TRAVELING WAVE AND

BROADBAND ANTENNAS

Veli YILDIRIM

2004513039

Mithat Sacit ATAR

2004513026

Prof. Dr. A.Hamit SERBEST

1

Contents Traveling wave antennas .................................................................................... 2

Calculation of radiation resistance .......................................................................................................6

Pattern function of traveling wave segments ......................................................................................8

Traveling wave antenna Terminations .............................................................................................. 11

Vee traveling wave antenna .............................................................................................................. 14

Rhombic antenna ............................................................................................................................... 16

Broadband Antennas……………………………………………………………………..18

Helical Antenna ................................................................................................ 19

Normal(Broadside) mode .................................................................................................................. 21

Axial (end-fire) Mode ........................................................................................................................ 24

Design Procedure .......................................................................................................................... 25

Feed Design ................................................................................................................................... 28

Yagi-uda antenna ............................................................................................. 29

History ............................................................................................................................................... 29

Effects of Elements ............................................................................................................................ 30

Optimization ...................................................................................................................................... 33

Input Impedance and Matching Techniques………. ............................................................................ 34

Design Procedure………. ..................................................................................................................... 37

References………. ................................................................................................................................ 39

2

Traveling Wave Antennas

Antennas with open-ended wires where the current must go to

zero (dipoles, monopoles, etc.) can be characterized as standing wave

antennas or resonant antennas. The current on these antennas can be

written as a sum of waves traveling in opposite directions (waves

which travel toward the end of the wire and are reflected in the

opposite direction). For example, the current on a dipole of length l is

given by

The current on the upper arm of the dipole can be written as

3

Traveling wave antennas are characterized by matched

terminations (not open circuits) so that the current is defined in terms

of waves traveling in only one direction (a complex exponential as

opposed to a sine or cosine). A traveling wave antenna can be formed

by a single wire transmission line (single wire over ground) which is

terminated with a matched load (no reflection). Typically, the length

of the transmission line is several wavelengths.

The antenna shown above is commonly called a Beverage or

wave antenna. This antenna can be analyzed as a rectangular loop,

according to image theory. However, the effects of an imperfect

ground may be significant and can be included using the reflection

coefficient approach. The contribution to the far fields due to the

vertical conductors is typically neglected since it is small if l >> h.

Note that the antenna does not radiate efficiently if the height h is

small relative to wavelength. In an alternative technique of analyzing

this antenna, the far field produced by a long isolated wire of length l

can be determined and the overall far field found using the 2 element

array factor. Traveling wave antennas are commonly formed using

wire segments with different geometries. Therefore, the antenna far

field can be obtained by superposition using the far fields of the

individual segments. Thus, the radiation characteristics of a long

straight segment of wire carrying a traveling wave type of current are

necessary to analyze the typical traveling wave antenna.

Consider a segment of a traveling wave antenna (an electrically

long wire of length l lying along the z-axis) as shown below. A

traveling wave current flows in the z-direction.

4

If the losses for the antenna are negligible (ohmic loss in the

conductors, loss due to imperfect ground, etc.), then the current can be

written as

The far field vector potential is

5

6

Calculation of radiation resistance The far fields in terms of the far field vector potential are

We know that the phase constant of a transmission line wave

(guided wave) can be very different than that of an unbounded

medium (unguided wave). However, for a traveling wave antenna, the

electrical height of the conductor above ground is typically large and

the phase constant approaches that of an unbounded medium (k). If we

assume that the phase constant of the traveling wave antenna is the

same as an unbounded medium (β = k), then

Given the far field of the traveling wave segment, we may determine

the time-average radiated power density according to the definition of

the Poynting vector such that

7

The total power radiated by the traveling wave segment is found

by integrating the Poynting vector.

The radiation resistance of the ideal traveling wave antenna (VSWR =

1) is purely real just as the input impedance of a matched transmission

line is purely real. Below is a plot of the radiation resistance of the

traveling wave segment as a function of segment length.

8

The radiation resistance of the traveling wave antenna is much

more uniform than that seen in resonant antennas. Thus, the traveling

wave antenna is classified as a broadband antenna.

Pattern function of traveling wave segments The pattern function of the traveling wave antenna segment is

given by

The normalized pattern function can be written as

The normalized pattern function of the traveling wave segment is

shown below for segment lengths of 5λ, 10 λ, 15 λ and 20 λ.

9

As the electrical length of the traveling wave segment increases,

the main beam becomes slightly sharper while the angle of the main

beam moves slightly toward the axis of the antenna.

Note that the pattern function of the traveling wave segment

always has a null at θ = 0o. Also note that with l >> λ, the sine

function in the normalized pattern function varies much more rapidly

(more peaks and

10

nulls) than the cotangent function. The approximate angle of the main

lobe for the traveling wave segment is found by determining the first

peak of the sine function in the normalized pattern function.

The values of m which yield 0o ≤θm≤180o (visible region) are

negative values of m. The smallest value of _m in the visible region

defines the location of main beam (m = -1)

If we also account for the cotangent function in the

determination of the main beam angle, we find

11

The maximum directivity can be approximated by

where the sine term in the numerator of the directivity function is

assumed to be unity at the main beam.

Traveling Wave Antenna Terminations Given a traveling wave antenna segment located horizontally above

a ground plane, the termination RL required to match the uniform

transmission line formed by the cylindrical conductor over ground

(radius = a, height over ground = s/2) is the characteristic impedance

of the corresponding one-wire transmission line. If the conductor

height above the ground plane varies with position, the conductor and

the ground plane form a non-uniform transmission line. The

characteristic impedance of a non-uniform transmission line is a

12

function of position. In either case, image theory may be employed to

determine the overall performance characteristics of the traveling

wave antenna.

13

14

Vee Traveling Wave Antenna

The main beam of a single electrically long wire guiding waves in

one direction (traveling wave segment) was found to be inclined at an

angle relative to the axis of the wire. Traveling wave antennas are

typically formed by multiple traveling wave segments. These traveling

wave segments can be oriented such that the main beams of the

component wires combine to enhance the directivity of the overall

antenna. A vee traveling wave antenna is formed by connecting two

matched traveling wave segments to the end of a transmission line

feed at an angle of 2θo relative to each other.

The beam angle of a traveling wave segment relative to the axis of the

wire (θmax) has been shown to be dependent on the length of the wire.

Given the length of the wires in the vee traveling wave antenna, the

angle 2θo may be chosen such that the main beams of the two tilted

wires combine to form an antenna with increased directivity over that

of a single wire.

15

A complete analysis which takes into account the spatial

separation effects of the antenna arms (the two wires are not co-

located) reveals that by choosing θo≈ 0.8 θmax, the total directivity of

the vee traveling wave antenna is approximately twice that of a single

conductor. Note that the overall pattern of the vee antenna is

essentially unidirectional given matched conductors.

If, on the other hand, the conductors of the vee traveling wave

antenna are resonant conductors (vee dipole antenna), there are

reflected waves which produce significant beams in the opposite

direction. Thus, traveling wave antennas, in general, have the

advantage of essentially unidirectional patterns when compared to the

patterns of most resonant antennas.

16

Rhombic Antenna

A rhombic antenna is formed by connecting two vee traveling

wave antennas at their open ends. The antenna feed is located at one

end of the rhombus and a matched termination is located at the

opposite end. As with all traveling wave antennas, we assume that the

reflections from the load are negligible. Typically, all four conductors

of the rhombic antenna are assumed to be the same length. Note that

the rhombic antenna is an example of a non-uniform transmission line.

A rhombic antenna can also be constructed using an inverted vee

antenna over a ground plane. The termination resistance is one-half

that required for the isolated rhombic antenna.

17

To produce an single antenna main lobe along the axis of the

rhombic antenna, the individual conductors of the rhombic antenna

should be aligned such that the components lobes numbered 2, 3, 5

and 8 are aligned (accounting for spatial separation effects). Beam

pairs (1, 7) and (4,6) combine to form significant sidelobes but at a

level smaller than the main lobe.

18

Broadband Antennas

Wideband antennas refer to a category of antennas with a

relatively constant performance over a wide frequency band.

Historically, this referred to an octave or more. However, this is a

general statement as an antenna has several electrical parameters like

the input impedance, gain, polarization, sidelobe level, loss, and

aperture efficiencies. This is due to the fact that an antenna can have

very diverse applications and its desirable parameters can vary

significantly. Even the size of its bandwidth can depend on the

application and the term broadband can mean a different frequency

range for different applications. Similar difficulties can also be

experienced in considering a specific antenna type, where the

bandwidth can depend on the design goals. For instance, a microstrip

antenna can be narrowband in one design and wideband in another.

Thus the antenna bandwidth definition, and classification of antennas

using the bandwidth.

A helical antenna is a quasi-broadband antenna, since its

geometry is angular dependent, which is the main requirement for

frequency-independent antennas. However, it has a finite length that

limits its bandwidth.

It is shown that the antenna has two distinct parts. One part is its

input end, the first couple of turns, which acts as a transducer and

converts the input electrical power to radiated wave. For this reason,

this section is known as the launcher section. The remaining turns

act as the directors and guide the wave energy. As one might expect,

the launcher section primarily influences the antenna input parameters

and its impedance bandwidth. The director section mostly controls the

radiation characteristics. This knowledge facilitates the antenna design

and optimization. The rotational nature of the helix geometry can also

be used to generate multifilar helices, which offers additional benefits

in both input impedance and radiation characteristics. These antennas

are also discussed, and we show that they can be designed for better

performance or geometrical simplicity. The special case is the

quadrifilar helix design, which can provide diverse performance

ranges and thus is used in many applications. It is discussed only

briefly, as historically it was not a wideband antenna.

Yagi–Uda antenna is shown that its operation is very similar to

the helix antenna and can also be viewed as having two distinct parts,

19

the launcher and the director sections. Because this antenna does not

enjoy an angular geometrical character, its bandwidth is not high,

especially in high gain applications. The gain optimization further

reduces its effective bandwidth.

Helical Antennas

Helical antennas consist of a conducting wire wound into a helix.

Its cross section, or view from its axis, can be circular, elliptical,

square, or any other shape, but the circular helix is the most common

antenna type. Its concept was established experimentally by Kraus

who also developed empirical rules for its design, also described by

others. It is one of the most important circularly polarized antennas

and relatively easy to design or fabricate. In addition, the simple

geometry of the helix also makes it convenient for numerical

investigation and optimization. Consequently, it is extensively

investigated and practically utilized.

20

Ln= the total length of the wire

D= Diameter

A helix has an interesting geometry and in the limit can be a loop

antenna (for S = 0) or dipole antenna (for D = d). As such, it enjoys

their properties but avoids some of their limitations. A circular loop

has a rotational symmetry and can support infinite azimuthal modes.

However, because of its finite size, it is a resonant structure and has a

narrow impedance bandwidth for each mode. The helix, on the other

hand, has many turns N and the mode currents can run along its length

as they radiate. Thus it behaves more like a traveling-wave antenna

than a resonant one and is significantly more wideband. In fact, as will

be shown later, it can be designed to have almost constant input

impedance for its modes. Another difference between the two

antennas is due to the pitch angle or the spacing between turns of the

helix. Because of this axial length, the helix current has an axial

component and can radiate a wideband circularly polarized wave with

a single feed. In this respect, the helix behaves as a combination of

loop and dipole antennas, fed in phase quadrature. The

interrelationship between the circular and axial components of the

current also provides the ability for beam shaping. This property

becomes an important tool for designing multifilar helices with shaped

conical beams.

For a uniform helical antenna, the conducting wire is wound

over a cylinder of constant diameter and its current distribution has

both axial and circumferential components. Thus, in general, its

components can be written

I (z,φ)n = An exp(jβnz) exp(jnφ), n = 0, 1, 2, . . .

where n is the mode number in the azimuthal direction φ, In is the nth

component of the helix current, βn is the axial propagation constant,

and An is the mode excitation constant. The axial propagation constant

21

can be related to the propagation constant along the helix wire by its

geometry. As is known in loop antennas, the nth azimuthal mode

resonates, when the circumference of the loop becomes about nλ,

where λ is the wavelength of the signal propagating through the helix

wire. In reality, the nth mode excites within a bandwidth around nλ,

the size of which depends on the antenna type. Since the loop antenna

is generally narrowband, the mode excitation is restricted to a small

frequency band around its resonance. These modes are well separated

from each other and provide appropriate modal radiation patterns and

characteristics. The situation, however, is different for a helical

antenna. Its bandwidth is wider, and adjacent modes can be excited

simultaneously, which will affect its performance, especially in

shaping its radiation pattern and causing large sidelobes.

In both loop and microstrip antennas, only the n = 1 mode

radiates axially. Other modes generate a boresight null. However, this

is not necessarily the case for helical antennas, as multifilar helices

can be used effectively to generate conical beams with the n = 1 mode,

with much smaller diameters. Since they are more compact and

simpler in design, they are preferred in communication applications,

especially in mobile communications. The geometry of the helix also

detrimentally affects the radiation beam of the higher order modes. Its

consecutive turns act as an endfire array and force the antenna beam

toward the axis, which counters the design goal of generating a

conical beam. Thus higher order modes of helix have not seen

widespread applications. The zero-order mode, known as the normal

mode, is different because it requires small helix dimensions in

wavelength and is an ideal antenna for circular polarization.

Normal Mode Helix (Broadside)

In the normal mode of operation the field radiated by the antenna

is maximum in a plane normal to the helix axis and minimum along its

axis. To achieve the normal mode of operation, the dimensions of the

helix are usually small compared to the wavelength (i.e., NL0 << λ0).

The geometry of the helix reduces to a loop of diameter D whenthe

pitch angle approaches zero and to a linear wire of length S whenit

approaches 90◦. Since the limiting geometries of the helix are a loop

and a dipole, the far field radiated by a small helix inthe normal mode

22

can be described interms of Eθ and Eφ components of the dipole and

loop, respectively.

In the normal mode, the helix can be simulated approximately by

N small loops and N short dipoles connected together in series

The fields are obtained by superposition of the fields from these

elemental radiators. The planes of the loops are parallel to each other

and perpendicular to the axes of the vertical dipoles. The axes of the

loops and dipoles coincide with the axis of the helix. Since in the

normal mode the helix dimensions are small, the current throughout

its length can be assumed to be constant and its relative far-field

pattern to be independent of the number of loops and short dipoles.

Thus its operation can be described accurately by the sum of the fields

radiated by a small loop of radius D and a short dipole of length S,

with its axis perpendicular to the plane of the loop, and each with the

same constant current distribution.

The far-zone electric field radiated by a short dipole of length S

and constant current I0 is Eθ

where l is being replaced by S. Inadditionthe electric field

radiated by a loop is Eφ

23

where D/2 is substituted for a. The ratio of the magnitudes of the Eθ

and Eφ components is defined here as the axial ratio (AR), and it is

given by

By varying the D and/or S the axial ratio attains values of 0 ≤

AR≤∞. The value of AR = 0 is a special case and occurs when Eθ = 0

leading to a linearly polarized wave of horizontal polarization (the

helix is a loop). When AR=∞, Eφ = 0 and the radiated wave is linearly

polarized with vertical polarization (the helix is a vertical dipole).

Another special case is the one when AR is unity (AR = 1) and occurs

when

When the dimensional parameters of the helix satisfy the above

relation, the radiated field is circularly polarized in all directions other

than θ = 0◦ where the fields vanish. When the dimensions of the helix

do not satisfy any of the above special cases, the field radiated by the

antenna is not circularly polarized. The progression of polarization

change can be described geometrically by beginning with the pitch

angle of zero degrees (α = 0◦), which reduces the helix to a loop with

linear horizontal polarization. As α increases, the polarization

becomes elliptical with the major axis being horizontally polarized.

When α, is such that C/λ0 = √2S/λ0,AR = 1 and we have circular

polarization. For greater values of α, the polarizationagain becomes

elliptical but with the major axis vertically polarized. Finally when α =

90◦ the helix reduces to a linearly polarized vertical dipole.

To achieve the normal mode of operation, it has been assumed

that the current throughout the length of the helix is of constant

magnitude and phase. This is satisfied to a large extent provided the

total length of the helix wire NL0 is very small compared to the

wavelength (Ln << λ0) and its end is terminated properly to reduce

multiple reflections. Because of the critical dependence of its radiation

24

characteristics on its geometrical dimensions, which must be very

small compared to the wavelength, this mode of operation is very

narrow in bandwidth and its radiation efficiency is very small.

Practically this mode of operationis limited, and it is seldom utilized.

Axial Mode (End-Fire)

A more practical mode of operation, which can be generated

with great ease, is the axial or end-fire mode. In this mode of

operation, there is only one major lobe and its maximum radiation

intensity is along the axis of the helix, The minor lobes are at oblique

angles to the axis.

To excite this mode, the diameter D and spacing S must be large

fractions of the wavelength. To achieve circular polarization,

primarily in the major lobe, the circumference of the helix must be in

the 3/4 < C/λ0 < 4/3 range (with C/λ0 = 1 near optimum), and the

spacing about S λ0/4. The pitch angle is usually 12◦ ≤ α ≤ 14◦. Most

often the antenna is used in conjunction with a ground plane, whose

diameter is at least λ0/2, and it is fed by a coaxial line. However, other

types of feeds (such as waveguides and dielectric rods) are possible,

especially at microwave frequencies. The dimensions of the helix for

this mode of operation are not as critical, thus resulting in a greater

bandwidth.

25

A monofilar helix, with mode index n = 1, radiates in the axial

direction, similar to other antennas supporting such a mode like a

loop, microstrip, or horn antenna. In its simplest form, it is a constant

diameter helix, having a circumference of about one wavelength,

C ≈ λ, wound in either right-hand or left-hand, similar to a screw.

When placed over a ground plane, it can be fed easily by a coaxial

input connector or microstrip line. An axial feeding maintains the

symmetry and can facilitate rotation, and microstrip feding can be

useful for impedance matching. In either case, the current induced on

the helix conductor radiates as it rotates and progresses along its

length, with the polarization being controlled by the direction of its

winding.

Design Procedure

The terminal impedance of a helix radiating in the axial mode is

nearly resistive with values between 100 and 200 ohms. Smaller

values, even near 50 ohms, can be obtained by properly designing the

feed. Empirical expressions, based on a large number of

26

measurements, have been derived, and they are used to determine a

number of parameters. The input impedance (purely resistive) is

obtained by

which is accurate to about ±20%,

the half-power beamwidth by

the beamwidth betweenn ulls by

the directivity by

the axial ratio (for the condition of increased directivity) by

and the normalized far-field pattern by

Where

For ordinary end-fire radiation

For Hansen-Woodyard end-fire

radiation

27

All these relations are approximately valid provided 12◦ < α <

14◦, 3/4 < C/λ0 < 4/3, and N >3.

The cos θ term in represents the field pattern of a single turn, and

the last term in is the array factor of a uniform array of N elements.

The total field is obtained by multiplying the field from one turn with

the array factor (pattern multiplication ).

The value of p in is the ratio of the velocity with which the wave

travels along the helix wire to that in free space, and it is selected

according to for ordinary end-fire radiation or for Hansen-Woodyard

end-fire radiation. These are derived as follows.

For ordinary end-fire the relative phase ψ among the various turns of

the helix (elements of the array) is given by

where d = S is the spacing between the turns of the helix. For an

end-fire design, the radiation from each one of the turns along θ = 0◦

must be inphase. Since the wave along the helix wire between turns

travels a distance L0 with a wave velocity v = pv0 (p < 1 where v0 is

the wave velocity infree space) and the desired maximum radiation

is along θ = 0◦, for ordinary end-fire radiationis equal to

For m = 0 an dp = 1, L0 = S. This corresponds to a straight wire

(α = 90◦ ), and not a helix. Therefore the next value is m = 1, and it

corresponds to the first transmission mode for a helix. Substituting

m = 1

In a similar manner, it can be shown that for Hansen-Woodyard

end-fire radiation is equal to

which when solved for p leads to

28

Feed Design

The nominal impedance of a helical antenna operating in the

axial mode, computed using, is 100–200 ohms. However, many

practical transmission lines (such as a coax) have characteristic

impedance of about 50 ohms. In order to provide a beter match, the

input impedance of the helix must be reduced to near that value. There

may be a number of ways by which this can be accomplished. One

way to effectively control the input impedance of the helix is to

properly design the first 1/4 turn of the helix which is next to the feed.

To bring the input impedance of the helix from nearly 150 ohms

downto 50 ohms, the wire of the first 1/4 turnshould be flat in the

form of a strip and the transition into a helix should be very gradual.

This is accomplished by making the wire from the feed, at the

beginning of the formation of the helix, inthe form of a strip of width

w by flattening it and nearly touching the ground plane which is

covered with a dielectric slab of height

where

w = width of strip conductor of the helix starting at the feed

Ir = dielectric constant of the dielectric slab covering the ground plane

Z0 = characteristic impedance of the input transmission line

Typically the strip configuration of the helix transitions from the

strip to the regular circular wire and the designed pitch angle of the

helix very gradually within the first 1/4–1/2 turn.

This modification decreases the characteristic impedance of the

conductor-ground plane effective transmission line, and it provides a

lower impedance over a substantial but reduced bandwidth. For

example, a 50-ohm helix has a VSWR of less than 2:1 over a 40%

bandwidth compared to a 70% bandwidth for a 140-ohm helix. In

29

addition, the 50-ohm helix has a VSWR of less than 1.2:1 over a 12%

bandwidth as contrasted to a 20% bandwidth for one of 140 ohms.

A simple and effective way of increasing the thickness of the

conductor near the feed point will be to bond a thin metal strip to the

helix conductor. For example, a metal strip 70-mm wide was used to

provide a 50-ohm impedance in a helix whose conducting wire was

13-mm in diameter and it was operating at 230.77 MHz.

Yagi-Uda

History of Yagi-Uda

The original design and operating principles of this radiator were

first described inJapan ese inarticles published inthe Journal of I.E.E.

of Japan by S. Uda of the Tohoku Imperial University in Japan. In a

later, but more widely circulated and read article, one of Professor

Uda’s colleagues, H. Yagi, described the operation of the same

radiator in English. This paper has been considered a classic, and it

was reprinted in1984 inits original form inthe Proceedings of the

IEEE, as part of IEEE’s centennial celebration. Despite the fact that

Yagi in his English written paper acknowledged the work of Professor

Uda on beam radiators at a wavelength of 4.4 m, it became customary

throughout the world to refer to this radiator as a Yagi antenna, a

generic term in the antenna dictionary. However, in order for the name

30

to reflect more appropriately the contributions of both inventors, it

should be called a Yagi-Uda antenna, a name that will be adopted in

this book. Although the work of Uda and Yagi was done in the early

1920s and published in the middle 1920s, full acclaim in the United

States was not received until 1928 when Yagi visited the United States

and presented papers at meetings of the Institute of Radio Engineers

(IRE) in New York, Washington, and Hartford. In addition, his work

was published in the Proceedings of IRE, June 1928, where J. H.

Dellinger, Chief of Radio Division, Bureau of Standards, Washington,

D.C., and himself a pioneer of radio waves, characterized it as

“exceptionally fundamental” and wrote “I have never listened to a

paper that I felt so sure was destined to be a classic.”

In 1984, IEEE celebrated its centennial year (1884–1984).

Actually, IEEE was formed in 1963 when the IRE and AIEE united to

form IEEE. During 1984, the Proceedings of the IEEE republished

some classic papers, intheir original form, in the different areas of

electrical engineering that had appeared previously either in the

Proceeding of the IRE or IEEE. In antennas, the only paper that was

republished was that by Yagi. Not only that, in 1997, the Proceedings

of the IEEE republished for the second time the original paper by

Yagi. That in itself tells us something of the impact this particular

classic antenna design had on the electrical engineering profession.

Effects of Elements

Another very practical radiator in the HF (3–30 MHz), VHF

(30–300 MHz), and UHF (300–3,000 MHz) ranges is the Yagi-Uda

antenna. This antenna consists of a number of linear dipole elements,

one of which is energized directly by a feed transmission line while

the others act as parasitic radiators whose currents are induced by

mutual coupling. A common feed element for a Yagi-Uda antenna is

a folded dipole. This radiator is exclusively designed to operate as an

end-fire array, and it is accomplished by having the parasitic elements

in the forward beam act as directors while those inthe rear act as

reflectors. Yagi designated the row of directors as a “wave canal.” The

Yagi-Uda array has been widely used as a home TV antenna

31

All of the elements in the array were assumed to be driven with

some source. A Yagi-Uda array is an example of a parasitic array.

Any element in an array which is not connected to the source (in the

case of a transmitting antenna) or the receiver (in the case of a

receiving antenna) is defined as a parasitic element. A parasitic array

is any array which employs parasitic elements.

Driven element - usually a resonant dipole or folded dipole.

Reflector - slightly longer than the driven element so that it is

inductive (its current lags that of the driven element).

Director - slightly shorter than the driven element so that it is

capacitive (its current leads that of the driven element).

Yagi-Uda Array Advantages

_ Lightweight

_ Low cost

_ Simple construction

_ Unidirectional beam (front-to-back ratio)

_ Increased directivity over other simple wire antennas

_ Practical for use at HF (3-30 MHz), VHF (30-300 MHz), and

UHF (300 MHz - 3 GHz)

32

Typical Yagi-Uda Array Parameters

Driven element - half-wave resonant dipole or folded dipole,

(Length = 0.45λ to 0.49λ, dependent on radius), folded dipoles are

employed as driven elements to increase the array input impedance.

Director - Length = 0.4λ to 0.45λ (approximately 10 to 20 %

shorter than the driven element), not necessarily uniform.

Reflector - Length ≈ 0.5λ (approximately 5 to 10 % longer than

the driven element).

Director spacing - approximately 0.2 to 0.4λ, not necessarily

uniform.

Reflector spacing - 0.1 to 0.25λ Since the length of each director is smaller than its

corresponding resonant length, the impedance of each is capacitive

and its current leads the induced emf. Similarly the impedances of the

reflectors is inductive and the phases of the currents lag those of the

induced emfs. The total phase of the currents in the directors and

reflectors is not determined solely by their lengths but also by their

spacing to the adjacent elements. Thus, properly spaced elements with

lengths slightly less than their corresponding resonant lengths (less

than λ/2) act as directors because they form anarray with currents

approximately equal in magnitude and with equal progressive phase

shifts which will reinforce the field of the energized element toward

the directors. Similarly, a properly spaced element with a length of λ/2

or slightly greater will act as a reflector. Thus a Yagi-Uda array may

be regarded as a structure supporting a traveling wave whose

performance is determined by the current distribution in each element

and the phase velocity of the traveling wave. It should be noted that

the previous discussion on the lengths of the directors, reflectors, and

driven elements is based on the first resonance. Higher resonances are

available near lengths of λ, 3λ/2, and so forth, but are seldom used.

The radiation characteristics that are usually of interest in a

Yagi-Uda antenna are the forward and backward gains, input

impedance, bandwidth, front-to-back ratio, and magnitude of minor

lobes. The lengths and diameters of the directors and reflectors, as

well as their respective spacings, determine the optimum

characteristics. For a number of years optimum designs were

accomplished experimentally. However, with the advent of high-speed

33

computers many different numerical techniques, based on analytical

formulations, have been utilized to derive the geometrical dimensions

of the array for optimum operational performance. Usually Yagi-Uda

arrays have low input impedance and relatively narrow bandwidth (on

the order of about 2%). Improvements in both can be achieved at the

expense of others (such as gain, magnitude of minor lobes, etc.).

Usually a compromise is made, and it depends on the particular

design. One way to increase the input impedance without affecting the

performance of other parameters is to use an impedance step-up

element as a feed (such as a two-element folded dipole with a step-up

ratio of about 4). Front-toback ratios of about 30 (≈15 dB) can be

achieved at wider than optimum element spacings, but they usually

are compromised somewhat to improve other desirable characteristics.

Optimization

The radiation characteristics of the array can be adjusted by

controlling the geometrical parameters of the array. for the 15-element

array using uniform lengths and making uniform variations in

spacings. However, these and other array characteristics can be

optimized by using nonuniform director lengths and spacings between

the directors. For example, the spacing between the directors can be

varied while holding the reflector–exciter spacing and the lengths of

all elements constant. Such a procedure was used by Cheng and Chen

to optimize the directivity of a six-element (four-director, reflector,

exciter) array using a perturbational technique. The results of the

initial and the optimized (perturbed) array are showninT able 10.1. For

the same array, they allowed all the spacings to vary while

maintaining constant all other parameters.

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Another optimization procedure is to maintain the spacings

between all the elements constant and vary the lengths so as to

optimize the directivity.

Input Impedance and Matching Techniques

The input impedance of a Yagi-Uda array, measured at the

center of the driven element, is usually small and it is strongly

influenced by the spacing between the reflector and feed element. For

a 13-element array using a resonant driven element. There are many

techniques that can be used to match a Yagi-Uda array to a

transmission line and eventually to the receiver, which in many cases

is a television set which has a large impedance (on the order of 300

ohms). Two common matching techniques are the use of the folded

dipole, as a driven element and simultaneously as an impedance

transformer, and the Gamma-match Which one of the two is used

depends primarily on the transmission line from the antenna to the

receiver.

The coaxial cable is now widely used as the primary

transmission line for television, especially with the wide spread and

use of cable TV; infact, most television sets are already prewired with

coaxial cable connections. Therefore, if the coax with a characteristic

impedance of about 78 ohms is the transmission line used from the

Yagi-Uda antenna to the receiver and since the input impedance of the

35

antenna is typically 30–70 ohms the Gamma-match is the most

prudent matching technique to use. This has been widely used in

commercial designs where a clamp is usually employed to vary the

positionof the short to achieve a best match.

Gamma Match

36

Omega Match

T-Match

Beta Match (Hair pin)

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Design Procedure

The basis of the designis the data included in

1. Table 10.6 which represents optimized antenna parameters for

six different lengths and for a d/λ = 0.0085

2.Uncompansated director and reflector lengths for 0.001 ≤ d/λ ≤

0.04

3. compensation length increase for all the parasitic elements

(directors and reflectors) as a function of boom-to-wavelength ratio

0.001 ≤ D/λ ≤ 0.04

The specified information is usually the center frequency,

antenna directivity, d/λ and D/λ ratios, and it is required to find the

optimum parasitic element lengths (directors and reflectors). The

spacing between the directors is uniform but not the same for all

designs. However, there is only one reflector and its spacing is s =

0.2λ for all designs.

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39

REFERENCES:

-ANTENNA THEORY ANALYSIS AND DESIGN (Constantine A.

Balanis)3th Edition

-MODERN ANTENNA HANDBOOK (Constantine A. Balanis)

-ANTENNAS FOR ALL APPLICATIONS (John D. Kraus)3th Edition

-http://www3.dogus.edu.tr/lsevgi/ (Prof. Dr. Levent Sevgi)

- http://www.educypedia.be/electronics/antennas.htm

-http://antenna-theory.com

-http://yagi-uda.com/