lect 04© 2012 raymond p. jefferis iii1 satellite communications electromagnetic wave propagation...

LECT 04 © 2012 Raymond P. Jefferis III 1

Satellite CommunicationsElectromagnetic WavePropagation• Overview• Electromagnetic Waves• Propagation• Polarization• Antennas• Antenna radiation

patterns• Propagation Losses

Goldstone antenna at twilight, NASA


Reference

Reference is specifically made to the following highly recommended source:Kraus, J. D. and Marhefka, R. J., Antennas For All Applications, Third Edition, McGraw-Hill, 2002

from which the antenna radiation equations used below were drawn.


Overview

• Satellite communication takes place through the propagation of focused and directed electromagnetic (EM) waves

• Since both received and transmitted waves are simultaneously present at very different power levels, in a satellite, both frequency separation and EM field polarization are used to decouple the channels

Maxwell’s Equations


Maxwell’s equations in terms of free charge and current, WIKIPEDIA

Wave Equation


∂2u

∂t 2= c(u)2∇2u

For scalar variable, u (E & M Fields)

Solutions are sinusoids in time and space (waves)


EM Wave Propagation

• Electromagnetic (EM) waves propagate energy, contained in their electric and magnetic fields, through space with velocity v, which is the speed of light under the conditions of propagation.

Wikipedia


Transverse EM (Plane) Wave Properties

• Velocity of propagation (near light speed)• Electric field is normal to the magnetic field• Both electric and magnetic fields are normal

to direction of propagation (plane wave)• The relation of electric to magnetic fields is

a constant for the medium (air, vacuum)• Waves are polarized, as determined by the

direction of the electric field orientation


Impedance• The electric field strength E and magnetic field

intensity H in a propagating wave are related by,

H =1η

E

where,

η =με

μ= magnetic permeability Henry/meter]

μπ1-7Henry/meter] in vacuumε= dielectric constant

[Farads/meter] ε0 = 1/36π*10-8 [Farads/meter] in vacuumη = impedance of the medium

(η0 =376.7 Ohms in free space)


Impedance Change At Boundaries

• At a boundary between two media of differing impedances (air and raindrops for instance), Z1 and Z2 [Ohms]

– Part of the incident wave from Medium1 is reflected

– Part of the incident wave is transmitted into Medium2

Z1 =μ1

ε1

Z2 =μ2

ε2


Wave Energy• The electric and magnetic

energy densities in a plane wave are equal. [J/m2]

• The total energy is the sum of these energies. [J/m2]

wE =12εE2

wH =12μH 2

wE =wH

wT =wE +wH

wT =12 εE2 + 1

2 μH 2


Wave Energy Density

• The energy density of a plane wave is the Poynting energy, S [Watts/m2]

SRMS =EH =1η

E2 =εμ

E2

SAv =12

EH =12η

E2 =12

εμ

E2


Vertical Polarization Behavior• Radio frequency energy at frequency, f,

propagates • The wave propagates away from the

observer (into the paper), along the z-axis• Energy propagates with velocity, v,• As a function of distance, z, and time, t,

the vertical electric field is described by,

E =Ey =Emcos 2π f t−zv

⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥


Horizontal Polarization• Radio frequency energy at frequency, f ,

propagates • The wave propagates away from the

observer, along the z-axis• Energy propagates with velocity, v,• As a function of distance, z, and time, t,

the horizontal E-field is described by,

E =Ex =Emcos 2π f t−zv

⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥

Manipulated Variable Example

Run mCos example:

• Vary the frequency and observe the results

• Pick a position (say z = 0.5), and change the z-variable to see how the wave propagates past the selected location

LECT 04 © 2012 Raymond P. Jefferis III Lect 00 - 14

Antennas• Electromagnetic circuits comparable in size

to the wavelength of an alternating current• Have alternating electric and magnetic fields

resulting in Electromagnetic (EM) radiation• Have a polarization specified by the electric field

direction (horizontal or vertical)• Radiation pattern is affected by the shape of the

current-carrying conductor(s)• The EM radiation propagates in space



Vertically Polarized Antenna• Total antenna length typically λ/2• Electric field shown normal to the plane

of the earth (vertical)• Oscillating electric fields produce

accelerating and decelerating conduction electrons, with consequent radiation of EM-energy

• A magnetic field surrounds the current-carrying wire

• The phases of the electric and magnetic fields differ by 90 degrees


Horizontally Polarized Antenna• Total antenna length typically λ/2

where λ = c/f• Electric field shown parallel to the plane

of the earth (horizontal)• Oscillating electric fields produce

accelerating and decelerating conduction electrons, with consequent radiation of EM-energy

• A magnetic field surrounds the current-carrying wire

• The phases of the electric and magnetic fields differ by 90 degrees


Polarization Match Angles• A match angle, θM, is defined as the angular

polarization difference between a transmitting and a receiving antenna

• Smaller match angles result in greater coupling between transmitting and receiving antennas

• If the antennas are at opposite polarizations (vertical - horizontal) the received power will be zero, theoretically.


Circular Polarization• Radio frequency energy at frequency, f,

propagates as an EM wave, away from the observer, along the z-axis (into the paper)

• The energy propagates with velocity, v• The electric and magnetic fields rotate in

time (space) according to,

Ex =Emcos 2π f t−zv

⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥

Ey =Emcos 2π f t−zv

⎛⎝⎜

⎞⎠⎟+

π2

⎡

⎣⎢

⎤

⎦⎥


Circularly Polarized Antenna

Circular Polarization, Wikipedia

Note the spiral net electric field resolves into time-varying Ex and Ey components.Conductor (black); Ex => Green; Ey => Red

The Isotropic (Ideal) Antenna

• The gains of antennas can be stated relative to an isotropic ideal antenna as G [dBi], where G > 0.

• This antenna is a (theoretical) point source of EM energy

• It radiates uniformly in all directions• A sphere centered on this antenna would exhibit

constant energy per unit area over its surface• The gain of an isotropic antenna is 0 dBi

Lect 05 © 2012 Raymond P. Jefferis III Lect 00 - 21


Radiation Patterns of Antennas• Electric field intensity is a function of the radial

distance and the angle from the antenna• A radiation pattern can be plotted to show field

strength (shown as a radial distance) vs angle• The angle between half-power points (denoted as

HPBW) is a measure of the focusing (Gain) of the antenna. [Note: Half-power = 3 dB]

• Note: Antenna Gain is with respect to an ideal isotropic antenna (Gain = 1.0 or 0.0 dBi)


Antenna Gain Calculation• G = PA/PI

where, PI is the power per unit area radiated by an isotropic antenna, and PA is the antenna power per unit area radiated by a non-isotropic antenna,G is the amount by which the isotropic power would be multiplied to give the same power per unit area as the gain antenna exhibits in the chosen direction


Antenna Gain Calculation

• Pr = radiated power per unit area• W = total applied power• Rr = antenna radiation resistance• Im = maximum value of antenna current

G =πr2Pr

W

W =Im

2⎛⎝⎜

⎞⎠⎟

2

Rr


Antenna Gain and Aperture Calculations

G =πAe

λ2

Ae =ηA

G = antenna gainAe = effective aperture area = carrier wavelengthη = aperture efficiencyA = aperture area (πr2)


Half-Wave Dipole Power

Eθ =6Im

r

cosπ2

cosθ⎛⎝⎜

⎞⎠⎟

sinθ

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥

Pr =15Im

2

πr2

cosπ2

cosθ⎛⎝⎜

⎞⎠⎟

sinθ

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥

2

θ is the angle normal to the antenna


Dipole Radiation Patterns• Two dipole lengths shown:

L = λ/2 (half wave dipole)HPBW = 78˚Gain = 2.15 dBi

L = λ(full wave dipole)HPBW = 47˚Gain = 3.8 dBi

• The longer antenna focuses the energy into a more narrow beam and thus has higher Gain.

Electric field intensity, half-wave dipole


Half-Wave Dipole RadiationThe radiated field and power of a half-wave dipole antenna are expressed by:

E =cos

π2

⎛⎝⎜

⎞⎠⎟cosθ⎡

⎣⎢⎤

⎦⎥

sinθP : E2

Radiated power pattern, half-wave dipole


Half-Wave Dipole Radiation Pattern

zro = 0.000001;e0 = 1.0;e1 = Cos[p/2*Cos[theta]]/Sin[theta];e2 = e1^2;PolarPlot[{e2}, {theta, zro, Pi}, PlotStyle -> {Directive[Thick, Black]}, PlotRange -> Automatic]


Half-Power Beam Width

• The Half-Power Beam Width (HPBW) is defined as the included angle between the half-power points on the radiation pattern. The power is down by 3 dB at these points.

• For a half-wave dipole antenna this is calculated as shown on the Mathematica® notebook output that continues below.


Half-Wave Dipole HPBW Calculation

r1 = FindRoot[e1^2 - 0.5 == 0.0, {theta, 60.0 Degree}];Print[r1]w1 = theta /. r1Print[w1/Degree]

r2 = FindRoot[e1^2 - 0.5 == 0.0, {theta, 120.0 Degree}];Print[r2]w2 = theta /. R2Print[w2/Degree]Print[(w2 - w1)/Degree]


HPBW for Half-Wave Dipole

• From the foregoing notebook, the Half-Power Beam Width is found to be:HPBW = 78.0777 degrees

• At the outer edges of the beam (HPBW), the power will be 70.7% of the maximum power value.


Full-Wave Dipole Radiation

Power pattern, full-wave dipole

The radiated field and power of a full-wave dipole antenna are expressed, as a function of angle, by:

E =cos π cosθ[ ] +1

sinθP : E2


Full-Wave Dipole Radiation Pattern

zro = 0.000001;e0 = 1.0;en = 2.0;e1 = (Cos[p*Cos[theta]] + 1)/(Sin[theta]*en);e2 = e1^2;PolarPlot[{e2}, {theta, zro, p}, PlotStyle -> {Directive[Thick, Black]}]


Half-Power Beam Width

• The Half-Power Beam Width (HPBW) is defined as the included angle between half-power points on the radiation pattern. The power is down by 3 dB at these points.

• For a full-wave dipole antenna this is calculated as shown on the Mathematica® notebook output that continues below.


Full-Wave HPBW Calculationr1 = FindRoot[e1^2 - 0.5 == 0.0, {theta, 60.0 Degree}];Print[r1]w1 = theta /. r1Print[w1/Degree]

r2 = FindRoot[e1^2 - 0.5 == 0.0, {theta, 120.0 Degree}];Print[r2]w2 = theta /. r2Print[w2/Degree]

Print[(w2 - w1)/Degree]


HPBW for Full-Wave Dipole

• From the foregoing notebook, the Half-Power Beam Width is found to be:HPBW = 47.8351 degrees

• At the outer edges of the beam (HPBW), the power will be 70.7% of the full value.


Circular Aperture Antenna

• The electric field of a circular aperture antenna can be calculated from:

E[φ] =2λπD

J 1[(πD / λ)sinφ]sinφ

where, D/λgives the aperture diameter in wavelengths and ϕ is the angle relative to the normal to the plane of the aperture.


Radiated E-Field of Aperture Antenna

0.2 0.4 0.6 0.8 1.0

- 0.03- 0.02- 0.01

0.000.010.020.03

The Mathematica® notebook follows, for D/λ= 10:

E-field for aperture with D/λ = 10


Radiation Pattern of Aperture Antenna

Dlam = 10;e2 = (2.0/p*Dlam)*(BesselJ[1, p*Dlam*Sin[theta]])/Sin[theta];PolarPlot[Abs[e2]/100, {theta, -p/6, p/6}, PlotStyle -> {Directive[Thick, Black]}]


Radiated Power from an Aperture

• The normalized radiated power can be found from E2[ϕ] as shown below:

0.2 0.4 0.6 0.8 1.0- 0.04- 0.02

0.000.020.04

Normalized radiated power for aperture with D/λ= 10


Radiated Power CalculationDlam = 10;

e2 = (2.0/p*Dlam)*(BesselJ[1, p*Dlam*Sin[theta]])/Sin[theta];

PolarPlot[Abs[e2/100], {theta, -p/6, p/6}, PlotStyle -> {Directive[Thick, Black]},

PlotRange -> {{0, 1}, {-0.04, 0.04}}]


Half Power Beam Width

• The HPBW of an aperture having D/λ= 10 is calculated to be:5.89831 Degrees

• The Mathematica® notebook for this calculation follows:


Aperture HPBW Calculation

p20 =((2.0/p*Dlam)*

(BesselJ[1,p*Dlam*Sin[0.00001]])/Sin[0.00001])^2p2 = ((2.0/p*Dlam)*

(BesselJ[1,p*Dlam*Sin[theta]])/Sin[theta])^2/p20;r1 = FindRoot[p2 - 0.5 == 0.0, {theta,1 Degree}];w1 = theta /. r1;Print[w1/Degree]r2 = FindRoot[p2 - 0.5 == 0.0,{theta,-1 Degree}];w2 = theta /. r2Print[w2/Degree]Print[Abs[(w2 - w1)]/Degree]

Workshop 04 - Antenna HPBW

• A circular aperture antenna has D/λ= 20. Plot the radiation pattern of this antenna and calculate its Half Power Beam Width.

• What can you say about the aiming requirements for such an antenna mounted on a satellite?



Transmission Losses

Transmitted electromagnetic energy from a satellite is lost on its way to the receiving station due to a number of factors, including:

– Antenna efficiency – Rain/Cloud loss– Antenna aperture gain – Atmospheric loss– Path loss – Diffraction loss


Antenna Gain and Link LossesPt = transmitted powerPr = received powerAt = transmit antenna apertureAr = receive antenna apertureLp = path lossLa = atmospheric attenuation lossLd = diffraction lossesAntenna Gain (t or r):Gt/r = 4πAe t/r/λ2

Combined Antenna Gain (t + r):G = GtGr


Antenna GainAe = effective antenna apertureG = 4πAe/λ2 (Antenna Gain)d = antenna diameterλ = wavelengthη= aperture efficiency

Ae =ηAπ(d / 2)2

G =πλ2 Ae

G =ηA

πdλ

⎛⎝⎜

⎞⎠⎟

2

Compensating for Link Losses

• Increase antenna gain

• Increase power input to antenna

• Net effect: increase EIRP (Equivalent Isotropically Radiated Power)

- Make sure tracking of beam is accurate (target on beam axis).


EIRP

• Equivalent Isotropic Radiated Power

• – the equivalent power input that would be needed for an isotropic antenna to radiate the same power over the angles of interest



Path Loss Calculation• Effective Aperture (transmit or receive):

Ae = ηA• Effective Radiated Power:

EIRP = PtGt = PtηtAt

• Path Loss (for path length R):Lp = (4πR/λ2

• Received Power:Pr = EIRP*Gr/Lp

where,Gt = 4πAet/λ2 Gr = 4πAer/λ2


Decibel (dB) Scale Definition

• PdB = 10 log10 Pt/Pr

• Logarithmic scale changes division and multiplication into subtraction and addition

• dBW refers to power with respect to 1 Watt.

• Received power (Pratt & Bostian, Eq. 4.11):

• Pr = EIRP + Gr - Lp [dBW]


Received Power - dB Model

• (Pratt & Bostian, Eq. 4.11)Pr = EIRP + Gr - Lp - La - Lt - Lr [dBW]– EIRP => Effective radiated power

– Gr => Receiving antenna gain

– Lp => Path loss

– La => Atmospheric attenuation loss

– Lt => Transmitting antenna losses

– Lr => Receiving antenna losses


End

lect 04© 2012 raymond p. jefferis iii1 satellite communications electromagnetic wave propagation...

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