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Antenna Theory
Wire Antennas Monopole Antenna
Long Wire or Traveling wave Antennas
Yagi – Uda Antenna
Reference: C. A. Balanis, J.D. Krauss
Prof. D. Kannadassan
Monopole antenna
Image theory, an intro
• A positive charge”+Q” (or a charged body) is located a height “h” from perfect ground, then an image as “-Q” will form at a depth of “h”.
• A dipole will form, and the filed lines will be closed.
• Both the poles will contribute the field present at point “P”,
located at (x, y, z)
Ground or
Perfect conducting plane
Monopole antenna - Theory
• Theory and derivation of
Monopole and Dipole are
completely same, but the
Power output will always
half to monopole.
• And Radiation resistance
will be half of that for
dipole, Rr=36.5Ω
V
P
V
Radiation pattern
• From the ground, at a very small height,
a λ/4 antenna is place vertically, called
monopole antenna.
• AM, FM applications.
Monopole antenna
Examples
1cm
Bluetooth dongle
Long wire antennas
Long wire antennas - Theory
• Consider a thin wire of length L is horizontally placed at a height from
ground plane. At one end – a RF source is connected and other end is
terminated by the characteristics impedance of the wire Z0.
• When the wire is excited with a sinusoidal signal, the wave should travel
along one direction and will not create any standing wave – so called
“Travelling waves”.
• We are gonna see the expression for electric field at a point P - located at a
distance of “r” from the wire and angle of θ with respect to the length of
wire.
~ Z0
Wave direction
h
Travelling wave structure – E field
• The retarded current in the wire shall be described as
• Where: v=p.c or p=v/c
• “p” is the ratio of the wave velocity at the wire to the free space, called “Relative
phase velocity”. Used to vary with the attenuation constant.
v
Z
C
rtII m
1sin
Z0
Wave direction
z
P
θ
r
Z-axis
z1
Radiation pattern
• We can find the radiation pattern as similar to the dipole case, will result:
• Here, η is wave impedance.
cos1
2sin.
cos1
sin
2
0 ppc
wL
pR
pIE
[Krauss]
θm or β
Maxima direction: Also called “Elevation angel” (θmax, θm, α, β)
Lm
37.01cos
For 3λ and 5λ
[Krauss]
Minor lob directions, Directivity
m=0 m=1 m=2
[Balanis]
Bidirectional long wire antenna
• The maxima direction oriented with the direction of wave in the wire, so –
by introducing wave on both the direction – we can introduce “Bi-
directional radiation”.
• This can be possible by “Open circuited long wire” or “Un-terminated”, so
called “Stand wave antenna”.
Wave direction
P
θ
R
Vee antennas
γ=2β
β
By terminating with Z0, we can get Uni-directional radiation
Design equation:
Φ=2×β where β is θmax of single long wire
Rhombic antenna
• Based on the principle of “Traveling wave” and “Vee antenna”, Rhombic
antenna is a very high directive antenna – has Diamond or Rhombus shape
β
Working of Rhombic antenna
• By properly selecting the tilt angle, the
rhombic antenna will give additive effect
of radiation pattern of each long wire
antenna
• The radiation mechanism is basically
depends on two factors:
– Tilt angle (φ)
– Height above the ground (h)
• These are design parameters of antenna
• Due to ground effect, the maximum
radiation is elevated about an angel (β)
Z0
β
Design equations of Rhombic antenna
• BBL field equation: (Bruce, Beck and Lowry – 1935)
• From this equation, we can deduce the condition to get the maximum
power direction with respect to height h and length of line L
About Dr. Bruce, E: http://ieeexplore.ieee.org/iel5/10933/35478/01685103.pdf
Original Article: www.alcatel-lucent.com/bstj/vol14-1935/articles/bstj14-1-135.pdf
Maxima with height
Maxima with Length L
Design formula
• Finally, the design formulae are: (also called BBL formula)
Design a rhombic antenna to operate at 20MHz when the angle of
elevation angle =10o.
ooo 801090
173.010sin o
44.1;36.12 hL
m15mhmL 795.3;715.5
Numerical Problems and Review Questions
• Explain about long wire and Rhombic antenna with its radiation pattern
• Design a rhombic antenna to operate at 20MHz when the angle of elevation
angle =10o.
• Explain resonant and non-resonant modes of Long Wire Antenna.
• If we assume the average beamwidth of rhombic antenna as 10o, then
design an antenna system such that it will radiate maximum power over the
ranges from 10o to 40o for the operating frequency of 10MHz
• Explain the working of Open circuited long wire antenna and V antenna
with radiation pattern
Yagi-Uda Antenna A high frequency and high directive Parasitic array antenna
Introduction
• Prof. S. Uda (japan) was invented this antenna by 1927, and collaborated with H.
Yagi
– S. Uda, "High angle radiation of short electric waves". Proceedings of the IRE, vol. 15, pp. 377-385,
May 1927.
• After the invention, more than 40 researcher were studied on the improvement.
• Latest article (2011): Application of bacteria foraging algorithm for the design
optimization of multi-objective Yagi-Uda array
Shintaro Uda Hidetsugu Yagi
Principle • A folded dipole or ordinary half wave dipole is centered between two types of parasitic
elements, called: • Directors and Reflectors.
• The coupling (capacitive) effect between the parasitic elements and active element(dipole), the directional properties are improved a high with endfire pattern
• Reflector: about 5% greater length than the active element, will reflects the power radiation at backward direction.
• Directors: 5% lesser length than the active element, will create a converging mechanism and increase the directivity along the forward direction.
• Spacing between the directors and reflector are depending on the optimality, in most of the case, the spacing should from 0.3λ to 0.4λ (at 1927, the spacing was λ/10)
• 12 to 20 element yagi-uda antennas are optimum and have improved directivity
Radiation properties • Basically End-fire radiation pattern, with high directivity (less HPBW)
• Due to the ground and parasitic element, the pattern maxima at elevation will not be
at 90o (along the axis), but 45 to 60 degree elevated so.
Radiation properties
• We can show that, while increasing the directors, the gain and directivity
will improve, however the side lobs will degrade the performance by
attracting the noise in unwanted direction.
Measurements
• Forward gain
• Backward gain (or back gain)
• Front to Back ratio (diff of F.gain and B.gain)
• Magnitude of side lobes
• Input impedance
• Bandwidth, quality factor
Simulation – 9GHz Yagi Uda
Atleast 1 or 2 λ
Dipole=0.5λ
Director=0.45λ
Reflector=0.53λ
Due to inductive effect at dipole
and capacitive effect at parasitic elements
fo=8.8GHz
θmax
@ 8.8GHz
Front gain
Approx=40dB
Back gain
Approx=25dB
@ 8.8GHz θmax
Front to back ratio=40-25 = 15dB
Front to back ratio=42-17 = 25dB
Back gain
Approx=17dB
Front gain
Approx=40dB
Optimized Design of N-element Yagi-Uda.
• For the frequency of operation f0, the λ will be estimated.
• Reflector: (mostly 1 element) length of 0.5λ with spacing of 0.25 to 0.3λ from dipole.
• Dipole length (active element): 0.475λ
• Directors (N-2 elements) 0.405λ with spacing of 0.3 to 0.4λ between each element.
• To match the dipole, usually the QWT section be utilized.
Example (from Balanis)
Various Yagi Uda antenna
Smallest Yagi Uda antenna!! Ivan S. Maksymov et al, “Optical Yagi-Uda nanoantennas”, http://arxiv.org/pdf/1204.0330.pdf