may be described as the superposition of two orthogonally

See text book for solution . . .

You might also like