Wave Diagnostics By: Jonathan Toro

Outline

• Waves

• Electromagnetic Waves

• Case Study

Waves

What is a Wave?

• Wave is energy transfer through a medium or space from one point to another.

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.

Mechanical Waves Examples

Water Waves

Acoustic or Sound Waves

Shock Waves Seismic

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.

Electromagnetic Spectrum

Courtesy from MicroWorlds

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.

Electromagnetic Waves

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 )

Lossy Di-electric

Lossless Di-electric

Free Space

Good Conductor

Reflection and Transmission of a Plane

at Normal Incidence

Reflection and Transmission of a Plane

at Oblique Incidence Parallel Polarization

Reflection and Transmission of a Plane

at Oblique Incidence

Perpendicular Polarization

Transmission Lines

• Consisted of two conductors to connect the source to a load.

• Only support TEM wave.

Transmission Lines

Characteristic Impedance (Z0)

Characteristic Impedance (Z0)

Waveguides

• Guide the transmitted wave energy.

• Provide better performance at 3-300GHz.

• Support TE and TM waves.

Rectangular TM Waveguide

• Three cases;

Cut-off mode Evanescent

Rectangular TM Waveguide

• Propagation ( Minimum TM11)

Rectangular TE Waveguide

• Minimum propagation mode;

▫ TE01 or TE10

Rectangular TE Waveguide

Antennas

• Is a transition between a transmission line and a medium.

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 Examples

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

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)

Scattering Parameters

2221212

212i111

VSVSV

VSVSV

Antenna Design

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

)

Experimental Setup

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/