reciprocity, babinet principle, slot, microstrip and wideband antennas
TRANSCRIPT
Reciprocity, Babinet principle, slot, microstrip and wideband antennas
P. Hazdra, M. Mazanek,…[email protected] of Electromagnetic FieldCzech Technical University in Prague, FEEwww.elmag.org
v. 14.3.2016
Outline
• Effective height and aperture of an antenna• Reciprocity and reaction theorem• The Babinet principle• The slot antenna• The slot waveguide antenna• Microstrip antennas• Frequency‐independent antennas• Helix antennas
Katedra elektromagnetického pole 2
Transmitting and receiving antennas
3
Maximum power delivered to antenna occurs for conjugate matching Z∗
Induced voltage
Maximum power delivered to load occurs for conjugate matching Z∗
Receiving antenna – effective height
4
⋅
effective length
1d
/
/
0.64 0.5
0.64 0.5
Antenna as an aperture - Effective area
5
• Describes power capturing characteristics of the antenna when a wave impinges on it.• Relation between power at load and incoming power density
12 . . forconjugatematchingandlosslessantenna 8
1
Available power at the terminals of a receiving antenna
Power density of incident plane wave / (Poynting vector)
example: Maximum effective area of a elementary( ≪ ), lossless ( 0) dipole
81
202
38 0.119
⋅
Effective area (aperture)
6
4 4
4Maximum effective area of antenna with maximum directivity
Directivity of any antenna is proportional to its aperture
Power at the receiver 4
38 Constant ⋅ D 4 ⋅
32
Elementary dipole
, 4 ,
Maximum effective aperture of antenna
7
The physical significance of these apertures is that power from the incident plane wave is absorbed over an area of this size by the antenna and is delivered to the terminating resistance
4 4 10 . / 0.131
!vs physical aperture!
f 440MHz14 3 3 20
4 4 10 . / 3.7
Small dipole illuminated by plane wave
Katedra elektromagnetického pole 8
/10Physical vs. effective area
Small dipole illuminated by plane wave
9
/10
Physical vs. effective area
Reciprocity theorem for antennas
10
• Voltage is applied to the terminals of an antenna A, current at the terminals of another antenna B is measured
• Voltage is applied to the terminals of an antenna B, current at the terminals of another antenna A is measured
linear, passive, isotropic medium
If then More generally
Reciprocity and reaction theorem for antennas
11
⋅ ⋅ ⋅
Two set of sources , that generate fields ,
0 for
⋅ ⋅ 0 0
Reaction (coupling) between a source and a field ,
• “in any network composed of linear, bilateral, lumped elements, if one places a constant current (voltage) generator between two nodes (in any branch) and places a voltage (current) meter between any other two nodes (in any other branch), makes observation of the meter reading, then interchanges the locations of the source and the meter, the meter reading will be unchanged”.
0 for source‐free region
, ,
Arbitrary RLC
network, In terms of reactions:
Physical and circuit antenna parameters
Katedra elektromagnetického pole 12
The Babinet principle
13
Complementary screen
The impedance of complementary antennas
Dipole antenna (“metal”)
Slot antenna (“air”)
435476
The slot antenna
14
. .
/2 @ 3 GHz
/50
35476
2/ /2
The slot antenna
15
Radiation pattern of slot and dipole
Katedra elektromagnetického pole 16
The slot antenna
17
3547673 486Ω
The slot antenna
18
35476
The slot antenna
19
The slot antenna
20
The bat-wing antenna
21
The slot antenna array – radiating cavity (standing-wave array)
22
The slot antenna array – radiating cavity (standing-wave array) 8 x slot
23
• Common phase• Arbitrary amplitude distribution
The slot antenna array – radiating cavity
24
Surface current
/2Few λ
The slot antenna array
25
FTR
The slot antenna array – radiating cavity (standing-wave array) 4 x slot
26
The slot antenna array
27
Microstrip antennas
28
• Planar resonator designed to radiate, 70s• Printed on substrate cheap, reproducible, mass producement• Moderate gain (single element 7‐9 dBi, arrays..)• Can easily produce CP• Integration with microwave circuit (active antenna)• Usually low bandwidth• Losses in substrate should be considered
Rectangular patch antenna
29
Surface current density J .. Jx
2Δ
Rectangular patch antenna
30
Ez
Hy
Model of radiation: two slots of length W, separated by distance L
2 2 3 3
Microstrip antennas - feeding
31
sin
H
Lp x Wp
Lv
Lh
Proximity feeding with L‐probe
Microstrip line feed
Probe feed (coaxial connector)
Microstrip antennas – circular polarization
32
Microstrip antennas – circular polarization
33
Re (Z)
Im (Z)
Microstrip antennas – circular polarization
34
LHCP RHCP
ARS
Compact Microstrip antennas
35
Frequency independent antennas
Katedra elektromagnetického pole 36
4
• Constant pattern, impedance, polarization and phase center• Antenna specified by angles rather than by linear dimensions• Self‐scaling behavior• Babinet principle self‐complementary antenna (translation, rotation)
4 .
Self-complementary spiral antenna
37Piksa, P., Mazanekm, M.: A Self‐Complementary 1.2 to 40 GHz Spiral Antenna with Impedance Matching, Radioengineering, 2006
1.2 – 40 GHz
38
Log-Periodic Antennas• Entire shape cannot be solely specified by angles not truly frequency independent• A log‐periodic antenna is defined as a structure whose electrical properties vary
periodically with the logarithm of frequency.• Current distribution is the same for two frequencies separated by ratio ln 1/
⋯, is geometric ratio
100‐1100MHz, Gain ~ 6dBi• Moving phase center
Helix antennas
39
x
z
Diameter D
Turn spacing S
Circumference CGround Plane > /2
Number of turns N
Normal mode of radiation (broad side) x Axial mode of radiation (end fire)
Pitch Angle α
tan
John D. Kraus, 1947
Helix antennas
40
x
z
Diameter D
Entire
helix
length Ly
Normal mode of radiation (broadside) appears if:
D << , entire L << radiation like from small
dipole
Standing‐wave current
Linear polarization
Helix antennas
41
x
z
y
C ~ (3/4 < C/ < 4/3)• Travelling current
• Circular polarization
• Narrow mainbeam with minor sidelobes (Gain 10‐15dBi)
• HPBW ~ 1/N
• Wide bandwidth (30%)
Circumference
Axial Mode of Radiation (endfire) occurs if:
15C
1402 12
≅ /4
≅ 12 14∘
2
Helix antennas
42
1Standing wave current
Normal mode (broadside)
1Travelling wave currentAxial mode (endfire)
Katedra elektromagnetického pole 43
Helix antennas 0.42
D 0.1470.46
0.93D 0.33
1.03
Katedra elektromagnetického pole 44
Helix antennas 0.42
D 0.1470.46
0.93D 0.33
1.03
Electric field above the helix
Helix antennas
45
The effective area of antenna - derivation
46
Flux density in the „matched“ polarization
Random wave (noise from blackbody radiation), the two orthogonal polarization components (V/H or RHC/LHC) will vary
rapidly in intestity (unpolarized radiation), but have equal powers when averaged over long times
P12 , Ω A
122
4
Blackbody cavity
Noise power (per Hz) generated by a resistor at temp. Tk .. Boltzmann constant
Blackbody radiation flux (Rayleigh‐Jeans) approximation
A 4
Microstrip antennas – fractal geometry
47
polarization
0.21λc x 0.21λc x 0.15λc