Notes 21
Introduction to Antennas
1
ECE 3317 Applied Electromagnetic Waves
Prof. David R. Jackson Fall 2018
Introduction to Antennas
Antennas
An antenna is a device that is used to transmit and/or receive an electromagnetic wave.
Examples:
Cell-phone antenna (transmit and receive) TV antenna in your home (receive only) Wireless LAN antenna (transmit and receive) FM radio antenna (receive only) Satellite dish antenna (receive only) AM radio broadcast tower (transmit only) GPS position location unit (receive only) GPS satellite (transmit only)
Note: The antenna itself can always transmit or receive, but it may be used for only one of these functions in an application.
2
Introduction to Antennas (cont.)
For communication over long distances, to have lower loss (see below)
Where waveguiding systems (e.g., transmission lines) are impractical or inconvenient
When it is desired to communicate with many users at once
Antennas are often used for a variety of reasons:
Power loss from waveguiding system:
Power loss from antenna broadcast: 21/ r2 re α−
(always better for very large r)
3
rA B
Main properties of antennas:
Radiation pattern Beamwidth and Directivity (how directional the beam is) Sidelobe level Efficiency (power radiated relative to total input power) Polarization (linear, CP) Input Impedance Bandwidth (the useable frequency range)
4
Introduction to Antennas (cont.)
Reflector (Dish) Antenna
Very high bandwidth Medium to high directivity (directivity is determined by the size) Linear or CP polarization (depending on how it is fed) Works by focusing the incoming wave to a collection (feed) point
5
Ideally, the dish is parabolic in shape.
Introduction to Antennas (cont.)
Dipole Wire Antenna
Very simple Moderate bandwidth Low directivity Omnidirectional in azimuth Most commonly fed by a twin-lead transmission line Linear polarization ( Eθ , assuming wire is along z axis) The antenna is resonant when the length is about one-half free-space wavelength
Current
0 / 2L λ≈
6
(resonant)
Introduction to Antennas (cont.)
[ ]73inZ = ΩAt resonance :
Dipole Wire Antenna (cont.)
7
Introduction to Antennas (cont.)
The bow-tie antenna has flared dipole arms, which increases the bandwidth.
Folded Dipole Antenna
8
Introduction to Antennas (cont.)
The folded dipole is a variation of the dipole antenna. It has an input impedance that is 4 times higher than that of the regular dipole antenna.
[ ]292inZ = ΩAt resonance :Compatible with TV twin lead
[ ]0 300Z = Ω
Monopole Wire Antenna
This is a variation of the dipole, using a ground plane instead of a second wire.
Similar properties as the dipole Mainly used when the antenna is mounted on a conducing object or platform Usually fed with a coaxial cable feed
9
Introduction to Antennas (cont.)
Feeding coax
0 / 4h λ≈h
[ ]36.5inZ = ΩAt resonance :
Monopole Wire Antenna (cont.)
10
Introduction to Antennas (cont.)
Yagi Antenna
This is a variation of the dipole, using multiples wires (with one “reflector” and one or more “directors”.
Low bandwidth Moderate to high directivity Commonly used as a UHF TV antenna
Prof. Yagi
11
Introduction to Antennas (cont.)
Yagi Antenna (cont.)
UHF Yagi VHF Log-periodic
UHF Yagi
UHF Yagi
12
Introduction to Antennas (cont.)
Log-Periodic Antenna
This consists of multiple dipole antennas of varying lengths, connected together.
High bandwidth Moderate directivity Commonly used as a VHF TV antenna
13
Introduction to Antennas (cont.)
Beam
Log Periodic Antenna (cont.)
14
Introduction to Antennas (cont.)
Typical Outdoor TV Antenna
VHF Log-periodic
UHF Yagi
15
Introduction to Antennas (cont.)
Horn Antenna
It acts like a “loudspeaker” for electromagnetic waves.
High bandwidth Moderate directivity Commonly used at microwave frequencies and above Often used as a feed for a reflector antenna
16
Introduction to Antennas (cont.)
Horn Antenna (cont.)
Arno A. Penzias and Robert W. Wilson used a large horn antenna to detect microwave signals from the “big bang”
(Nobel Prize, 1978).
17
Introduction to Antennas (cont.)
Horn Antenna (cont.)
This is a variety called the “hoghorn” antenna (a combination of horn+reflector).
18
Introduction to Antennas (cont.)
Microstrip (Patch) Antenna
It consists of a printed “patch” of metal that is on top of a grounded dielectric substrate.
Low bandwidth Low directivity (unless used in an array) Low-profile (h can be made very small, at the expense of bandwidth) Can be made by etching Easily fed by microstrip line or coaxial cable Can be made conformable (mounted on a curved surface) Commonly used at microwave frequencies and above
01/ 22d
r
L λλε
≈ =
19
Introduction to Antennas (cont.)
Current
rεx
y
hL
W
Microstrip (Patch) Antenna (cont.)
20
Introduction to Antennas (cont.)
Dielectric Resonator Antenna (DRA)
It consists of a dielectric material (such as ceramic) on top of a grounded dielectric substrate.
Moderate to large bandwidth Low directivity (unless used in an array) Commonly used at microwave frequencies and above
The dielectric resonator antenna was invented by our
very own Prof. Long! rε
Cylindrical DRA
21
Introduction to Antennas (cont.)
Dielectric Resonator Antenna (cont.)
GPS antenna
22
Introduction to Antennas (cont.)
Leaky-Wave Antenna
23
2
0 00
1k kk aπβ
= − <
The wave is a “fast wave.”
pv c>
0pv c
kω ωβ
= > =Note:
This allows the wave to radiate from the slot.
Introduction to Antennas (cont.)
Rectangular waveguide
Slot
Air
x
y
24
0 0coszk k θ β= =
0 0cos / kθ β=
A narrow beam is created at angle θ0.
Leaky-Wave Antenna (cont.)
Introduction to Antennas (cont.)
0kβ <
0θ
z
y k
b
Antenna Radiation
We consider here the radiation from an arbitrary antenna.
The far-field radiation acts like a plane wave going in the radial direction. 25
r →∞"far field"
+ -
( ), ,r r θ φ
S
x
y
z
r
How far do we have to go to be in the far field?
26
2
0
2Drλ
>
Antenna Radiation (cont.)
+ -
( ), ,r r θ φSphere of minimum diameter D that encloses the antenna.
r
A derivation is given in the Antenna Engineering book: C. A. Balanis, Antenna Engineering, 4th Ed., 2016, Wiley.
Antenna Radiation (cont.)
The far-field has the following form: ˆ ˆ
ˆ ˆE E E
H H Hθ φ
θ φ
θ φ
θ φ
= +
= +
0EH
θ
φ
η=
0
EH
φ
θ
η= −
27
TMz
TEz
Depending on the type of antenna, either or both polarizations may be radiated (e.g., a vertical wire antenna radiates only TMz polarization.
x
y
z
E
HS
x
y
z
EH
S
The far-field Poynting vector is now calculated:
( ) ( )( )
*
* *
* *
0 0
22
0 0
121 ˆ ˆ ˆ ˆ21 ˆ2
1 ˆ2
1 ˆ2
S E H
E E H H
r E H E H
EEr E E
EEr
θ φ θ φ
θ φ φ θ
φθθ φ
φθ
θ φ θ φ
η η
η η
= ×
= + × +
= −
= + = +
0EH
θ
φ
η=
0
EH
φ
θ
η= −
28
Antenna Radiation (cont.)
Hence we have
( )22
0
1ˆ2
S r E Eθ φ η
= +
2
0
ˆ2E
S rη
=
or
Note: In the far field, the Poynting vector is pure real (no reactive power flow).
29
Antenna Radiation (cont.)
Radiation Pattern
The far field always has the following form:
( ) ( )0
, , ,jk r
FeE r Er
θ φ θ φ−
=
( ),FE θ φ ≡ Normalized ar - field electric fieldf
In dB:
( )( )( )10
,dB , 20log
,
F
Fm m
EE
θ φθ φ
θ φ
=
( ),m mθ φ = direction of maximum radiation
30
Radiation Pattern (cont.)
The far-field pattern is usually shown vs. the angle θ (for a fixed angle φ) in polar coordinates.
( )( )( )10
,dB , 20log
,
F
Fm m
EE
θ φθ φ
θ φ
=
31
0 dB
θ 30° 30°
60°
120°
150° 150°
120°
60°
mθ
0φ =
-10 dB
-20 dB
-30 dB
z
A “pattern cut”
Radiated Power
The Poynting vector in the far field is
( )( ) 2
20
, 1ˆ, ,2
FES r r
rθ φ
θ φη
=
The total power radiated is then given by
( )( ) 2
2 22
00 0 0 0
,ˆ sin sin
2
F
rad
EP S r r d d d d
π π π π θ φθ θ φ θ θ φ
η
= ⋅ =
∫ ∫ ∫ ∫
Hence we have
( )2
2
0 0 0
1 , sin2
FradP E d d
π π
θ φ θ θ φη
= ∫ ∫32
Directivity
In dB,
( ) ( )( )2
,,
/ 4r
rad
SD r
P rθ φ
θ φπ
≡ → ∞
The directivity in a particular direction is the ratio of the power density radiated in that direction to the power density that would be radiated in that direction if the antenna were an isotropic radiator (i.e., one that radiates equally in all directions).
( ) ( )dB 10, 10log ,D Dθ φ θ φ=
The directivity of the antenna in the directions (θ, φ) is defined as
Note: The directivity is sometimes referred to as the
“directivity with respect to an isotropic radiator”. 33
Directivity (cont.) The directivity is now expressed in terms of the far field pattern.
( ) ( )( )2
,,
/ 4r
rad
SD r
P rθ φ
θ φπ
≡ → ∞
( )
( )
( )
2
20
22
2
0 0 0
, 12
, 41 , sin
2
F
F
Er
D r rE d d
π π
θ φη
θ φ πθ φ θ θ φ
η
= → ∞
∫ ∫
Therefore,
( )( )
( )
2
22
0 0
4 ,,
, sin
F
F
ED
E d dπ π
π θ φθ φ
θ φ θ θ φ=
∫ ∫
Hence we have
34
Resonant half-wavelength dipole:
35
( )/ 2,maxD D D π φ= =
/ 2mθ π=
-9 -3 -6
0 dB
θ30° 30°
60°
120°
150° 150°
120°
60°
z
Short dipole
Directivity (cont.)
1.643D =
Feed 2l h=
x
y
z
h
h−
Short dipole: 1.5D =
( ) ˆsinFE θ θ θ=
Short dipole
Beamwidth
The beamwidth measures how narrow the beam is. (The narrower the beamwidth, the higher the directivity).
HPBW = half-power beamwidth
36
Sidelobes
The sidelobe level measures how strong the sidelobes are.
37
In this example the sidelobe level is about -13 dB
Sidelobes
Sidelobe level
Main beam
13dB−
Gain and Efficiency The radiation efficiency of an antenna is defined as
radr
in
PeP
≡
The gain of an antenna in the directions (θ, φ) is defined as
( ) ( ), ,rG e Dθ φ θ φ≡
( ) ( )dB 10, 10log ,G Gθ φ θ φ=
In dB, we have
38
rad
in
PP
==
power radiated by antenna
power input to antenna
Gain and Efficiency (cont.) The gain tells us how strong the radiated power density is in a
certain direction, for a given amount of input power.
39
( ) ( ) ( )2, / 4 ,r r inS e P r Dθ φ π θ φ =
( ) ( ) ( )2, / 4 ,r inS P r Gθ φ π θ φ =
( ) ( )( )2
,,
/ 4r
rad
SD r
P rθ φ
θ φπ
≡ → ∞
( ) ( ) ( )2, / 4 ,r radS P r Dθ φ π θ φ =
Therefore, in the far field:
Recall that
Receive Antenna
The Thévenin equivalent circuit of a wire antenna being used as a receive antenna is shown below.
Th inZ Z=
40
+
- ThVincE
+ - ThV
ThZ
2
2
0
W/m2
incinc
d
EP
η =
2W/mincdP = incident power density
[ ] ( )73inZ = Ω resonant half - wavelength dipole
41
The effective area determines the Thévenin voltage.
Assume an optimum conjugate-matched load:
+ -
*L ThZ Z=
incL eff dP A P=
Receive Antenna (cont.)
ThZ
ThV
LP = power absorbed by load
effA = effective area of antenna
2W/mincdP = incident power density
42
We have the following general formula*:
( ) ( )20, ,
4effA G λθ φ θ φπ
=
*A poof is given in the Antenna Engineering book: C. A. Balanis, Antenna Engineering, 4th Ed., 2016, Wiley.
Receive Antenna (cont.)
( ),G θ φ = gain of antenna in the direction of the incident signal
This assumes that the incoming signal is polarized in the optimum direction.
43
( ) ( )
( )
2o o 0
20
2
90 , 90 ,4
1.6434
21.643
4
effA G
l
λφ φπ
λπ
π
=
=
=
Effective area of a lossless resonant half-wave dipole antenna:
( )o 290 , 0.5230effA lφ =
Hence
Assuming the incident electric field is aligned along the wire and θ = 90o:
( )0 / 2l λ=
Receive Antenna (cont.)
+ - ThV
l
incE
44
Example
Find the receive power in wireless system shown below, assuming that the receiver is connected to an optimum conjugate-matched load.
[ ][ ]
[ ]
1 GHz
10 W
1 kmin
f
P
r
=
=
=
[ ]( )0 29.979 cmλ =
Receive Antenna (cont.)
Assume lossless antennas (G = D =1.643)
Receive Transmit
o90θ =
* 73 [ ]L ThZ Z= = Ω
x
z
r
2W/mincdP
rad inP P=
[ ]WinP
o90θ =
45
( ) ( )2
o 0290 , 1.643 , 1.643
4 4inc rad
eff dPA P
rλφπ π
= =
incL eff dP A P=
( )20
21.643 1.6434 4
radL
PPr
λπ π
=
81.54 10 [W]LP −= ×
Hence
The result is
Receive Antenna (cont.)
Recall: Gain of transmit antenna Gain of receive antenna
46
Effective area of dish antenna
( ) ( ) 20
4, ,effG A πθ φ θ φλ
=
eff phy apA A e=
In the maximum gain direction:
The aperture efficiency is usually less than 1 (less than 100%).
Receive Antenna (cont.)
phy
ap
Ae
=
=
physical area of dish
aperture efficiency