ENE 428 Microwave Engineering

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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

from

W/m2

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

the microwave oven?

RS

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

RS

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 of two linearly poloraized waves,
• Linear polarization occurs when two linearly polarized waves are

in phase

out of phase

RS

Elliptically polarized wave
• Super position of two linearly polarized waves that
• If x = 0 and y = 45, we have

RS

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 wave
• Phasor forms:

for RHCP,

for LHCP,

from

Note: There are also RHEP and LHEP

RS

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
• 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

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

then we can show that

RS

Reflected wave (1)
• From boundary conditions,

At z = 0, we have

and

 1 = 2are media the same?

RS

Reflected wave (2)
• There must be a reflected wave

and

This wave travels in –z direction.

RS

Reflection and transmission coefficients (1)
• Boundary conditions (reflected wave is included)

from

therefore at z = 0

(1)

RS

Reflection and transmission coefficients (2)
• Boundary conditions (reflected wave is included)

from

therefore at z = 0

(2)

RS

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)

From

 .

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

RS

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

This can be shown in an instantaneous form as

Standing wave

RS

Standing waves (1)

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)

Since

and ,

the magnetic field is

or .

Hy1 is maximum when Ex1 = 0

Poynting vector

RS

Power transmission for 2 perfect dielectrics (1)

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

Average incident power densities

RS

Ex3 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 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)

Assume lossless media, we have

then we can show that

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Wave reflection from multiple interfaces (2)

Assume lossless media, we have

then we can show that

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Wave impedance w (1)

Use Euler’s identity, we can show that

RS

Wave impedance w (2)

Since from B.C.

at z = -l

we may write

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Input impedance in

solve to get

RS

Refractive index

Under lossless conditions,

RS