Ø Plane Wave depending on media. l general (lossy), lossless. Ø Power in a Wave Ø Applications and Concepts. Ø Start taking the curl of Faraday s law

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1 EM Waves INEL 4151 Ch 10 Outline Plane Wave depending on media l general (lossy), lossless. Power in a Wave Applications and Concepts Sandra Cruz-Pol, Ph. D. ECE Mayagüez, PR The wave equation for E Start taking the curl of Faraday s law Then apply the vectorial identity 10.1 Plane waves And you re left with Cruz-Pol, A Wave To change back to time domain From phasor Let s look at a special case for simplicity without loosing generality: The electric field has only an x-component The field travels in z direction Then we have to time domain Cruz-Pol, Cruz-Pol, Electrical Engineering, 1

Several Cases of Media 1. Free space 2. Lossless dielectric 3. Lossy dielectric (general) 4. Good Conductor 10.3-10.

Free space EM wave Spectrum There are no losses, e.g.

2 Several Cases of Media 1. Free space 2. Lossless dielectric 3. Lossy dielectric (general) 4. Good Conductor Plane wave Propagation in Several Media Recall: Permittivity eo=8.854 x [F/m] Permeability µo= 4p x 10-7 [H/m] Cruz-Pol, 1. Free space EM wave Spectrum There are no losses, e.g. Let s define The phase of the wave The angular frequency Phase constant The phase velocity of the wave The period T and wavelength l In what direction does it moves? Cruz-Pol, Cruz-Pol, Where does it moves? Choose 3 times: Plot: +z Cruz-Pol, Cruz-Pol, Electrical Engineering, 2

general, we had and From these we obtain

(b) wavelength in the material (c) phase

3 Wave like this So Moves towards: 3. General Case (Lossy Dielectrics) In general, we had and From these we obtain So, for a known material and frequency, we can find g=a+jb Cruz-Pol, Cruz-Pol, Intrinsic Impedance, h Note If we divide E by H, we get units of ohms and the definition of the intrinsic impedance of a medium at a given frequency. *Not in-phase for a lossy medium E and H are perpendicular to one another Travel is perpendicular to the direction of propagation The amplitude is related by the impedance And so is the phase Cruz-Pol, Cruz-Pol, Example: Wave Propagation in Lossless materials A wave in a nonmagnetic material is given by Find: (a) direction of wave propagation, (b) wavelength in the material (c) phase velocity Answer: +y, l=1.26m, u p= 2x10 8 m/s, Cruz-Pol, Cruz-Pol, Electrical Engineering, 3

4 Loss Tangent Relation between tanq and e c If we divide the conduction current by the displacement current Cruz-Pol, Cruz-Pol, Any medium Summary Lossless Low-loss medium medium (e /e <1/100) (s=0) Good conductor (e /e >100) Units b can also be written as: a b h [Np/m] [rad/m] If we substitute: u c l w/b [m/s] [m] **In free space; Cruz-Pol, eo =8.85 x F/m µo=4p x 10-7 H/m Cruz-Pol, Applet Review: 1. Free Space Substituting in the general equations: Harmonic oscillator damping pplets/flash/fluids,%20oscillations%20 and%20waves/dampedshm.swf pplets/applets_by_topic/oscillations.ht ml Cruz-Pol, Cruz-Pol, Electrical Engineering, 4

2. Lossless dielectric Substituting in the general equations: 4.

medium medium (s=0) (e /e <1/100) Good conductor Units [Np/m]

wave in a nonmagnetic material is given by d) Relative

25, u c w/b [m/s] l [m] **In free space; Cruz-Pol, eo =8.

5 2. Lossless dielectric Substituting in the general equations: 4. Good Conductors Substituting in the general equations: Is water a good conductor??? Cruz-Pol, Cruz-Pol, a b h Any medium Summary Lossless Low-loss medium medium (s=0) (e /e <1/100) Good conductor Units [Np/m] [rad/m] Find: Example: Wave Propagation in Lossless materials A wave in a nonmagnetic material is given by d) Relative permittivity of material e) Electric field phasor 2.25, u c w/b [m/s] l [m] **In free space; Cruz-Pol, eo =8.85 x F/m µo=4p x 10-7 H/m Cruz-Pol, In a free space, Example Find J d and E (use phasors) Example: Water Cruz-Pol, Cruz-Pol, Electrical Engineering, 5

Permittivity of water vs. freq. http://www.

Example Water @ 10GHz, (microwaves) Find a, b and h

Exercise: Lossy media propagation For each of the

GHZ (b) Animal tissue with µ r=1, e r=12 and s=0.

s=10-4 S/m at 1 khz Answer: (a) low-loss, a= 8.

34x10 8, hc=168 W (b) (c) general, a= 9.

28(1+j) W Cruz-Pol, Skin depth Short cut!

6 Permittivity of water vs. freq. Example 60Hz, (low freq) Find a, b and h Attenuation const. For distilled water Phase constant For sea water Example 10GHz, (microwaves) Find a, b and h Attenuation const. Phase constant For distilled water For sea water Exercise: Lossy media propagation For each of the following determine if the material is low-loss dielectric, good conductor, etc. (a) Glass with µ r=1, e r=5 and s=10-12 S/m at 10 GHZ (b) Animal tissue with µ r=1, e r=12 and s=0.3 S/m at 100 MHZ (c) Wood with µ r=1, e r=3 and s=10-4 S/m at 1 khz Answer: (a) low-loss, a= 8.4x10-11 Np/m, b= 468 r/m, l= 1.34 cm, up=1.34x10 8, hc=168 W (b) (c) general, a= 9.75, b=12, l=52 cm, up=0.5x10 8 m/s, hc=39.5+j31.7 W Good conductor, a= 6.3x10-4, b= 6.3x10-4, l= 10km, up=0.1x10 8, hc=6.28(1+j) W Cruz-Pol, Skin depth Short cut! J Power Today s class Skin depth, d We know that a wave attenuates in a lossy medium until it vanishes, but how deep does it go? Is defined as the depth at which the electric amplitude is decreased to 37% Cruz-Pol, Cruz-Pol, Electrical Engineering, 6

Microwave Oven Most food are lossy media at

The power reaches the inside as soon as the oven

Cruz-Pol, where k is the direction of propagation

wave, i.e., the direction in which the EM wave is

Cruz-Pol, Waves - Summary Static charges > static

magnetic field, H Static magnet > static magnetic

& H(t) that are interdependent > electromagnetic

wave EM waves don t need a medium to propagate

7 Microwave Oven Most food are lossy media at microwave frequencies, therefore EM power is lost in the food as heat. Shortcut! You can use Maxwell s or use Find depth of penetration for potato which at 2.45 GHz has the complex permittivity given. The power reaches the inside as soon as the oven in turned on! Cruz-Pol, where k is the direction of propagation of the wave, i.e., the direction in which the EM wave is traveling (a unitary vector). Cruz-Pol, Waves - Summary Static charges > static electric field, E Steady current > static magnetic field, H Static magnet > static magnetic field, H Time-varying current > time varying E(t) & H(t) that are interdependent > electromagnetic wave Time-varying magnet > time varying E(t) & H(t) that are interdependent > electromagnetic wave EM waves don t need a medium to propagate Sound waves need a medium like air or water to propagate EM waves don t. They can travel in free space in the complete absence of matter. Look at a wind wave ; the energy moves, the plants stay at the same place. Cruz-Pol, Cruz-Pol, Power in a wave A wave carries power and transmits it wherever it goes Power and Poynting Vector The power density per area carried by a wave is given by the Poynting vector. Cruz-Pol, Electrical Engineering, 7

Power in a wave To get Power density in W/m 2 carried by an electromagnetic wave: Poynting

vector that shows where is the power going That s the Poynting Vector.

rst term Poynting Vector Derivation Taking the integral wrt volume Applying Theorem of

stored energy in E or H Which means that the total power coming out of a volume is either

Cruz-Pol, Ohmic losses due to conduction current Power: Poynting Vector Bluetooth antenna

a given volume is = to the decrease in time in energy stored minus the conduction losses.

8 Power in a wave To get Power density in W/m 2 carried by an electromagnetic wave: Poynting Vector Derivation Start with E dot Ampere s Apply vector identity But we need to have a vector that shows where is the power going That s the Poynting Vector. And end up with: Cruz-Pol, Cruz-Pol, Poynting Vector Derivation Substitute Faraday in 1 rst term Poynting Vector Derivation Taking the integral wrt volume Applying Theorem of Divergence Rearrange Cruz-Pol, Total power across surface of volume Rate of change of stored energy in E or H Which means that the total power coming out of a volume is either due to the electric or magnetic field energy variations or is lost in ohmic losses. Cruz-Pol, Ohmic losses due to conduction current Power: Poynting Vector Bluetooth antenna in car Waves carry energy and information Poynting says that the net power flowing out of a given volume is = to the decrease in time in energy stored minus the conduction losses. Cruz-Pol, Represents the instantaneous power density vector associated to the electromagnetic wave. Cruz-Pol, Electrical Engineering, 8

Cellphone power radiation Time Average Power

For the general case wave: Source: AnSys= Fred

The total power through a surface S is Note that

surface area needs to be perpendicular to the

thru. (give example of receiver antenna)

given S=3m 2 a z Cruz-Pol, Cruz-Pol, Solar

7 In free space, solar TEM wave at some latitude

panel of side 10cm on plane Answer; P tot =

9 Cellphone power radiation Time Average Power Density The Poynting vector averaged in time is For the general case wave: Source: AnSys= Fred German Cruz-Pol, Cruz-Pol, Total AVE Power in W The total power through a surface S is Note that the units now are in Watts Note that power nomenclature, P is not cursive. Note that the dot product indicates that the surface area needs to be perpendicular to the Poynting vector so that all the power will go thru. (give example of receiver antenna) Exercise Find average power received by antenna given S=3m 2 a z Cruz-Pol, Cruz-Pol, Solar Panels Optimum inclination of solar panels for maximum power transmission depends on geographical location. PE 10.7 In free space, solar TEM wave at some latitude & season can be measured to be H=0.2 cos (wt-bx) z A/m. Find the total power passing through a solar panel of side 10cm on plane Answer; P tot = =53mW x square plate at Hz Answer; P tot = 0mW! Ey magazine.php?issue_number= &article=gonzalez Cruz-Pol, Electrical Engineering, 9

by Determine the direction of wave travel and the average power density

Cell phone & brain Computer model for Cell phone Radiation inside the

6W/kg, (depends on frequency) http://www.ewg.

Phone/Samsung/Impression+%28SGH-a877%29/ Cruz-Pol, Human absorption 30-300

http://handheld-safety.com/sar.aspx http://www.fcc.

htm Cruz-Pol, * The FCC limit in the US for public exposure from cellular

6 W/kg) as averaged over one gram of tissue.

Cellphone Tower Safe Power Level At microwave frequencies, the power

10 Exercises: Power 2. A 5GHz wave traveling In a nonmagnetic medium with e r=9 is characterized by Determine the direction of wave travel and the average power density carried by the wave Answer: EM Wave propagation Applications and Concepts Cell phone & brain Computer model for Cell phone Radiation inside the Human Brain SAR=Specific Absorption Rate [W/Kg] FCC limit 1.6W/kg, (depends on frequency) Phone/Samsung/Impression+%28SGH-a877%29/ Cruz-Pol, Human absorption MHz is where the human body absorbs RF energy most efficiently nts/bulletins/oet56/oet56e4.pdf Cruz-Pol, * The FCC limit in the US for public exposure from cellular telephones at the ear level is a SAR level of 1.6 watts per kilogram (1.6 W/kg) as averaged over one gram of tissue. ICNIRP= Intl Commission of Non-ionizing radiation protection Exercise: Cellphone Tower Safe Power Level At microwave frequencies, the power density considered safe for humans is 1 mw/cm 2.(SAR varies by frequency and country) A cellphone tower radiates a wave with an electric field amplitude E that decays with distance as E(R) = 40/R [kv/m], where R is the distance in meters. What is the radius of the unsafe region? Answer: R = 460 m *(Europe) For 1000 mw/cm 2 R=15 m *(U.S.) Cruz-Pol, R Electrical Engineering, 10

Information Package, Sage Associates, Montecito, CA, 2000, www. sageassocciates.net.

Radiación en Teléfonos móviles Radar bands 6 Tips para Protegerte: 1. 2. 3. 4. 5.

pesar de que producen radiación noionizante Cruz-Pol, 6. 7. Mantén las llamadas cortas. Mantén distancia de 1 (2.

texto en vez *Coteja el nivel de radiación en tu modelo. Depende de la región.

com SAR levels Band Name HF, VHF, UHF L Nominal Freq Range 3-30 MHz0, 30-300 MHz, 3001000MHz Specific Bands 138-144 MHz 216-225,

11 Dr. S. Cruz-Pol, INEL 4152 Some internationally allowed standard levels of the of cell tower radiation Antennas hiding Australian standard limits the radiation level to 200 mw/cm2 Russia, Italy and Canada allows only 10 mw/cm2 China, 6 mw/cm2 Zealand 0.02 mw/cm2. United States allows 580 to 1,000 mw/cm2 New Radiofrequency Radiation Health Studies, Cruz-Pol, Wireless Antenna Site Consumer Information Package, Sage Associates, Montecito, CA, 2000, www. sageassocciates.net. (b) Tower concerns should be health, not aesthetics, Burlington Free Press, January 12, Radiación en Teléfonos móviles Radar bands 6 Tips para Protegerte: En 2011, la Organización Mundial de la Salud de la ONU clasificó a los teléfonos celulares en Categoría de Peligro de Cáncer, a pesar de que producen radiación noionizante Cruz-Pol, Mantén las llamadas cortas. Mantén distancia de 1 (2.5 cm) del cuerpo) Usa el cable auricular Usa bocina altoparlante, Apaga el bluetooth y WiFi cuando no lo estés usando Envía texto en vez *Coteja el nivel de radiación en tu modelo. Depende de la región. Los mismos modelos en Europa emiten menos radiación debido a exigencias de sus leyes. Busca en sarvalues.com SAR levels Band Name HF, VHF, UHF L Nominal Freq Range 3-30 MHz0, MHz, MHz Specific Bands MHz , MHz GHz (15-30 cm) GHz S 2-4 GHz (8-15 cm) GHz > C 4-8 GHz (4-8 cm) GHz X 8-12 GHz (2.5 4 cm) GHz Ku GHz GHz, K GHz GHz Ka GHz GHz V GHz GHz W GHz millimeter GHz GH, GHz Cruz-Pol, Electromagnetic Spectrum Radares Cruz-Pol, Cruz-Pol, Electrical Engineering, Application TV, Radio, Clear air, soil moist Weather observations Cellular phones TV stations, short range Weather Cloud, light rain, airplane weather. Police radar. Weather studies Water vapor content Cloud, rain Intra-building comm. Rain, tornadoes Tornado chasers 11

Decibel Scale In many applications need comparison of two powers, a power ratio, e.g.

rate, A Represents the rate of decrease of the magnitude of P ave(z) as a function of

land. a) Determine the power density incident upon the submarine antenna due to the EM wave

Yes, it s turquoise-blue due to its electromagnetic spectrum emission http://ece.uprm.

initial value at z=0 (sea surface)? Answer= 18.

are Antennas Designed to see the Visible part of RF Spectrum Normally humans have 3 types of

700nm(red) http://book.bionumbers.org/how-big-is-a-photoreceptor/ https://nei.nih.

org/wiki/tetrachromacy http://www.popsci.

12 Decibel Scale In many applications need comparison of two powers, a power ratio, e.g. reflected power, attenuated power, gain, The decibel (db) scale is logarithmic Attenuation rate, A Represents the rate of decrease of the magnitude of P ave(z) as a function of propagation distance` Note that for voltages, fields, and electric currents, the log is multiplied by 20 instead of 10. Cruz-Pol, A submarine at a depth of 200m receives signals at 1kHz from an antenna array on land. a) Determine the power density incident upon the submarine antenna due to the EM wave with Eo = 10V/m. [At 1kHz, sea water has er=81, s=4]. Submarine antenna Pure Water is blue? Yes, it s turquoise-blue due to its electromagnetic spectrum emission b) At what depth the amplitude of the power has decreased to 1% its initial value at z=0 (sea surface)? Answer= 18.3m Cruz-Pol, Remember Perfect dielectric = lossless Nonmagnetic means h r =1 Cruz-Pol, Eyes are Antennas Designed to see the Visible part of RF Spectrum Normally humans have 3 types of cones in their eyes that allows them to see short to long waves within 400nm(violet) to 700nm(red) e_size_of_cone_and_rod_cells_of_our_eyes Cruz-Pol, Electrical Engineering, 12

13 Light spectra Cruz-Pol, Electrical Engineering, 13

Electromagnetic Waves

Electromagnetic Waves Maxwell s equations predict the propagation of electromagnetic energy away from time-varying sources (current and charge) in the form of waves. Consider a linear, homogeneous, isotropic