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ENE 428 Microwave Engineering . Lecture 3 Polarization, Reflection and Transmission at normal incidence. RS. Uniform plane wave (UPW) power transmission. from. W/m 2. Question: Have you ever wondered why aluminum foil is not allowed in the microwave oven?. Polarization.

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ENE 428Microwave Engineering

Lecture 3 Polarization, Reflection and Transmission at normal incidence

RS

RS


Uniform plane wave upw power transmission
Uniform plane wave (UPW) power transmission

from

W/m2

Question: Have you ever wondered why aluminum foil is not allowed in

the microwave oven?

RS


Polarization
Polarization

  • UPW is characterized by its propagation direction and frequency.

  • Its attenuation and phase are determined by medium’s parameters.

  • Polarization determines the orientation of the electric field in a fixed spatial plane orthogonal to the direction of the propagation.

RS


Linear polarization
Linear polarization

  • Consider in free space,

  • At plane z = 0, a tip of field traces straight line segment called “linearly polarized wave”

RS


Linear polarization1
Linear polarization

  • A pair of linearly polarized wave also produces linear polarization

At z = 0 plane

At t = 0, both linearly polarized waves

Have their maximum values

RS


More generalized linear polarization
More generalized linear polarization

  • More generalized of two linearly poloraized waves,

  • Linear polarization occurs when two linearly polarized waves are

in phase

out of phase

RS


Elliptically polarized wave
Elliptically polarized wave

  • Super position of two linearly polarized waves that

  • If x = 0 and y = 45, we have

RS


Circularly polarized wave
Circularly polarized wave

  • occurs when Exoand Eyo are equal and

  • Right hand circularly polarized (RHCP) wave

  • Left hand circularly polarized (LHCP) wave

RS


Circularly polarized wave1
Circularly polarized wave

  • Phasor forms:

    for RHCP,

    for LHCP,

from

Note: There are also RHEP and LHEP

RS


Ex1 given determine the polarization of this wave
Ex1 Given,determine the polarization of this wave

RS


Ex2 the electric field of a uniform plane wave in free space is given by determine
Ex2 The electric field of a uniform plane wave in free space is given by , determine

  • f

  • The magnetic field intensity

RS


c)

d) Describe the polarization of the wave

RS



Incident wave
Incident wave

  • Normal incidence – the propagation direction is normal to the boundary

Assume the medium is lossless, let the incident electric field to be

or in a phasor form

since

then we can show that

RS


Transmitted wave
Transmitted wave

  • Transmitted wave

Assume the medium is lossless, let the transmitted electric field to be

then we can show that

RS


Reflected wave 1
Reflected wave (1)

  • From boundary conditions,

At z = 0, we have

and

 1 = 2are media the same?

RS


Reflected wave 2
Reflected wave (2)

  • There must be a reflected wave

and

This wave travels in –z direction.

RS


Reflection and transmission coefficients 1
Reflection and transmission coefficients (1)

  • Boundary conditions (reflected wave is included)

from

therefore at z = 0

(1)

RS


Reflection and transmission coefficients 2
Reflection and transmission coefficients (2)

  • Boundary conditions (reflected wave is included)

from

therefore at z = 0

(2)

RS


Reflection and transmission coefficients 3
Reflection and transmission coefficients (3)

  • Solve Eqs. (1) and (2) to get

Reflection coefficient

Transmission coefficient

RS


Types of boundaries perfect dielectric and perfect conductor 1
Types of boundaries: perfect dielectric and perfect conductor (1)

From

 .

Since 2 = 0 then  = -1 and Ex10+=Ex10-

RS


Types of boundaries perfect dielectric and perfect conductor 2
Types of boundaries: perfect dielectric and perfect conductor (2)

This can be shown in an instantaneous form as

Standing wave

RS


Standing waves 1
Standing waves (1) conductor (2)

When t = m, Ex1 is 0 at all positions.

and when z = m, Ex1 is 0 at all time.

Null positions occur at

RS


Standing waves 2
Standing waves (2) conductor (2)

Since

and ,

the magnetic field is

or .

Hy1 is maximum when Ex1 = 0

Poynting vector

RS


Power transmission for 2 perfect dielectrics 1
Power transmission for 2 perfect dielectrics (1) conductor (2)

Then 1and 2are both real positive quantities and 1 = 2= 0

Average incident power densities

RS


Ex3 conductor (2) Let medium 1 have 1 = 100  and medium 2 have 2 = 300 , given Ex10+ = 100 V/m. Calculate average incident, reflected, and transmitted power densities

RS


Wave reflection from multiple interfaces 1
Wave reflection from multiple interfaces (1) conductor (2)

  • Wave reflection from materials that are finite in extent such as interfaces between air, glass, and coating

  • At steady state, there will be 5 total waves

RS


Wave reflection from multiple interfaces 2
Wave reflection from multiple interfaces (2) conductor (2)

Assume lossless media, we have

then we can show that

RS


Wave reflection from multiple interfaces 21
Wave reflection from multiple interfaces (2) conductor (2)

Assume lossless media, we have

then we can show that

RS


Wave impedance w 1
Wave impedance conductor (2)w (1)

Use Euler’s identity, we can show that

RS


Wave impedance w 2
Wave impedance conductor (2)w (2)

Since from B.C.

at z = -l

we may write

RS


Input impedance in
Input impedance conductor (2)in

solve to get

RS



Refractive index
Refractive index conductor (2)

Under lossless conditions,

RS


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