1. 1
Chapter 2
Fundamental Properties
of Antennas
ECE 5318/6352
Antenna Engineering
Dr. Stuart Long
2. 2
IEEE Standards
Definition of Terms for Antennas
IEEE Standard 145-1983
IEEE Transactions on Antennas and
Propagation Vol. AP-31, No. 6, Part II, Nov. 1983
3. 3
Radiation Pattern
(or Antenna Pattern)
“The spatial distribution of a quantity which
characterizes the electromagnetic field
generated by an antenna.”
4. 4
Distribution can be a
Mathematical function
Graphical representation
Collection of experimental data points
5. 5
Quantity plotted can be a
Power flux density W[W/m²]
Radiation intensity U [W/sr]
Field strength E [V/m]
Directivity D
7. 7
Graph can be
Amplitude field |E| or power |E|² patterns
(in linear scale) (in dB)
8. 8
Graph can be
2-dimensional or 3-D
most usually several 2-D “cuts” in principle
planes
9. 9
Radiation pattern can be
Isotropic
Equal radiation in all directions (not physically realizable, but valuable for comparison purposes)
Directional
Radiates (or receives)
more effectively
in some directions than in others
Omni-directional
nondirectional in azimuth, directional in elevation
10. 10
Principle patterns
E-plane
Plane defined by E-field and direction of maximum radiation
H-plane
Plane defined by H-field and direction of maximum radiation
(usually coincide with principle planes of the coordinate system)
12. 12
Radiation pattern lobes
Major lobe (main beam) in direction of maximum radiation (may be more than one)
Minor lobe - any lobe but a major one
Side lobe - lobe adjacent to major one
Back lobe – minor lobe in direction exactly opposite to major one
13. 13
Side lobe level or ratio (SLR)
(side lobe magnitude / major lobe magnitude)
- 20 dB typical
< -50 dB very difficult
Plot routine included on CD for rectangular and polar graphs
14. 14
Polar Pattern
Fig. 2.3(a) Radiation lobes and
beamwidths of an antenna pattern
15. 15
Linear Pattern
Fig. 2.3(b) Linear plot of power pattern and
its associated lobes and beamwidths
16. 16
Field Regions
Reactive near field
energy stored not radiated
λ= wavelength
D= largest dimension of the antenna
362.0DR
17. 17
Field Regions
Radiating near field (Fresnel)
radiating fields predominate
pattern still depend on R
radial component may still be appreciable
λ= wavelength
D= largest dimension of the antenna 23262.0DRD
18. 18
Field Regions
Far field (
Fraunhofer Fraunhofer)
field distribution independent of R
field components are essentially transverse 22DR
19. 19
Radian
Fig. 2.10(a) Geometrical arrangements for defining a radian
r
2 radians in full circle
arc length of circle
20. 20
Steradian
one steradian subtends an area of
4π steradians in entire sphere
ddrdAsin2
Fig. 2.10(b) Geometrical arrangements
for defining a steradian.
ddrdAdsin2 2rA
21. 21
Radiation power density
HEW
Instantaneous Poynting vector
Time average Poynting vector
[ W/m ² ]
Total instantaneous
Power
Average radiated
Power
[ W/m ² ]
ssWP d
[ W ]
HEW Re21avg savgraddPsW
[ W ]
[2-8]
[2-9]
[2-4]
[2-3]
22. 22
Radiation intensity
“Power radiated per unit solid angle”
avgWrU2
far zone fields without 1/r factor
22),,( 2),( rrUE 222),,(),,( 2 rErEr
[W/unit solid angle]
[2-12a]
22oo1(,)(,) 2EE
Note: This final equation does not have an r in it. The “zero” superscript means that the 1/r term is removed.
23. 23
Directive Gain
Ratio of radiation intensity in a given direction to the radiation intensity averaged over all directions
radogPUUUD4
Directivity Gain
(Dg) -- directivity in a given direction
[2-16]
04radPU
(This is the radiation intensity if the antenna radiated its power equally in all directions.)
201,sin4SUUdd
Note:
24. 24
Directivity
radmaxomaxoPUUUD4
Do (isotropic) = 1.0
ogDD0
Directivity
-- Do
value of directive gain in direction of maximum radiation intensity
25. 25
Beamwidth
Half power beamwidth
Angle between adjacent points where field strength is 0.707 times the maximum, or the power is 0.5 times the maximum
(-3dB below maximum)
First null beamwidth
Angle between nulls in pattern
Fig. 2.11(b) 2-D power patterns (in linear scale)
of U()=cos²()cos³()
26. 26
Approximate directivity for
omnidirectional patterns
McDonald
2HPBW0027.0HPBW 101 oD
π
π
Pozar
(HPBW in degrees)
Results shown with exact values in Fig. 2.18
HPBW1818.01914.172oD nUsin
Better if no minor lobes [2-33b]
[2-32]
[2-33a]
For example
27. 27
Approximate directivity for directional patterns
Kraus
1212441,253orrddD
π/2
π
Tai & Pereira
Antennas with only one narrow main lobe and very negligible minor lobes
22212221815,7218.22ddrroD nUcos
[2-30b]
[2-31]
[2-27]
For example
( ) HPBW in two perpendicular planes in radians or in degrees)
12,rr12,dd
Note: According to Elliott, a better number to use in the Kraus formula is 32,400 (Eq. 2-271 in Balanis). In fact, the 41,253 is really wrong (it is derived assuming a rectangular beam footprint instead of the correct elliptical one).
28. 28
Approximate directivity for
directional patterns
Can calculate directivity directly (sect.2.5),
can evaluate directivity numerically (sect. 2.6)
(when integral for Prad cannot be done analytically,
analytical formulas cannot be used )
29. 29
Gain
Like directivity but also takes into account efficiency of antenna
(includes reflection, conductor, and dielectric losses)
oinoinZZZZ ;12
eo : overall eff.
er : reflection eff.
ec : conduction eff.
ed : dielectric eff.
Efficiency source) isotropic(lossless,PUPUeDeGinmaxradmaxooooabs 44 dcroeeee dccdeee
[2-49c]
radcdinPeP radoincPeP
30. 30
Gain
By IEEE definition “gain does not include losses arising from impedance
mismatches (reflection losses) and polarization mismatches (losses)” source) isotropic(lossless,PUDeGinmaxocdo 4
[2-49a]
31. 31
Bandwidth
“frequency range over which some characteristic conforms to a standard”
Pattern bandwidth
Beamwidth, side lobe level, gain, polarization, beam direction
polarization bandwidth example: circular polarization with axial ratio < 3 dB
Impedance bandwidth
usually based on reflection coefficient
under 2 to 1 VSWR typical
32. 32
Bandwidth
Broadband antennas
usually use ratio (e.g. 10:1)
Narrow band antennas
usually use percentage (e.g. 5%)
33. 33
Polarization
Linear
Circular
Elliptical
Right or left handed
rotation in time
34. 34
Polarization
Polarization loss factor
p is angle between wave and antenna polarization
22 ˆˆcoswapPLF
[2-71]
35. 35
Input impedance
“Ratio of voltage to current at terminals of antenna”
ZA = RA + jXA
RA = Rr + RL
Rr = radiation resistance
RL = loss resistance
ZA = antenna impedance at terminals a-b
36. 36
Input impedance
Antenna radiation efficiency
2221211() 22grrcdrLgrgLIRPowerRadiatedbyAntennaPePowerDeliveredtoAntennaPPIRIR
[2-90]
LrrcdRRRe
Note: this works well for those antennas that are modeled as a series RLC circuit – like wire antennas. For those that are modeled as parallel RLC circuit (like a microstrip antenna), we would use G values instead of R values.
37. 37
Friis Transmission Equation
Fig. 2.31 Geometrical orientation of transmitting and receiving antennas for Friis transmission equation
38. 38
Friis Transmission Equation
et = efficiency of transmitting antenna
er = efficiency of receiving antenna
Dt= directive gain of transmitting antenna
Dr = directive gain of receiving antenna
= wavelength
R = distance between antennas
assuming impedance and
polarization matches
224),(),( RDDeePPrrrtttrttr
[2-117]
39. 39
Radar Range Equation
Fig. 2.32 Geometrical arrangement of
transmitter, target, and receiver for
radar range equation22144),(),( RRDDeePPrrrttttrcdrcdt
[2-123]
40. 40
Radar Cross Section
RCS
Usually given symbol
Far field characteristic
Units in [m²]
4rincUW incident power density on body from transmit directionincW scattered power intensity in receive directionrU
Physical interpretation: The radar cross section is the area of an equivalent ideal “black body” absorber that absorbs all incident power that then radiates it equally in all directions.
41. 41
Radar Cross Section (
RCS)
Function of
Polarization of the wave
Angle of incidence
Angle of observation
Geometry of target
Electrical properties of target
Frequency