fundamentals of antennas carlos a. fernandes
TRANSCRIPT
Antennas and Propagation - Master in Aerospace Engineering
Carlos A. Fernandes
Fundamentals of Antennas
ANTENNAS AND PROPAGATION - MAero [email protected] 2
Source Transmission structure Antenna Radiation
4.1 Introduction to antennas
𝒁𝟎𝒁𝑻𝑬
ANTENNAS AND PROPAGATION - MAero [email protected] 3
Source Transmission structure Antenna Radiation
4.1 Introduction to antennas
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4.1 Introduction to antennas
Most visible type of antennas
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Half-wavelength dipole radiation
l / 2
4.4 Antenna radiation
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Can be viewed as a section of a largerantenna
jyx
z
r
Rq
iq
ijir
dldl < l
4.2 Hertz dipole
ഥ𝐀 =𝜇
4𝜋ҧ𝐉 𝑑𝑉
𝑒−𝑗𝑘 𝑅
𝑅
Infinitesimal current
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Radiation fields
4.2 Hertz dipole
2𝜋 Τ𝑅 𝜆 sphericalwave
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Radiation fields
4.2 Hertz dipole
jy
x
z
r
Rq
iq
ijir
dl
Infinitesimal current
sphericalwave
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4.3 Radiation pattern
= ℜ 𝑺 + 𝑗 ℑ 𝑺 (𝑔𝑒𝑛𝑒𝑟𝑎𝑙 𝑐𝑎𝑠𝑒)
𝑈 = 𝑟2 𝑺
z
x
y
j
3𝐷 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑈/𝑈𝑚𝑎𝑥∝ (sin 𝜃)𝟐
(𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑜𝑓 𝜑 𝑓𝑜𝑟 𝐻. 𝐷. )
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Polar representation
4.3 Radiation pattern
𝐸 − 𝑝𝑙𝑎𝑛𝑒 𝐻 − 𝑝𝑙𝑎𝑛𝑒
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Polar representation
4.3 Radiation pattern
𝐸 − 𝑝𝑙𝑎𝑛𝑒 𝐻 − 𝑝𝑙𝑎𝑛𝑒
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50 40 30 20 10 0
(u1)
(u2) (u3)AL360P AL560
AL760
Anechoic chamber – roll over azimuth configuration
(g2) (g3)
(g1)
RXTX
Controller
PC
4.3 Radiation pattern
Antena under test
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Receive antenna
Antenna under test
Main lobe
Secondary lobes
4.3 Radiation pattern
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Anechoic chamber – roll over azimuth configuration
4.6 Radiation pattern
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4.3 Radiation pattern
Types of radiation pattern
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Rectangular horn (directive pattern)
4.3 Radiation pattern
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4.3 Radiation pattern characterization
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4.4 Directivity and Gain
Directivity of Hertz dipole
,
නsin3𝜃 = −3
4cos( 𝜃) +
1
12cos(3𝜃)
𝑈(𝜃)
→ 𝐷 = 1.5 @ 𝜃 =𝜋
2(1.76 dBi)
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4.4 Directivity and Gain
Directivity estimation𝜃1
𝑃𝑟 ≈ 𝑈𝑚න
0
2𝜋
න
0
𝜃1
sin 𝜃 𝑑𝜃 𝑑𝜑 = 2𝜋𝑈𝑚 −cos𝜃 0𝜃1
= 2𝜋𝑈𝑚 −cos𝜃1 + 1 𝑆𝑒 𝜃 ≪ 1, cos𝜃 ≈ 1 −𝜃2
2
= 𝜋 𝑈𝑚 𝜃12 =
𝜋
4𝑈𝑚 𝜃3𝑑𝐵
2 ≈ 𝑈𝑚 𝜃3𝑑𝐵2
(𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑣𝑖𝑡𝑦)
𝐷 =4𝜋 𝑈𝑚
𝑈𝑚 𝜃3𝑑𝐵2
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4.4 Directivity and Gain𝐷(𝜃, 𝜑) =
𝑈(𝜃, 𝜑)
𝑃𝑟/4𝜋
~𝑃𝑖
𝑃𝑟
Gain
𝐺(𝜃, 𝜑) =𝑈(𝜃, 𝜑)
𝑃𝑖/4𝜋
[dBi]
𝐺𝑑𝐵 = 10 log𝐺
𝐺𝑑𝑖𝑝[dBd]
Τλ 2 dipole
𝐺𝑑𝑖𝑝 = 1.64
Γi = 0=𝑃𝑟𝑃𝑖
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1 medida
2 medida
~
AETSonda
PP
Sonda
P~P
Cornetapadrao
G [dBi]
f [GHz]
Aspecto tipico da curva de calibracao
de uma corneta padrao
Gain comparison method
𝐺𝑑𝐵 = 𝐺𝑝𝑑𝐵 + 𝑃1𝑑𝐵𝑚 − 𝑃2𝑑𝐵𝑚
𝐺
𝐺𝑝
4.4 Directivity and Gain
𝑃𝑖 𝑃1
𝑃2𝑃𝑖
1𝑠𝑡 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡
2𝑛𝑑 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡
𝐴𝑈𝑇𝑝𝑟𝑜𝑏𝑒
𝑝𝑟𝑜𝑏𝑒𝑆𝑡𝑑 𝑔𝑎𝑖𝑛ℎ𝑜𝑟𝑛
𝑃1 ∝ 𝐺 𝑃𝑖
𝑃2 ∝ 𝐺𝑝 𝑃𝑖
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4.5 Input impedance
𝑍𝐴 = 𝑅𝑟 + 𝑅𝐿 + 𝑗 𝑋𝐴
~𝑅𝐴
𝑋𝐴
𝑃𝑟
Application to the Hertz dipole
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Hertz dipole l/2 dipole
4.5 Input impedance
𝑍𝐴 = 𝑅𝑟 + 𝑅𝐿 + 𝑗 𝑋𝐴 = 𝑅𝐴 + 𝑗 𝑋𝐴
= 0 in the resonance
𝐹𝑟𝑒𝑞 [GHz] 𝐹𝑟𝑒𝑞 [GHz]
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4.5 Input impedance (l/2 dipole)
|𝛤|
1.5 GHz
2.2 GHz
𝑩~𝟏𝟎%
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Polarization elipse
4.6 Polarization
iq
ij
ℰ(t)
b
a g
Eq
Ejleft-hand
right-hand
linear,
circular
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Polarization mismatch (coordinate system)
4.6 Polarization
𝑐𝑝 = ത𝐞i ∙ ത𝐞a∗ 2 = cos ҧ𝜉
2Ƹ𝐢𝜃
Ƹ𝐢𝜑
ො𝐞a
ො𝐞i𝜉
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q
180 90 0 90 180
180 90 0 90 180
4.7 Phase center
d
Eixo de rotação
Posição do centro de fase
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4.7 Phase center
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4.7 Phase center
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4.8 Band width
Gain, SLL
Input impedance
Polarization
Efficiency
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Input reflection of l/2 dipole vs frequency
4.8 Band width
Reflection coefficient – magnitude and phase
𝐿𝐵 =0.15 GHz
1.8 GHz= 8.33%
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Input reflection of a UWB antenna
4.8 Band width
Reflection coefficient – magnitude
𝐿𝐵 3.5 ∶ 1
10.5 𝐺𝐻𝑧
3 GHz
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Received power, Friis formula
4.8 Effective aperture
𝑆𝑖 𝐴
[W/m2] [m2]
𝑒𝑀
𝑍𝐿Antenna
Load
𝑃𝑅 =1
2𝑅𝐿 𝐼𝐿
2 =𝑉𝐿
2𝑅𝐿2 𝑍𝐴 + 𝑍𝐿
2=
𝑉𝐿2
8 𝑅𝑟𝑐𝑜𝑚 𝑍𝐿 = 𝑍𝐴
∗
𝑃𝑅 =
ഥ𝑬 𝟐
2 𝑍0
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Received power, Friis formula
4.8 Effective aperture
𝑍𝐿Antenna
Load𝑃𝑅 = 𝑆𝑖𝐴𝑒𝑀 𝑃𝑅 =
𝑉𝐿2
8 𝑅𝑟𝐴𝑒𝑀 =
1
𝑆𝑖
𝑉𝐿2
8 𝑅𝑟
Application to the Hertz dipole
𝑑ℓ ≪ ℓ
𝑉 = ത𝐸 𝑑ℓ
=ഥ𝑬 2
2 𝑍0𝐴𝑒𝑀 =
3𝜆2
8 𝜋
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Received power, Friis formula
4.8 Effective aperture
𝑍𝐿Antenna
Load
𝑑ℓ ≪ ℓ
𝐴𝑒𝑀 =3𝜆2
8 𝜋
𝐷 = 𝑐𝑘 𝐴𝑒𝑀
3
2= 𝑐𝑘
3𝜆2
8 𝜋𝑐𝑘 =
4𝜋
𝜆2𝐷 =
4𝜋
𝜆2𝐴𝑒𝑀
𝜃2𝜃1 =𝜆2
𝐴𝑒𝑀
Universal constant
Use Hertz dipole results to obtain 𝑐𝑘
𝐷 = 1.5
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Received power, Friis formula
4.8 Effective aperture
𝐺𝑇(𝜃𝑇, 𝜑𝑇)
𝑟 𝐺𝑅(𝜃𝑅 , 𝜑𝑅)
ReceiverMatchingcircuit
Matchingcircuit
Free space loss
𝑆𝑖 𝑟 =𝑃𝑖
4𝜋𝑟2[𝑊/𝑚2]𝐺𝑇 𝜃𝑇 , 𝜑𝑇
𝑃𝑅 𝑟 =𝑃𝑖
4𝜋𝑟2[𝑊]𝐺𝑇 𝜃𝑇, 𝜑𝑇 𝐴𝑒𝑅(𝜃𝑅, 𝜑𝑅)
𝑃𝑅(𝑟) = 𝑃𝑖 𝐺𝑇 𝜃𝑇 , 𝜑𝑇 𝐺𝑅 𝜃𝑅 , 𝜑𝑅
𝜆
4 𝜋 𝑟
2
[𝑊]𝑐𝑝 𝑐𝑖 𝑐𝑚
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Received power, Friis formula
4.8 Effective aperture
𝑟
𝐺𝑇(𝜃𝑇, 𝜑𝑇)𝐺𝑅(𝜃𝑅 , 𝜑𝑅)
ReceiverMatchingcircuit
Matchingcircuit
𝑃𝑅 = 𝑃𝑖 𝐺𝑇 𝜃𝑇 , 𝜑𝑇 𝐺𝑅 𝜃𝑅, 𝜑𝑅
𝜆
4 𝜋 𝑟
2
𝑐𝑝 𝑐𝑖 𝑐𝑚
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What is the limit on the received power (ex communications)
𝑃𝑖 = 43 𝑑𝐵𝑚, 𝐺𝑇 = 20 𝑑𝐵𝑖, 𝐺𝑅 = 73 𝑑𝐵𝑖, 𝑑 = 280 Mkm, 𝑓 = 8 GHz
𝑃𝑅 = −143. 5 𝑑𝐵𝑚 (down-link usually not done directly )
4.9 Thermal noise
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4.9 Thermal noise
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4.9 Thermal noiseEffect on received power (ex radiation pattern measurement)
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Noise in a resistor
Electrons in any resistor 𝑅 at physical temperature 𝑇 ≠ 0 exhibit random
motion, responsible for a fluctuating resistance, and associated fluctuating
voltage across the resistor terminals 𝑉 = 0, 𝑉𝑟𝑚𝑠 = 𝑉2 ≠ 0. It exists
even if a current is not flowing in the resistor.
𝑅
𝑇
Physical resistor in open circuit
𝑉𝑟𝑚𝑠
𝐾 Boltzman constant, 1.38 × 10−23 [J/K]
𝑇 Absolute physical temperature [K]
∆𝑓 Bandwidth [Hz]
Ex: 𝑇 = 300 𝐾, 𝑅 = 50 𝛺, ∆𝑓 = 10 𝑀𝐻𝑧 → 𝑉𝑟𝑚𝑠 = 2.88 𝜇𝑉
𝑉𝑟𝑚𝑠 = 4 𝐾 𝑇 𝑅 ∆𝑓 [V]
Nyquist and Johnson (researchers from Bell
Labs) showed in 1928 that, in open circuit,
the root mean square of this voltage is
4.9 Thermal noise
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the noise power transferred to the load is
4.9 Thermal noiseNoise in a resistor
𝑁 =𝑉𝑟𝑚𝑠2
4 𝑅
𝑅
𝑅𝑁
Equivalent circuit
𝑅
𝑇
Physical resistor
“Ideal noiseless”
resistors
Resistor 𝑅 connected to a load with the same value 𝑅
The transferred noise power is independent of 𝑅 value (as long
as the load has the same value as the resistor).
𝑉𝑟𝑚𝑠
𝑉𝑟𝑚𝑠
Ex: 𝑇 = 300 𝐾, ∆𝑓 = 10 𝑀𝐻𝑧 → 𝑁 = 0.0414 𝑝𝑊 (−103 𝑑𝐵𝑚)
𝑉𝑟𝑚𝑠 = 4 𝐾 𝑇 𝑅 ∆𝑓
𝑇 = 150 𝐾 → 𝑁 = 0.0414 𝑝𝑊 (−106 𝑑𝐵𝑚)
= 𝐾 𝑇 ∆𝑓
4.9 Thermal noiseEquivalent noise temperature
Very small noise power values are impractical to handle in calculations. It is easier to introduce the concept of equivalent noise temperature 𝑇𝑒 even if the loss mechanism is not purely thermal, and work only with these temperatures instead.
𝑇𝑒 =𝑁
𝐾 ∆𝑓
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4.10 Antenna noise temperatureInternal noise temperature
Antennas contribute with two noise terms:
𝑁𝐴𝑖 associated with its loss resistance 𝑅𝐿𝑁𝐴𝑒 associated with external noise captured through the radiation
pattern.
𝑃𝑅 = 𝜂 𝑃𝑖𝑛 =𝑅𝑟𝑎𝑑
𝑅𝑟𝑎𝑑 + 𝑅𝐿𝑃𝑖𝑛
𝑁𝐴𝑖 = 𝐾 𝑇𝐴 1 − 𝜂 𝛥𝑓
𝑃𝑖𝑛 = 𝑆𝑖 𝐴𝑒𝑀 𝑃𝑅
𝑁𝐴 = 𝑁𝐴𝑖 + 𝑁𝐴𝑒
𝑇𝐴𝑖 = 𝑇𝐴 1 − 𝜂
𝐾 𝛥𝑓 𝑇𝐴 = 𝐾 𝛥𝑓( 𝑇𝐴𝑖 + 𝑇𝐴𝑒) 𝑇𝐴 = 𝑇𝐴𝑖 + 𝑇𝐴𝑒
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4.10 Antenna noise temperatureExternal noise temperature
𝑇𝐴𝑒 =1
4𝜋න
0
2𝜋
න
0
𝜋
𝑇𝐵 𝜃, 𝜑 𝐺 𝜃, 𝜑 sin 𝜃 𝑑𝜃 𝑑𝜑
𝐺 𝜃, 𝜑 - Antenna radiation pattern
External noise sources associated with 𝑁𝐴𝑒:
• Man-made noise;
• Atmospheric noise;
• Galactic noise;
• Cosmic background.
𝑁𝐴𝑒 = 𝐾 𝑇𝐴𝑒 ∆𝑓
𝑇𝐵 𝜃, 𝜑 = 𝜖 𝑇𝑝 is the brightness temperature of the source, where 𝑇𝑝is the physical temperature of the source and its emissivity is 0 < 𝜖 < 1
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4.14 Noise temperatureBrightness temperature
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A – Quiet Sun
B – Moon
C – Galactic noise
D – Cosmic background
4.14 Noise temperatureBrightness temperature
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Antenna noise temperatureExternal noise temperature
𝑇𝐴𝑒 ≈ 𝑇𝐵 𝜃0, 𝜑01
4𝜋න
0
2𝜋
න
0
𝜋
𝐺 𝜃, 𝜑 sin 𝜃 𝑑𝜃 𝑑𝜑
External noise sources associated with 𝑁𝐴𝑒:
In the specific case of a high directivity antenna, when its beamwidthcaptures only a small portion of an extended noise source, so that 𝑇𝐵 𝜃, 𝜑 can be considered constant within the antenna main beam, we can write:
= 1𝑇𝐴𝑒 ≈ 𝑇𝐵 𝜃0, 𝜑0
Extendednoise source