Electromagnetism INEL 4152 Ch 10 Sandra Cruz-Pol, Ph. D. ECE UPRM Mayag ü ez, PR

Outline  Plane Wave types general, lossy, lossless…. general, lossy, lossless….  Power in a Wave  Applications and Concepts

Cruz-Pol, Electromagnetics UPRM

Plane waves 10.1

Cruz-Pol, Electromagnetics UPRM A wave!  Start taking the curl of Faraday’s law  Then apply the vectorial identity  And you’re left with

Cruz-Pol, Electromagnetics UPRM A Wave Let’s look at a special case for simplicity without loosing generality: The electric field has only an x-componentThe electric field has only an x-component The field travels in z directionThe field travels in z direction Then we have

Cruz-Pol, Electromagnetics UPRM To change back to time domain  From phasor  …to time domain

Plane wave Propagation in Several Media

Cruz-Pol, Electromagnetics UPRM Several Cases of Media 1. Free space 2. Lossless dielectric 3. Lossy dielectric (general) 4. Good Conductor Recall: Permittivity  o =8.854 x [F/m] Permeability  o = 4  x [H/m]

Cruz-Pol, Electromagnetics UPRM 1. Free space 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 and wavelength  In what direction does it moves?

Where does it moves? Pick 3 times:  Plot Cruz-Pol, Electromagnetics UPRM

3. General Case (Lossy Dielectrics)  In general, we had and  From these we obtain  So, for a known material and frequency, we can find  j 

Cruz-Pol, Electromagnetics UPRMSummary Any medium Lossless medium (  =0) Low-loss medium (  ”/  ’<1/100) Good conductor (  ”/  ’>100) Units  [Np/m]  [rad/m]  u p  [m/s] [m] **In free space; **In free space;  o =8.85 x F/m  o =4  x H/m

Example: Water Cruz-Pol, Electromagnetics UPRM

Permittivity of water vs. freq.

Example 60Hz, (Low freq.) Find ,  and   For distilled water  For sea water  Attenuation const.  Phase constant

Example 10GHz, (microwaves) Find ,  and   For distilled water  For sea water  Attenuation const.  Phase constant

Cruz-Pol, Electromagnetics UPRM Intrinsic Impedance,   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

Applet Cruz-Pol, Electromagnetics UPRM See Applet by Daniel Roth at

Cruz-Pol, Electromagnetics UPRM Note…  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, Electromagnetics UPRM Loss Tangent  If we divide the conduction current by the displacement current

Cruz-Pol, Electromagnetics UPRM Relation between tan  and  c

Cruz-Pol, Electromagnetics UPRM 2. Lossless dielectric  Substituting in the general equations:

Cruz-Pol, Electromagnetics UPRM Review: 1. Free Space  Substituting in the general equations:

Cruz-Pol, Electromagnetics UPRM 4. Good Conductors  Substituting in the general equations: Is water a good conductor???

Cruz-Pol, Electromagnetics UPRMSummary Any medium Lossless medium (  =0) Low-loss medium (  ”/  ’<1/100) Good conductor (  ”/  ’>100) Units  [Np/m]  [rad/m]  u c  [m/s] [m] **In free space; **In free space;  o =8.85 x F/m  o =4  x H/m

Ejemplo  In a free space,  Find J d and E Cruz-Pol, Electromagnetics UPRM

Skin depth,   Is defined as the depth at which the electric amplitude is decreased to 37% We know that a wave attenuates in a lossy medium until it vanishes, but how deep does it go?

Cruz-Pol, Electromagnetics UPRM Microwave Oven Most food are lossy media at microwave frequencies, therefore EM power is lost in the food as heat.  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, Electromagnetics UPRM Short Cut!  You can use Maxwell’s or use 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, Electromagnetics UPRM 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

Cruz-Pol, Electromagnetics UPRM 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, Electromagnetics UPRM Exercises: 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 (d) Relative permittivity of material (e) Electric field phasor Answer: +y, =1.26m, u p = 2 x 10 8 m/s,2.25,

Power and Poynting Vector

Cruz-Pol, Electromagnetics UPRM Power in a wave  A wave carries power and transmits it wherever it goes The power density per area carried by a wave is given by the Poynting vector.

Cruz-Pol, Electromagnetics UPRM Poynting Vector Derivation  Start with E dot Ampere’s  Apply vector identity  And end up with:

Cruz-Pol, Electromagnetics UPRM Poynting Vector Derivation…  Substitute Faraday in 1 rst term Rearrange

Cruz-Pol, Electromagnetics UPRM Poynting Vector Derivation…  Taking the integral wrt volume  Applying Theorem of Divergence  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. Total power across surface of volume Rate of change of stored energy in E or H Ohmic losses due to conduction current

Cruz-Pol, Electromagnetics UPRM Power: Poynting Vector  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. Represents the instantaneous power density vector associated to the electromagnetic wave.

Bluetooth antenna in car car Cruz-Pol, Electromagnetics UPRM

Cellphone power radiation Cruz-Pol, Electromagnetics UPRM Source: AnSys= Fred German

Cruz-Pol, Electromagnetics UPRM Time Average Power density  The Poynting vector averaged in time is  For the general case wave:

Cruz-Pol, Electromagnetics UPRM Total 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)

Cruz-Pol, Electromagnetics UPRM PE 10.7 In free space, solar TEM wave at some latitude & season can be measured to be H=0.2 cos (  t-  x) z A/m. Find the total power passing through a solar panel of side 10cm on plane  square plate at Answer; P tot = =53mW HzHz EyEy x Answer; P tot = 0mW!

Solar Panels magazine.php?issue_number= &article=gonzalez Optimum inclination of solar panels for maximum power transmission depends on geographical location.

Exercises: Power 2. A 5GHz wave traveling In a nonmagnetic medium with  r =9 is characterized by Determine the direction of wave travel and the average power density carried by the wave   Answer:

Cruz-Pol, Electromagnetics UPRM TEM wave Transverse ElectroMagnetic = plane wave   There are no fields parallel to the direction of propagation,   Only perpendicular (=transverse).   If have an electric field E x (z) …then must have a corresponding magnetic field H y (z)   The direction of propagation is

Cruz-Pol, Electromagnetics UPRM Polarization: Why do we care??  Antenna  Antenna applications – Antenna can only TX or RX a polarization it is designed to support. Straight wires, square waveguides, and similar rectangular systems support linear waves (polarized in one direction) Round waveguides, helical or flat spiral antennas produce circular or elliptical waves.  Remote  Remote Sensing and Radar Applications – Many targets will reflect or absorb EM waves differently for different polarizations. Using multiple polarizations can give more information and improve results.  Absorption  Absorption applications – Human body, for instance, will absorb waves with E oriented from head to toe better than side-to-side, esp. in grounded cases. Also, the frequency at which maximum absorption occurs is different for these two polarizations. This has ramifications in safety guidelines and studies.

Cruz-Pol, Electromagnetics UPRM

Outline  Origin  Maxwell Equations explain waves  Phasors and Time Harmonic fields Maxwell eqs for time-harmonic fields Maxwell eqs for time-harmonic fields  Cases general, lossy, lossless…. general, lossy, lossless….  Wave Power  Applications and Concepts

Cruz-Pol, Electromagnetics UPRM Cell phone & brain  Computer model for Cell phone Radiation inside the Human Brain  SAR= Specific Absorption Rate [W/Kg] FCC limit 1.6W/kg, ~.2mW/cm 2 for 30mins Phone/Samsung/Impression+%28SGH-a877%29/ Phone/Samsung/Impression+%28SGH-a877%29/

Human absorption  MHz is where the human body absorbs RF energy most efficiently   nts/bulletins/oet56/oet56e4.pdf nts/bulletins/oet56/oet56e4.pdf nts/bulletins/oet56/oet56e4.pdf  permissible-exposure.htm  * 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. Cruz-Pol, Electromagnetics UPRM

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)|=3000/R [V/m], where R is the distance in meters. What is the radius of the unsafe region?   Answer: m

Radiación en Teléfonos móviles 6 Tips para Protegerte: 6 Tips para Protegerte: Mantén las llamadas cortas Mantén distancia de 1“ (2.5 cm) del cuerpo) Usa el cable auricular Usa bocina altoparlante, Apaga el bluetooth, GPS 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 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 no-ionizante

Cruz-Pol, Electromagnetics UPRM Radar bands Band Name Nominal Freq Range Specific Bands Application HF, VHF, UHF 3-30 MHz0, MHz, MHz MHz , MHz TV, Radio, L 1-2 GHz (15-30 cm) GHz Clear air, soil moist S 2-4 GHz (8-15 cm) GHz > Weather observations Cellular phones C 4-8 GHz (4-8 cm) GHz TV stations, short range Weather X 8-12 GHz (2.5–4 cm) GHz Cloud, light rain, airplane weather. Police radar. Ku GHz GHz, Weather studies K GHz GHz Water vapor content Ka GHz GHz Cloud, rain V GHz GHz Intra-building comm. W GHz GH, GHz Rain, tornadoes millimeter GHz Tornado chasers

Cruz-Pol, Electromagnetics UPRM Electromagnetic Spectrum

Radares UPRM Cruz-Pol, Electromagnetics UPRM

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  Note that for voltages, fields, and electric currents, the log is multiplied by 20 instead of 10.

Attenuation rate, A  Represents the rate of decrease of the magnitude of P ave (z) as a function of propagation distance`

Cruz-Pol, Electromagnetics UPRM Submarine antenna A submarine at a depth of 200m uses an antenna array to receive signal transmissions at 1kHz.   Determine the power density incident upon the submarine antenna due to the EM wave with |E o |= 10V/m.   [At 1kHz, sea water has  r =81,  =4].   At what depth the amplitude of E has decreased to 1% its initial value at z=0 (sea surface)?

Cruz-Pol, Electromagnetics UPRMSummary Any medium Lossless medium (  =0) Low-loss medium (  ”/  ’<1/100) Good conductor (  ”/  ’>100) Units  [Np/m]  [rad/m]  u c  [m/s] [m] **In free space; **In free space;  o =8.85 x F/m  o =4  x H/m

Cruz-Pol, Electromagnetics UPRM Exercise: Lossy media propagation For each of the following determine if the material is low-loss dielectric, good conductor, etc. (a) (a) Glass with  r =1,  r =5 and  = S/m at 10 GHZ (b) (b) Animal tissue with  r =1,  r =12 and  =0.3 S/m at 100 MHZ (c) (c) Wood with  r =1,  r =3 and  =10 -4 S/m at 1 kHZ Answer: (a) (a) low-loss,  x   Np/m  r/m  cm  u p  x    c  (b) (b) general,  cm  u p  x   m/s  c  j31.7  (c) (c) Good conductor,  x    x    km  u p  x    c  j 

Cruz-Pol, Electromagnetics UPRM Who was NikolaTesla?  Find out what inventions he made  His relation to Thomas Edison  Why is he not well known? v=i-j-1j2gD28&feature=related

Pure Water is blue  Is turquoise blue due to its electromagnetic spectrum emission  Cruz-Pol, Electromagnetics UPRM