Normal incidence at a plane dielectric boundary Normal incidence at a plane conducting boundary

1. ELECTROMAGNETIC FIELDS
Dr.K.G.SHANTHI
Professor/ECE
shanthiece@rmkcet.ac.in
Normal incidence at a plane dielectric boundary
Normal incidence at a plane conducting boundary

2. REFLECTION OF A PLANE WAVE -Normal incidence
at a plane dielectric boundary
✘ When a plane wave from one medium meets a different
medium, it is partly reflected and partly transmitted.
✘ The proportion of the incident wave that is reflected or
transmitted depends on the constitutive parameters
(Permittivity ε,Permeability μ,Conductivity σ) of the two
media involved.
✘ Suppose that a plane wave propagating along the +z-
direction is incident normally on the boundary z = 0
between dielectric medium 1 (z < 0) characterized by
ε1,μ1,σ1 and dielectric medium 2 (z > 0) characterized by
ε2,μ2,σ2.
2

3. 3
In the figure,
subscripts i, r, and t
denote incident,
reflected, and
transmitted waves,
respectively.
Incident
wave
Reflected
wave
Transmitted
wave
Z=0
Normal incidence at a plane dielectric boundary

4. ✘ (Ei ,Hi) is traveling along + az in medium 1 is the incident wave.
✘ Let Ei be electric field strength of incident wave. Hi be Magnetic field
strength of incident wave.
✘ (Er ,Hr) is traveling along - az in medium 1 is the reflected wave.
✘ Er be electric field strength of reflected wave. Hr be Magnetic field
strength of reflected wave.
✘ (Et ,Ht) is traveling along + az in medium 2 is the transmitted wave.
✘ Et be electric field strength of transmitted wave. Ht be Magnetic field
strength of incident wave.
✘ Total fields in medium 1 comprises both the incident and reflected
fields are given by
✘ The totally reflected wave combines with the incident wave to form a
standing wave.
4
E1 =Ei+Er H1 =Hi+Hr

5. ✘ Total fields in medium 2 are given by
✘ The transmitted wave in medium 2 is a purely traveling wave
and consequently there are no maxima or minima in this region.
✘ At the interface z = 0, the boundary conditions require that the
tangential components of E and H fields must be continuous.
Since the waves are transverse, E and H fields are entirely
tangential to the interface.
✘ Thus at the interface z = 0
✘ Relation between E and H is given by
5
E2 =Et H2 =Ht
E1tan =E2tan H1tan =H2tan
Ei+Er =Et and Hi+Hr =Ht
H
E


As the direction of reflected wave is
opposite to that of incident wave

6. 6
The reflection coefficient (Г):
It is the ratio of the complex amplitude
of the reflected wave to that
of the incident wave.

7. 7
The transmission coefficient
It is defined as ratio of
transmitted voltage wave
amplitude to incident voltage
wave amplitude
i.e. Et/Ei


8. Important results: 8
1.
2.
3.

9. ✘ Consider the when medium
1 is a perfect dielectric
(lossless, σ1= 0) and
medium 2 is a perfect
conductor(σ2= ).
✘ For a perfect conductor,
both magnetic and electric
field are zero. Hence
intrinsic impedance is zero.
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REFLECTION OF A PLANE WAVE -Normal incidence
at a plane conducting boundary

0
2 

t
t
H
E


10. ✘ The transmission coefficient:
✘ The reflection coefficient:
✘ The plane wave incident on a perfect conductor gets entirely
reflected because no field exists within the conductor. so there
can be no transmitted wave (E2 = 0).
✘ The totally reflected wave combines with the incident wave to
form a standing wave.
10
REFLECTION OF A PLANE WAVE -Normal incidence
at a plane conducting boundary

11. ✘ A standing wave "stands" and does not travel; it consists of two
traveling waves: Ei - incident wave and Er - reflected wave .Both
the waves have same amplitudes but travel in opposite
directions.
✘ The standing wave in medium 1 is denoted as
✘ Medium 1 is a perfect dielectric (lossless, σ1= 0)
✘ The Propagation Constant is given by
11

12. 12
Simplifying the above equation,
Hence the Electric field in Medium 1 is given by
The magnetic field component of the wave in Medium 1 is given by
The standing wave in medium 1 is denoted as

13. The electric field magnitude varies sinusoidally with respect to distance
from the reflecting plane. It is zero at the surface and at multiples of half
wavelength.
13
2
2
0
sin
0









n
n
n
z
n
z
z
at
E







|E| is maximum at odd multiples of quarter wavelength.
4
)
1
2
(
2
2
)
1
2
(
2
)
1
2
(
2
)
1
2
(
1
sin




















n
n
n
z
n
z
z
at
E
E x
a
m
Where n=0,1,2…….
Where n=0,1,2…….
|H| minimum occurs whenever there is |E| maximum and vice versa.

14. Standing waves curves
14

15. Standing-wave ratio -S
✘ The ratio of |E1 |max to |E1 |min (or) | H1 |max to |H1 |min is called the
standing-wave ratio
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THANK YOU

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