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Origin of waves
• Wave Equation
• One Dimensional (Discovered by french scientist Jean Baptiste le Rond d’Alembert)
• Three Dimensional (Discovered by swiss mathematician and physicist Leonhard Euler)
Types of Waves
• Mechanical
▫ Propagate through a material medium (solid, liquid or gas)
▫ Wave speed depends on the elastic and inertial properties of the medium.
▫ Longitudinal and transverse waves
• Electromagnetic
▫ Propagate through free space or a medium.
▫ Transverse waves.
Electromagnetic Waves
• The oscillation of electric and magnetic fields.
• James Maxwell formulated EM Waves.
• Are categorized in near-field and far-field region.
Maxwell Equations
• Differential Equations; ▫ The electric flux density leaving a
volume is proportional to the charge inside.
▫ The total magnetic flux around a closed surface is zero. ( No monopoles)
▫ The accumulated electric field around a closed circuit is proportional to the time rate of change of the magnetic flux it encloses.
▫ Electric currents and changes in electric density flux are proportional to the magnetic field circulating about the area.
Near-Field and Far-Field
• Near-Field – Complex to predict E and H.
• Far-Field – Maximum radiation is achieved.
Properties of a Wave
• Transmission – Energy transport from one point to another through a medium.
• Reflection – Changes the direction of the incident wave by a reflective surface.
• Absorption – Transformation of energy in the medium.
• Interference – A superposition of two or more waves creating a new one.
Properties of a Wave
• Refraction – Changes the speed of the wave.
• Diffraction – Exhibits bending of the wave after pass through an orifice.
• Polarization – Changes the orientation of the wave along a plane.
• Dispersion – Wave velocity depends on wave frequency.
EM Wave Propagation
• Is the propagation of a wave form by an electric and magnetic field.
• Electric field – Electric force per unit charge.
• Magnetic Field – induce of electric currents with magnetic materials.
• Travel at speed of light; c= 3 x 10 8 m/s
EM Wave Propagation
• Transmit energy through free space or a particular medium (water, soil, concrete, or any material).
• Wave changes occur in space and time.
• Single or multiple medium can pass through at the same time.
• Transmission lines or waveguides can be used to transmit wave energy.
Components of a Wave
• Amplitude (A)
• Phase ( βz)
• Period (T)
• Frequency (f)
• Angular frequency (w)
• Wavelength (λ)
• Attenuation Constant (α)
• Constant Phase (β)
Types of Medium
• Free Space (σ=0 ε= ε0 μ= μ0)
• Lossless Di-electric (σ=0 ε= εr ε0 μ= μrμ0)
• Lossy Di-electric (σ≠0 ε= εr ε0 μ= μrμ0 )
• Good Conductor (σ≈∞ ε=ε0 μ= μrμ0 )
Transmission Lines
• Consisted of two conductors to connect the source to a load.
• Only support TEM wave.
Waveguides
• Guide the transmitted wave energy.
• Provide better performance at 3-300GHz.
• Support TE and TM waves.
Antennas
• Many types of antennas (Helix, Parabolic, Horns, Microstrip, Aperture)
• Different polarizations • Different sizes (few nm hundred of meters) • Provide duality properties (either transmit or
receive a signal). • Design for a particular frequency or ultra wide
frequency bands. • Design to transmit on near-field or far-field
region.
Antenna Characteristics
• Radiation Pattern – Is the amplitude voltage pattern or power pattern at far-field.
• Radiation Intensity – Is the total radiated power.
• Directive Gain – The radiated power pattern estimation at a particular direction.
• Power Gain – Is the ratio of radiation intensity with input power.
Case Study
• The use of cross-well borehole radar in sandy and clayed soilbed to detect TCE.
• Antenna design using a simulator and experimental measurements were performed.
• Estimation of the EM parameters are obtained from the s-parameter measurements to for sandy soil under different conditions (dry, wet, dry with TCE, wet with TCE)
Return Loss (S11)
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
x 109
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
Frequency (Hz)
Ret
urn
Loss
(dB
)
Insertion Loss (S21)
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
x 109
-110
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
Frequency (Hz)
Insert
ion L
oss (
dB
)
Return Loss
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
x 109
-12
-10
-8
-6
-4
-2
0
Frequency (Hz)
Retu
rn L
oss (
dB
)
Simulation
Measurements
Insertion Loss
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
x 109
-120
-110
-100
-90
-80
-70
-60
-50
-40
-30
-20
Frequency (Hz)
Insert
ion L
oss (
dB
)
Simulation
Measurements
Estimation of the EM Properties
εr=((phase(S21f 2)- phase(S21f 1))*c/ 2π(f2-f1)*d)2
T=e-(α+jβ)d= e-αd (cos(βd)-jsin(βd))
εr=(Δθ*c/ 2πΔf d)2
S21= T
Relative Permittivity for Dry Sand Forward
Transmission
Response Raypath
# of 360 degrees
phase shifts
r
S51 6 960 MHz 3.52
S61 4 520 MHz 5.32
S71 3 350 MHz 6.61
S81 2 320 MHz 3.52
S52 6 980 MHz 3.37
S62 5 740 MHz 4.11
S72 4 630 MHz 3.63
S82 5 700 MHz 4.59
Relative Permittivity for Dry Sand
Forward
Transmission
Response Raypath
# of 360 degrees
phase shifts
r
S53 5 700 MHz 4.59
S63 3 490 MHz 3.37
S73 6 950 MHz 3.59
S83 7 1 GHz 4.11
S54 7 800 MHz 6.89
S64 5 720 MHz 4.34
S74 5 780 MHz 3.70
S84 6 940 MHz 4.59
Relative Permittivity for Dry Sand with
TCE Transmission
Response
# of 360 degrees
phase shifts r
S51 4 600 MHz 4
S52 5 700 MHz 4.59
S53 6 680 MHz 7.01
S54 3 320 MHz 7.91
S61 2 250 MHz 5.76
S62 5 530 MHz 8.01
S63 10 900 MHz 11.11
S64 4 420 MHz 8.16
Relative Permittivity for Dry Sand with
TCE Transmission
Response
# of 360 degrees
phase shifts r
S71 5 660 MHz 5.17
S72 4 510 MHz 5.54
S73 4 660 MHz 3.31
S74 5 660 MHz 5.17
S81 7 800 MHz 6.89
S82 5 600 MHz 6.25
S83 5 660 MHz 5.17
S84 5 760 MHz 3.89
References • Matthew Sadiku, Elements of Electromagnetic 2nd Edition • https://en.wikipedia.org/wiki/Wave_equation • http://www2.lbl.gov/MicroWorlds/ALSTool/EMSpec/EMSpec2.html • https://en.wikipedia.org/wiki/Electromagnetic_wave_equation • http://www.geosphereinc.com/gpr_gpradar.html • http://brightmags.com/how-does-sonar-work/ • http://sciencelearn.org.nz/Contexts/Earthquakes/Sci-
Media/Images/Seismic-waves • http://www.bu.edu/synapse/tag/seismic-wave/ • http://laschoolreport.com/la-unified-close-to-completing-solar-power-
systems/ • https://unorthodoxbigcitydreams.wordpress.com/2014/07/13/towers-
towers-everywhere/ • http://www.visionlearning.com/blog/2012/11/09/image-of-the-week-how-
to-look-inside-a-fish/