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